Back Tracking $1$ Back Tracking $[30$ marks$]$

Problem: Given is a set of $n$ integers, $a1,a2,$dots,$an,$ split the set into two subsets A and $B,$ if

possible, such that $|{\displaystyle \underset{i=1}{\overset{n}{}}}AA{a}_i$inA$|=|{\displaystyle \underset{i=1}{\overset{n}{}}}AA{b}_i$inB$|$ and $AB=.$

You are required to:

Implement a brute force Backtracking algorithm to find that.

Implement an algorithm that uses Backtracking with Heuristics to implement the above

problem.

Provide the time difference in finding the solution for the problem with the above approaches.

Implement your algorithm in $C++$ or Java. Here is specification for the input an output of your

program.

Input: Standard input. First line provides total number of elements in the set. Then the next $n$

lines give the elements of that set.

Sample input:

$5$

$1$

$2$

$3$

$4$

$5$

Output:

$5+1=4+2$

$5+2=4+3$

$(etc)$

Problem: Given is a set of n integers, a$1,$a$2,...,$an$,,$ split the set into two subsets A and B$,$ if possible, such that $|\backslash$Sigma ni$=1$ai in A $|=|\backslash$Sigma ni$=1$bi in B $|$andA$\backslash$cap B$=\backslash$phi $.$

You are required to:

$1.$ Implement a brute force Backtracking algorithm to find that.

$2.$ Implement an algorithm that uses Backtracking with Heuristics to implement the above problem.

$3.$ Provide the time difference in finding the solution for the problem with the above approaches.

Implement your algorithm in C$++$ or Java. Here is specification for the input an output of your program.

Input: Standard input. First line provides total number of elements in the set. Then the next n lines give the elements of that set.

Sample input:

$512345$

Output:

$5+1=4+2$

$5+2=4+3$

$($etc$)$