Flip String to Monotone Increasing in C++

Suppose a string of '0's and '1's is given. That string will be monotonic increasing if it consists of some number of '0's (possibly 0), followed by some number of '1's (also possibly 0.). We have a string S of '0's and '1's, and we may flip any '0' to a '1' or a '1' to a '0'. Find the minimum number of flips to make S monotone increasing. So if the input is like “010110”, then the output will be 2. By flipping we can get “011111” or “000111”.

To solve this, we will follow these steps −

• n := size of S, set flipCount := 0, oneCount := 0

• for i in range 0 to n – 1

  • if S[i] is 0, then

    • if oneCount = 0, then skip to the next iteration

    • increase the flipCount by 1

  • otherwise increase oneCount by 1

  • if oneCount < flipCount, then set flipCount := oneCount

• return flipCount

Let us see the following implementation to get better understanding −

Example

#include <bits/stdc++.h>
using namespace std;
class Solution {
   public:
   int minFlipsMonoIncr(string S) {
      int n = S.size();
      int flipCount = 0;
      int oneCount = 0;
      for(int i = 0; i < n; i++){
         if(S[i] == '0'){
            if(oneCount == 0) continue;
            flipCount++;
         } else oneCount++;
            if(oneCount < flipCount) flipCount = oneCount;
      }
      return flipCount;
   }
};
main(){
   Solution ob;
   cout << (ob.minFlipsMonoIncr("010110"));
}

Input

"010110"

Output

2