Problem 221. Boolean algebra

Created by Tomasz

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Your contractor from Elbonia has sent you the prototype of the new logical unit. It turns out that the only logical relation it understands is "nand":<pre class="language-matlab">nand(a,b) := ~(a&b)
</pre>Your team has been developing code using the usual logical operators following MATLAB syntax: <tt>~,&</tt> and <tt>|</tt>. To save the project you need to write a translator that expresses MATLAB logical expressions using only the <tt>nand</tt> function.Input<ul><li>expr: a string containing a valid logical expression in MATLAB, that relates the two logical variables <tt>a</tt> and <tt>b</tt></li></ul>Output<ul><li>out: a string containing an equivalent logical expression that may only use the function <tt>nand(a,b)</tt>.</li></ul>Example 1:<pre> expr = 'a|(~b)'
 =>out = 'nand(nand(a,a),b)'</pre>Example 2:<pre> expr = '(a & ~a) | ~(a|b)'
 =>out = 'nand(nand(nand(a,a),nand(b,b)),nand(nand(a,a),nand(b,b)))'</pre>Remarks:It is not necessary to provide the shortest solution. A solution always exists. The input string is non-empty and always evaluates to true or false, if <tt>a</tt> and <tt>b</tt> are logical variables. All substrings in the output that are not 'a','b','0','1','true','false','(',')' or'nand' will be ignored.

Your contractor from Elbonia has sent you the prototype of the new logical unit. It turns out that the only logical relation it understands is "nand":

nand(a,b) := ~(a&b)

Your team has been developing code using the usual logical operators following MATLAB syntax: |~,&| and |||. To save the project you need to write a translator that expresses MATLAB logical expressions using only the |nand| function.

Input

* expr: a string containing a valid logical expression in MATLAB, that relates the two logical variables |a| and |b|

Output

* out: a string containing an equivalent logical expression that may only use the function |nand(a,b)|.

Example 1:

expr = 'a|(~b)'
  =>out  = 'nand(nand(a,a),b)'

Example 2:

expr = '(a & ~a) | ~(a|b)'
  =>out  = 'nand(nand(nand(a,a),nand(b,b)),nand(nand(a,a),nand(b,b)))'

Remarks:

It is not necessary to provide the shortest solution. A solution always exists. The input string is non-empty and always evaluates to true or false, if |a| and |b| are logical variables. All substrings in the output that are not 'a','b','0','1','true','false','(',')' or'nand' will be ignored.

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Problem 221. Boolean algebra

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