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Tug-Of-War
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#include <bits/stdc++.h>
using namespace std;
void TOWUtil(int* arr, int n, bool* curr_elements, int no_of_selected_elements,
bool* soln, int* min_diff, int sum, int curr_sum, int curr_position)
{
if (curr_position == n)
return;
if ((n/2 - no_of_selected_elements) > (n - curr_position))
return;
// considering the cases when current element is not included in the solution
TOWUtil(arr, n, curr_elements, no_of_selected_elements,
soln, min_diff, sum, curr_sum, curr_position+1);
// Adding the current element to the solution
no_of_selected_elements++;
curr_sum = curr_sum + arr[curr_position];
curr_elements[curr_position] = true;
// checks if a solution is formed
if (no_of_selected_elements == n/2)
{
// checks if the solution formed is better than the best solution so far
if (abs(sum/2 - curr_sum) < *min_diff)
{
*min_diff = abs(sum/2 - curr_sum);
for (int i = 0; i<n; i++)
soln[i] = curr_elements[i];
}
}
else
{
// considering the cases where current element is included in the solution
TOWUtil(arr, n, curr_elements, no_of_selected_elements, soln,
min_diff, sum, curr_sum, curr_position+1);
}
// removes current element before returning to the caller of this function
curr_elements[curr_position] = false;
}
// main function that generate an arr
void tugOfWar(int *arr, int n)
{
// the boolean array that contains the inclusion and exclusion of an element
// in current set. The number excluded automatically form the other set
bool* curr_elements = new bool[n];
// The inclusion/exclusion array for final solution
bool* soln = new bool[n];
int min_diff = INT_MAX;
int sum = 0;
for (int i=0; i<n; i++)
{
sum += arr[i];
curr_elements[i] = soln[i] = false;
}
// Find the solution using recursive function TOWUtil()
TOWUtil(arr, n, curr_elements, 0, soln, &min_diff, sum, 0, 0);
// Print the solution
cout << "The first subset is: ";
for (int i=0; i<n; i++)
{
if (soln[i] == true)
cout << arr[i] << " ";
}
cout << "\nThe second subset is: ";
for (int i=0; i<n; i++)
{
if (soln[i] == false)
cout << arr[i] << " ";
}
}
int main()
{
int arr[] = {23, 45, -34, 12, 0, 98, -99, 4, 189, -1, 4};
int n = sizeof(arr)/sizeof(arr[0]);
tugOfWar(arr, n);
return 0;
}