Check XOR Game Results in C++

Suppose we have an array A with N elements and another binary string S. Consider two players are playing a game. They are numbered as 0 and 1. There is one variable x whose initial value is 0. The games has N rounds. In ith round person S[i] does one of the following: replace x with x XOR A[i], otherwise do nothing. Person 0 wants 0 at the end of this game but person 1 wants non-zero. We have to check whether x becomes 0 at the end or not.

So, if the input is like A = [1, 2]; S = "10", then the output will be 1, because person1 changes x with 0 XOR 1 = 1, so it will always be 1 regardless the choice by person0.

Steps

To solve this, we will follow these steps −

N := size of A
Define an array judge of size: 60.
z := 0
fill judge with 0
for initialize n := N - 1, when 0 <= n, update (decrease n by 1), do:
   x := A[n]
   loop through the following unconditionally, do:
      if x is same as 0, then:
         Come out from the loop
      y := x
      I := -1
      for initialize i := 0, when i < 60, update (increase i by 1), do:
         if y mod 2 is same as 1, then:
            I := i
         y := y / 2
      if judge[I] is same as 0, then:
         judge[I] := x
         Come out from the loop
      x := x XOR judge[I]
   if S[n] is not equal to '0', then:
      if x is not equal to 0, then:
         z := 1
return z

Example

Let us see the following implementation to get better understanding −

#include <bits/stdc++.h>
using namespace std;

int solve(vector<int> A, string S){
   int N = A.size();
   int judge[60];
   int z = 0;
   fill(judge, judge + 60, 0);
   for (int n = N - 1; 0 <= n; n--){
      int x = A[n];
      while (1){
         if (x == 0)
            break;
         int y = x;
         int I = -1;
         for (int i = 0; i < 60; i++){
            if (y % 2 == 1)
               I = i;
               y /= 2;
         }
         if (judge[I] == 0){
            judge[I] = x;
            break;
         }
         x ^= judge[I];
      }
      if (S[n] != '0'){
         if (x != 0)
            z = 1;
      }
   }
   return z;
}
int main(){
   vector<int> A = { 1, 2 };
   string S = "10";
   cout << solve(A, S) << endl;
}

Input

{ 1, 2 }, "10"

Output

1