Find Minimum Correct String from Given Binary String in C++

Suppose we have a binary string S with n bits. There are no redundant leading zeroes. We can perform two different operations on S −

• Swap any pair of adjacent bits

• Replace all "11" with "1"

Let val(S) is decimal representation of S. We have to find minimum correct string, where correct string A is less than another correct string 'B' when val(A) < val(B)

So, if the input is like S = "1001", then the output will be 100, because we can perform the operation like "1001" -> "1010" -> "1100" -> "100".

Steps

To solve this, we will follow these steps −

n := size of S
res := a blank string
res := res + S[0]
for initialize i := 1, when i < n, update (increase i by 1), do:
   if S[i] is same as '0', then:
      res := res concatenate "0"
return res

Example

Let us see the following implementation to get better understanding −

#include <bits/stdc++.h>
using namespace std;
string solve(string S){
   int n = S.size();
   string res = "";
   res += S[0];
   for (int i = 1; i < n; i++){
      if (S[i] == '0'){
         res += "0";
      }
   }
   return res;
}
int main(){
   string S = "1001";
   cout << solve(S) << endl;
}

Input

"1001"

Output

100