{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":852,"title":"Index of neighbor pixel with steepest gradient","description":"Unlike in various applications, where the gradient of a two dimensional matrix is calculated in x and y direction, the gradient of a digital elevation model (DEM) is usually returned as the steepest gradient. The steepest gradient is the largest downward slope of a pixel to one of its eight neighbors.\r\nIn this problem, your task will be to return the linear index of the steepest neighbor for each pixel in a gridded DEM. Pixels that don't have downward neighbors should receive the index value zero.\r\nAn example should help. The DEM is\r\ndem = [1 5 9; ...\r\n       4 5 6; ...\r\n       8 7 3];\r\nThe result should be\r\nIX  = [0 1 4; ...\r\n       1 1 9; ...\r\n       2 9 0];\r\nThe results may not be unique, but the test cases have been built so that this is not a problem. The spatial resolution of the dem is dx=1 and dy=1. Note that the diagonal distance is hypot(dx,dy).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 369.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 184.8px; transform-origin: 407px 184.8px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 358.5px 8px; transform-origin: 358.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUnlike in various applications, where the gradient of a two dimensional matrix is calculated in x and y direction, the gradient of a digital elevation model (DEM) is usually returned as the steepest gradient. The steepest gradient is the largest downward slope of a pixel to one of its eight neighbors.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.5px 8px; transform-origin: 382.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this problem, your task will be to return the linear index of the steepest neighbor for each pixel in a gridded DEM. Pixels that don't have downward neighbors should receive the index value zero.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115.5px 8px; transform-origin: 115.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn example should help. The DEM is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 61.3px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30.65px; transform-origin: 404px 30.65px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 56px 8.5px; transform-origin: 56px 8.5px; \"\u003edem = [1 5 9; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 56px 8.5px; transform-origin: 56px 8.5px; \"\u003e       4 5 6; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 56px 8.5px; tab-size: 4; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e       8 7 3];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65px 8px; transform-origin: 65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe result should be\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 61.3px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30.65px; transform-origin: 404px 30.65px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 56px 8.5px; transform-origin: 56px 8.5px; \"\u003eIX  = [0 1 4; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 56px 8.5px; transform-origin: 56px 8.5px; \"\u003e       1 1 9; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 56px 8.5px; tab-size: 4; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e       2 9 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377.5px 8px; transform-origin: 377.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe results may not be unique, but the test cases have been built so that this is not a problem. The spatial resolution of the dem is dx=1 and dy=1. Note that the diagonal distance is hypot(dx,dy).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function IX = sgix(dem)\r\n  IX = [];\r\nend","test_suite":"%%\r\ndem = [1 5 9; ...\r\n       4 5 6; ...\r\n       8 7 3];\r\nIX  = [0 1 4; ...\r\n       1 1 9; ...\r\n       2 9 0];\r\nassert(isequal(sgix(dem),IX))\r\n\r\n%%\r\ndem = [1 4 7; ...\r\n       2 5 8; ...\r\n       3 6 9];\r\nIX  = [0 1 4; ...\r\n       1 2 5; ...\r\n       2 3 6];\r\nassert(isequal(sgix(dem),IX))\r\n\r\n%%\r\ndem = [1 2 ; ...\r\n       3 4];\r\ndem = dem + randi(1e3);\r\nIX  = [0 1; ...\r\n       1 1];\r\nassert(isequal(sgix(dem),IX))\r\n\r\n\r\n%%\r\ndem = [1 5 4 9; ...\r\n       4 5 7 7; ...\r\n       6 6 6 8];\r\nIX  = [0 1 0 7; ...\r\n       1 1 7 7; ...\r\n       2 2 5 9];\r\nassert(isequal(sgix(dem),IX))","published":true,"deleted":false,"likes_count":2,"comments_count":7,"created_by":569,"edited_by":223089,"edited_at":"2022-12-22T13:29:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":65,"test_suite_updated_at":"2022-12-22T13:29:53.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-07-20T08:58:26.000Z","updated_at":"2026-04-11T11:25:58.000Z","published_at":"2012-07-20T08:58:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUnlike in various applications, where the gradient of a two dimensional matrix is calculated in x and y direction, the gradient of a digital elevation model (DEM) is usually returned as the steepest gradient. The steepest gradient is the largest downward slope of a pixel to one of its eight neighbors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, your task will be to return the linear index of the steepest neighbor for each pixel in a gridded DEM. Pixels that don't have downward neighbors should receive the index value zero.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn example should help. The DEM is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[dem = [1 5 9; ...\\n       4 5 6; ...\\n       8 7 3];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe result should be\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[IX  = [0 1 4; ...\\n       1 1 9; ...\\n       2 9 0];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe results may not be unique, but the test cases have been built so that this is not a problem. The spatial resolution of the dem is dx=1 and dy=1. Note that the diagonal distance is hypot(dx,dy).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42616,"title":"Detect circles in images","description":"Given an image and a target radius range, specified as [rmin rmax], find circles in the image. Your function should output an m-by-2 array of circle centers (x,y positions in the image) and an m-by-1 vector of radii corresponding to m circles.\r\n\r\nYour detector will be judged on its \u003chttps://en.wikipedia.org/wiki/Precision_and_recall precision and recall\u003e. The recall must be 0.75 or higher and the precision must be 0.5 or higher to pass. \r\n\r\nFor example, if an image has 4 true circles, you can miss at most 1 of the circles and have at most 4 false detections.\r\n\r\n*Additional notes:*\r\n\r\n* Circles can be brighter or darker than the background.\r\n* A detection is considered a match if its position and radius is within 5 pixels of a true circle.\r\n* To make things easier, the target number of circles (N) is provided as an input. Pat yourself on the back if you do not need it.","description_html":"\u003cp\u003eGiven an image and a target radius range, specified as [rmin rmax], find circles in the image. Your function should output an m-by-2 array of circle centers (x,y positions in the image) and an m-by-1 vector of radii corresponding to m circles.\u003c/p\u003e\u003cp\u003eYour detector will be judged on its \u003ca href = \"https://en.wikipedia.org/wiki/Precision_and_recall\"\u003eprecision and recall\u003c/a\u003e. The recall must be 0.75 or higher and the precision must be 0.5 or higher to pass.\u003c/p\u003e\u003cp\u003eFor example, if an image has 4 true circles, you can miss at most 1 of the circles and have at most 4 false detections.\u003c/p\u003e\u003cp\u003e\u003cb\u003eAdditional notes:\u003c/b\u003e\u003c/p\u003e\u003cul\u003e\u003cli\u003eCircles can be brighter or darker than the background.\u003c/li\u003e\u003cli\u003eA detection is considered a match if its position and radius is within 5 pixels of a true circle.\u003c/li\u003e\u003cli\u003eTo make things easier, the target number of circles (N) is provided as an input. Pat yourself on the back if you do not need it.\u003c/li\u003e\u003c/ul\u003e","function_template":"function [centers,radii] = detectcircles(I,R,N)\r\n  centers = [];\r\n  radii = [];\r\nend","test_suite":"%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','circles.png'));\r\n[centers,radii] = detectcircles(I,[18 20],13);\r\nc = [119 222; 185 218; 124 116; 37 37; 178 184; 93 167; 37 72; 71 38; 93 132; 122 186; 97 96; 71 74; 151 204];\r\nr = 19*ones(13,1);\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','circlesBrightDark.png'));\r\n[centers,radii] = detectcircles(I,[32 64],6);\r\nc = [75 250; 100 100; 250 400; 300 120; 450 240; 330 370];\r\nr = [35; 50; 60; 40; 50; 55];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','coins.png'));\r\n[centers,radii] = detectcircles(I,[24 30],10);\r\nc = [236 174; 149 35; 56 50; 266 103; 217 71; 120 209; 110 85; 175 120; 96 146; 37 107];\r\nr = [25; 29; 25; 24; 29; 29; 24; 29; 29; 29];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','coloredChips.png'));\r\n[centers,radii] = detectcircles(I,[20 28],26);\r\nc = [83 177; 304 336; 420 88; 434 165; 244 166; 327 297; 273 53; 130 44; 271 281; 408 265; 312 192; 420 346; 146 199; 228 232; 329 135; 175 297; 366 224; 150 258; 217 107; 345 119; 445 68; 372 293; 150 342; 251 8; 259 217; 198 107];\r\nr = [23; 24; 23; 23; 23; 23; 23; 23; 23; 23; 23; 24; 23; 23; 23; 24; 23; 24; 23; 23; 23; 24; 25; 23; 23; 25];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','eight.tif'));\r\n[centers,radii] = detectcircles(I,[35 40],4);\r\nc = [198 189; 247 72; 62 141; 124 58];\r\nr = [37; 37; 38; 37];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','moon.tif'));\r\n[centers,radii] = detectcircles(I,[200 210],1);\r\nc = [253 287];\r\nr = [205];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','pillsetc.png'));\r\n[centers,radii] = detectcircles(I,[15 55],4);\r\nc = [103 240; 252 326; 119 130; 319 84];\r\nr = [17; 17; 50; 37];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','tape.png'));\r\n[centers,radii] = detectcircles(I,[75 85],1);\r\nc = [236 172];\r\nr = [80];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','testpat1.png'));\r\n[centers,radii] = detectcircles(I,[110 120],1);\r\nc = [128 128];\r\nr = [116];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','toysnoflash.png'));\r\n[centers,radii] = detectcircles(I,[90 100],1);\r\nc = [267 506];\r\nr = [94];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)","published":true,"deleted":false,"likes_count":4,"comments_count":4,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2015-09-18T20:16:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-09-17T22:38:48.000Z","updated_at":"2026-04-11T11:11:43.000Z","published_at":"2015-09-17T23:22:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an image and a target radius range, specified as [rmin rmax], find circles in the image. Your function should output an m-by-2 array of circle centers (x,y positions in the image) and an m-by-1 vector of radii corresponding to m circles.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour detector will be judged on its\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Precision_and_recall\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eprecision and recall\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The recall must be 0.75 or higher and the precision must be 0.5 or higher to pass.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if an image has 4 true circles, you can miss at most 1 of the circles and have at most 4 false detections.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAdditional notes:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCircles can be brighter or darker than the background.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA detection is considered a match if its position and radius is within 5 pixels of a true circle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo make things easier, the target number of circles (N) is provided as an input. Pat yourself on the back if you do not need it.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":852,"title":"Index of neighbor pixel with steepest gradient","description":"Unlike in various applications, where the gradient of a two dimensional matrix is calculated in x and y direction, the gradient of a digital elevation model (DEM) is usually returned as the steepest gradient. The steepest gradient is the largest downward slope of a pixel to one of its eight neighbors.\r\nIn this problem, your task will be to return the linear index of the steepest neighbor for each pixel in a gridded DEM. Pixels that don't have downward neighbors should receive the index value zero.\r\nAn example should help. The DEM is\r\ndem = [1 5 9; ...\r\n       4 5 6; ...\r\n       8 7 3];\r\nThe result should be\r\nIX  = [0 1 4; ...\r\n       1 1 9; ...\r\n       2 9 0];\r\nThe results may not be unique, but the test cases have been built so that this is not a problem. The spatial resolution of the dem is dx=1 and dy=1. Note that the diagonal distance is hypot(dx,dy).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 369.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 184.8px; transform-origin: 407px 184.8px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 358.5px 8px; transform-origin: 358.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUnlike in various applications, where the gradient of a two dimensional matrix is calculated in x and y direction, the gradient of a digital elevation model (DEM) is usually returned as the steepest gradient. The steepest gradient is the largest downward slope of a pixel to one of its eight neighbors.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.5px 8px; transform-origin: 382.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this problem, your task will be to return the linear index of the steepest neighbor for each pixel in a gridded DEM. Pixels that don't have downward neighbors should receive the index value zero.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115.5px 8px; transform-origin: 115.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn example should help. The DEM is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 61.3px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30.65px; transform-origin: 404px 30.65px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 56px 8.5px; transform-origin: 56px 8.5px; \"\u003edem = [1 5 9; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 56px 8.5px; transform-origin: 56px 8.5px; \"\u003e       4 5 6; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 56px 8.5px; tab-size: 4; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e       8 7 3];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65px 8px; transform-origin: 65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe result should be\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 61.3px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30.65px; transform-origin: 404px 30.65px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 56px 8.5px; transform-origin: 56px 8.5px; \"\u003eIX  = [0 1 4; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 56px 8.5px; transform-origin: 56px 8.5px; \"\u003e       1 1 9; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 56px 8.5px; tab-size: 4; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e       2 9 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377.5px 8px; transform-origin: 377.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe results may not be unique, but the test cases have been built so that this is not a problem. The spatial resolution of the dem is dx=1 and dy=1. Note that the diagonal distance is hypot(dx,dy).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function IX = sgix(dem)\r\n  IX = [];\r\nend","test_suite":"%%\r\ndem = [1 5 9; ...\r\n       4 5 6; ...\r\n       8 7 3];\r\nIX  = [0 1 4; ...\r\n       1 1 9; ...\r\n       2 9 0];\r\nassert(isequal(sgix(dem),IX))\r\n\r\n%%\r\ndem = [1 4 7; ...\r\n       2 5 8; ...\r\n       3 6 9];\r\nIX  = [0 1 4; ...\r\n       1 2 5; ...\r\n       2 3 6];\r\nassert(isequal(sgix(dem),IX))\r\n\r\n%%\r\ndem = [1 2 ; ...\r\n       3 4];\r\ndem = dem + randi(1e3);\r\nIX  = [0 1; ...\r\n       1 1];\r\nassert(isequal(sgix(dem),IX))\r\n\r\n\r\n%%\r\ndem = [1 5 4 9; ...\r\n       4 5 7 7; ...\r\n       6 6 6 8];\r\nIX  = [0 1 0 7; ...\r\n       1 1 7 7; ...\r\n       2 2 5 9];\r\nassert(isequal(sgix(dem),IX))","published":true,"deleted":false,"likes_count":2,"comments_count":7,"created_by":569,"edited_by":223089,"edited_at":"2022-12-22T13:29:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":65,"test_suite_updated_at":"2022-12-22T13:29:53.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-07-20T08:58:26.000Z","updated_at":"2026-04-11T11:25:58.000Z","published_at":"2012-07-20T08:58:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUnlike in various applications, where the gradient of a two dimensional matrix is calculated in x and y direction, the gradient of a digital elevation model (DEM) is usually returned as the steepest gradient. The steepest gradient is the largest downward slope of a pixel to one of its eight neighbors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, your task will be to return the linear index of the steepest neighbor for each pixel in a gridded DEM. Pixels that don't have downward neighbors should receive the index value zero.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn example should help. The DEM is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[dem = [1 5 9; ...\\n       4 5 6; ...\\n       8 7 3];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe result should be\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[IX  = [0 1 4; ...\\n       1 1 9; ...\\n       2 9 0];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe results may not be unique, but the test cases have been built so that this is not a problem. The spatial resolution of the dem is dx=1 and dy=1. Note that the diagonal distance is hypot(dx,dy).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42616,"title":"Detect circles in images","description":"Given an image and a target radius range, specified as [rmin rmax], find circles in the image. Your function should output an m-by-2 array of circle centers (x,y positions in the image) and an m-by-1 vector of radii corresponding to m circles.\r\n\r\nYour detector will be judged on its \u003chttps://en.wikipedia.org/wiki/Precision_and_recall precision and recall\u003e. The recall must be 0.75 or higher and the precision must be 0.5 or higher to pass. \r\n\r\nFor example, if an image has 4 true circles, you can miss at most 1 of the circles and have at most 4 false detections.\r\n\r\n*Additional notes:*\r\n\r\n* Circles can be brighter or darker than the background.\r\n* A detection is considered a match if its position and radius is within 5 pixels of a true circle.\r\n* To make things easier, the target number of circles (N) is provided as an input. Pat yourself on the back if you do not need it.","description_html":"\u003cp\u003eGiven an image and a target radius range, specified as [rmin rmax], find circles in the image. Your function should output an m-by-2 array of circle centers (x,y positions in the image) and an m-by-1 vector of radii corresponding to m circles.\u003c/p\u003e\u003cp\u003eYour detector will be judged on its \u003ca href = \"https://en.wikipedia.org/wiki/Precision_and_recall\"\u003eprecision and recall\u003c/a\u003e. The recall must be 0.75 or higher and the precision must be 0.5 or higher to pass.\u003c/p\u003e\u003cp\u003eFor example, if an image has 4 true circles, you can miss at most 1 of the circles and have at most 4 false detections.\u003c/p\u003e\u003cp\u003e\u003cb\u003eAdditional notes:\u003c/b\u003e\u003c/p\u003e\u003cul\u003e\u003cli\u003eCircles can be brighter or darker than the background.\u003c/li\u003e\u003cli\u003eA detection is considered a match if its position and radius is within 5 pixels of a true circle.\u003c/li\u003e\u003cli\u003eTo make things easier, the target number of circles (N) is provided as an input. Pat yourself on the back if you do not need it.\u003c/li\u003e\u003c/ul\u003e","function_template":"function [centers,radii] = detectcircles(I,R,N)\r\n  centers = [];\r\n  radii = [];\r\nend","test_suite":"%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','circles.png'));\r\n[centers,radii] = detectcircles(I,[18 20],13);\r\nc = [119 222; 185 218; 124 116; 37 37; 178 184; 93 167; 37 72; 71 38; 93 132; 122 186; 97 96; 71 74; 151 204];\r\nr = 19*ones(13,1);\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','circlesBrightDark.png'));\r\n[centers,radii] = detectcircles(I,[32 64],6);\r\nc = [75 250; 100 100; 250 400; 300 120; 450 240; 330 370];\r\nr = [35; 50; 60; 40; 50; 55];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','coins.png'));\r\n[centers,radii] = detectcircles(I,[24 30],10);\r\nc = [236 174; 149 35; 56 50; 266 103; 217 71; 120 209; 110 85; 175 120; 96 146; 37 107];\r\nr = [25; 29; 25; 24; 29; 29; 24; 29; 29; 29];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','coloredChips.png'));\r\n[centers,radii] = detectcircles(I,[20 28],26);\r\nc = [83 177; 304 336; 420 88; 434 165; 244 166; 327 297; 273 53; 130 44; 271 281; 408 265; 312 192; 420 346; 146 199; 228 232; 329 135; 175 297; 366 224; 150 258; 217 107; 345 119; 445 68; 372 293; 150 342; 251 8; 259 217; 198 107];\r\nr = [23; 24; 23; 23; 23; 23; 23; 23; 23; 23; 23; 24; 23; 23; 23; 24; 23; 24; 23; 23; 23; 24; 25; 23; 23; 25];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','eight.tif'));\r\n[centers,radii] = detectcircles(I,[35 40],4);\r\nc = [198 189; 247 72; 62 141; 124 58];\r\nr = [37; 37; 38; 37];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','moon.tif'));\r\n[centers,radii] = detectcircles(I,[200 210],1);\r\nc = [253 287];\r\nr = [205];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','pillsetc.png'));\r\n[centers,radii] = detectcircles(I,[15 55],4);\r\nc = [103 240; 252 326; 119 130; 319 84];\r\nr = [17; 17; 50; 37];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','tape.png'));\r\n[centers,radii] = detectcircles(I,[75 85],1);\r\nc = [236 172];\r\nr = [80];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','testpat1.png'));\r\n[centers,radii] = detectcircles(I,[110 120],1);\r\nc = [128 128];\r\nr = [116];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','toysnoflash.png'));\r\n[centers,radii] = detectcircles(I,[90 100],1);\r\nc = [267 506];\r\nr = [94];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)","published":true,"deleted":false,"likes_count":4,"comments_count":4,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2015-09-18T20:16:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-09-17T22:38:48.000Z","updated_at":"2026-04-11T11:11:43.000Z","published_at":"2015-09-17T23:22:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an image and a target radius range, specified as [rmin rmax], find circles in the image. 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The recall must be 0.75 or higher and the precision must be 0.5 or higher to pass.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if an image has 4 true circles, you can miss at most 1 of the circles and have at most 4 false detections.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAdditional notes:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCircles can be brighter or darker than the background.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA detection is considered a match if its position and radius is within 5 pixels of a true circle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo make things easier, the target number of circles (N) is provided as an input. 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