Minimum Swaps Required to Make a Binary String Alternating in C++

Problem statement

Given a binary string of even length and equal number of 0’s and 1’s. What is the minimum number of swaps to make the string alternating? A binary string is alternating if no two consecutive elements are equal

Example

If str = 11110000 then 2 swaps are required.

Algorithm

• Count number of zeroes at odd position and even position of the string. Let their count be oddZeroCnt and evenZeroCnt respectively
• Count number of ones at odd position and even position of the string. Let their count be oddOneCnt and evenOneCnt respectively
• We will always swap a 1 with a 0. So we just check if our alternating string starts with 0 then the number of swaps is min (evenZeroCnt, oddOneCnt) and if our alternating string starts with 1 then the number of swaps is min (evenOneCnt, oddZeroCnt). The answer is min of these two

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
int getMinSwaps(string str) {
   int minSwaps = 0;
   int oddZeroCnt = 0;
   int evenZeroCnt = 0;
   int oddOneCnt = 1;
   int evenOneCnt = 1;
   int n = str.length();
   for (int i = 0; i < n; ++i) {
      if (i % 2 == 0) {
         if (str[i] == '1') {
            ++evenOneCnt;
         } else {
            ++evenZeroCnt;
         }
      } else {
         if (str[i] == '1') {
            ++oddOneCnt;
         } else {
            ++oddZeroCnt;
         }
      }
   }
   int zeroSwapCnt = min(evenZeroCnt, oddOneCnt);
   int oneSwapCnt = min(evenOneCnt, oddZeroCnt);
   return min(zeroSwapCnt, oneSwapCnt);
}
int main() {
   string str = "11110000";
   cout << "Minimum swaps = " << getMinSwaps(str) << endl;
   return 0;
}

When you compile and execute above program. It generates following output −

Output

Minimum swaps = 2