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Maximize sum by splitting given binary strings based on given conditions

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  • Last Updated : 15 Feb, 2022

Given two binary strings str1 and str2 each of length N, the task is to split the strings in such a way that the sum is maximum with given conditions.

  • Split both strings at the same position into equal length substrings.
  • If both the substrings have only 0’s then the value of that substring to be added is 1.
  • If both the substrings have only 1’s then the value of that substring to be added is 0.
  • If both the substrings have 0’s and 1’s then the value of that substring to be added is 2.

Return the maximum sum possible.

Examples: 

Input: str1 = “0101000”, str2 = “1101100”
Output: 8
Explanation:
Split like this:
Take “0” from str1 and “1” from str2 -> 2
Take “10” from str1 and “10” from str2 -> 2
Take “1” from str1 and “1” from str2 -> 0
Take “0” from str1 and “1” from str2 -> 2
Take “0” from str1 and “0” from str2 -> 1
Take “0” from str1 and “0” from str2 -> 1
Sum is 2 + 2 + 0 + 2 + 1 + 1 => 8

Input: str1 = “01”, str2 = “01”
Output: 2

 

Approach: This problem can be solved using the greedy approach. First, take some of the distinct pair means (0, 1) because it gives the maximum value 2 or with a distinct value pair with the same value pair,  the maximum value is 2 so there is no benefit. then try to make pair of (0, 0) with (1, 1) or vice versa to maximize the sum.

  • Initialize the MaxSum to 0.
  • Traverse the strings. If Ai is not equal to Bi, increment the MaxSum by 2.
  • Traverse the strings again and try to pair with opposite value means 0 with 1 or 1 with 0.
  • Check previous and next value of string if it’s opposite increment MaxSum by 2.
  • Else if the pair is only (0, 0) increment MaxSum by 1.

Below is the implementation of the above-mentioned approach:

C++




// C++ program to split two
// binary strings in such a way
// such that sum is maximum.
#include <iostream>
using namespace std;
 
// Function to split strings
// to find maximum sum
int MaxSum(string a, string b)
{
    int ans = 0;
    for (int i = 0; i < a.length(); i++) {
        if (a[i] != b[i])
            ans += 2;
    }
    int n = a.length();
 
    // Traverse the strings.
    for (int i = 0; i < n; i++) {
        if (a[i] == b[i]) {
            if (a[i] == '0') {
 
                // If Ai is not equal to Bi,
                // increment the MaxSum by 2
                if (i + 1 < n and a[i + 1] == '1'
                    and b[i + 1] == '1') {
                    ans += 2, i++;
                }
 
                // Else if the pair is only (0, 0)
                // increment MaxSum by 1.
                else {
                    ans += 1;
                }
            }
            else {
                if (i + 1 < n and a[i + 1] == '0'
                    and b[i + 1] == '0') {
                    ans += 2, i++;
                }
                else {
                    ans += 0;
                }
            }
        }
    }
    return ans;
}
 
// Driver Code
int main()
{
 
    string a = "0101000";
    string b = "1101100";
    cout << MaxSum(a, b);
    return 0;
}

Java




// Java program to split two
// binary Strings in such a way
// such that sum is maximum.
class GFG {
 
  // Function to split Strings
  // to find maximum sum
  static int MaxSum(String a, String b) {
    int ans = 0;
    for (int i = 0; i < a.length(); i++) {
      if (a.charAt(i) != b.charAt(i))
        ans += 2;
    }
    int n = a.length();
 
    // Traverse the Strings.
    for (int i = 0; i < n; i++) {
      if (a.charAt(i) == b.charAt(i)) {
        if (a.charAt(i) == '0') {
 
          // If Ai is not equal to Bi,
          // increment the MaxSum by 2
          if (i + 1 < n && a.charAt(i + 1) == '1'
              && b.charAt(i + 1) == '1') {
            ans += 2;
            i++;
          }
 
          // Else if the pair is only (0, 0)
          // increment MaxSum by 1.
          else {
            ans += 1;
          }
        } else {
          if (i + 1 < n && a.charAt(i + 1) == '0'
              && b.charAt(i + 1) == '0') {
            ans += 2;
            i++;
          } else {
            ans += 0;
          }
        }
      }
    }
    return ans;
  }
 
  // Driver Code
  public static void main(String args[]) {
 
    String a = "0101000";
    String b = "1101100";
    System.out.println(MaxSum(a, b));
  }
}
 
// This code is contributed by Saurabh Jaiswal

Python3




# python3 program to split two
# binary strings in such a way
# such that sum is maximum.
 
# Function to split strings
# to find maximum sum
def MaxSum(a, b):
 
    ans = 0
    for i in range(0, len(a)):
        if (a[i] != b[i]):
            ans += 2
 
    n = len(a)
 
    # Traverse the strings.
    i = 0
    while i < n:
        if (a[i] == b[i]):
            if (a[i] == '0'):
 
                # If Ai is not equal to Bi,
                # increment the MaxSum by 2
                if (i + 1 < n and a[i + 1] == '1'
                        and b[i + 1] == '1'):
                    ans, i = ans + 2, i + 1
 
                # Else if the pair is only (0, 0)
                # increment MaxSum by 1.
                else:
                    ans += 1
 
            else:
                if (i + 1 < n and a[i + 1] == '0'
                        and b[i + 1] == '0'):
                    ans, i = ans + 2, i + 1
 
                else:
                    ans += 0
        i += 1
    return ans
 
# Driver Code
if __name__ == "__main__":
 
    a = "0101000"
    b = "1101100"
    print(MaxSum(a, b))
 
    # This code is contributed by rakeshsahni

C#




// C# program to split two
// binary strings in such a way
// such that sum is maximum.
using System;
class GFG
{
 
  // Function to split strings
  // to find maximum sum
  static int MaxSum(string a, string b)
  {
    int ans = 0;
    for (int i = 0; i < a.Length; i++) {
      if (a[i] != b[i])
        ans += 2;
    }
    int n = a.Length;
 
    // Traverse the strings.
    for (int i = 0; i < n; i++) {
      if (a[i] == b[i]) {
        if (a[i] == '0') {
 
          // If Ai is not equal to Bi,
          // increment the MaxSum by 2
          if (i + 1 < n && a[i + 1] == '1'
              && b[i + 1] == '1') {
            ans += 2;
            i++;
          }
 
          // Else if the pair is only (0, 0)
          // increment MaxSum by 1.
          else {
            ans += 1;
          }
        }
        else {
          if (i + 1 < n && a[i + 1] == '0'
              && b[i + 1] == '0') {
            ans += 2;
            i++;
          }
          else {
            ans += 0;
          }
        }
      }
    }
    return ans;
  }
 
  // Driver Code
  public static void Main()
  {
 
    string a = "0101000";
    string b = "1101100";
    Console.Write(MaxSum(a, b));
  }
}
 
// This code is contributed by Samim Hossain Mondal.

Javascript




<script>
       // JavaScript code for the above approach
 
       // Function to split strings
       // to find maximum sum
       function MaxSum(a, b) {
           let ans = 0;
           for (let i = 0; i < a.length; i++) {
               if (a[i] != b[i])
                   ans += 2;
           }
           let n = a.length;
 
           // Traverse the strings.
           for (let i = 0; i < n; i++) {
               if (a[i] == b[i]) {
                   if (a[i] == '0') {
 
                       // If Ai is not equal to Bi,
                       // increment the MaxSum by 2
                       if (i + 1 < n && a[i + 1] == '1'
                           && b[i + 1] == '1') {
                           ans += 2, i++;
                       }
 
                       // Else if the pair is only (0, 0)
                       // increment MaxSum by 1.
                       else {
                           ans += 1;
                       }
                   }
                   else {
                       if (i + 1 < n && a[i + 1] == '0'
                           && b[i + 1] == '0') {
                           ans += 2, i++;
                       }
                       else {
                           ans += 0;
                       }
                   }
               }
           }
           return ans;
       }
 
       // Driver Code
       let a = "0101000";
       let b = "1101100";
       document.write(MaxSum(a, b));
 
      // This code is contributed by Potta Lokesh
   </script>

Output

8

Time Complexity: O(N)
Auxiliary Space: O(1)


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