C++ code to find minimum k to get more votes from students

Suppose we have an array A with n elements. There are n students in a school and each of them has exactly k votes and all votes should be used. There are two parties. The A[i] represents ith student has given A[i] amount of votes to first party and this implies the second party will get k- A[i] number of votes. The second party wants to set k in such a way that they win. What will be the minimum possible value of k.

So, if the input is like A = [2, 2, 3, 2, 2], then the output will be 5, because first party is getting 2 + 2 + 3 + 2 + 2 = 11 votes. if k = 5, then second party will get 3 + 3 + 2 + 3 + 3 = 14 votes and win the election.

Steps

To solve this, we will follow these steps −

n := size of A
for initialize k := 0, when k < n, update (increase k by 1), do:
   x := A[k]
   m := maximum of m and x
   s := s + x
return maximum of m and (2 * s / n + 1)

Example

Let us see the following implementation to get better understanding −

#include <bits/stdc++.h>
using namespace std;
int solve(vector<int> A){
   int n = A.size(), k = 0, s = 0, m = 0;
   for (int k = 0; k < n; k++){
      int x = A[k];
      m = max(m, x);
      s += x;
   }
   return max(m, 2 * s / n + 1);
}
int main(){
   vector<int> A = { 2, 2, 3, 2, 2 };
   cout << solve(A) << endl;
}

Input

{ 2, 2, 3, 2, 2 }

Output

5