Count of sub-strings with equal consecutive 0’s and 1’s


Given a binary string str of 0’s and 1’s only. The task is to count the total numbers of substrings of string str such that each substring has an equal number of consecutive 0’s and 1’s in it.

Examples

Input: str = “010011”
Output: 4
Explanation:
The substrings with consecutive 0’s and 1’s are “01”, “10”, “0011”, “01”. Hence, the count is 4.
Note:
The two “01” are at different positions: [0, 1] and [3, 4].
“010011” has the same number of 0’s and 1’s but they are not consecutive.

Input: str = “0001110010”
Output: 7
Explanation:
The substrings with consecutive 0’s and 1’s are “000111”, “0011”, “01”, “1100”, “10”, “01”, “10”.

Approach:



  • Count the number of consecutive 0’s (or 1’s) from start of the string.
  • Then count the number of consecutive 1’s (or 0’s) from the position in the string str where count of 0’s (or 1’s) ends.
  • The total number of substrings with consecutive 0’s and 1’s is the minimum of the count of consecutive 0’s and 1’s found in above two steps.
  • Repeat the above steps till the end of the string str.

Below is the implementation of the above approach:

C++

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// C++ implementation of the
// above approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to find the count
// of substrings with equal no.
// of consecutive 0's and 1's
int countSubstring(string& S, int& n)
{
    // To store the total count
    // of substrings
    int ans = 0;
  
    int i = 0;
  
    // Traversing the string
    while (i < n) {
  
        // Count of consecutive
        // 0's & 1's
        int cnt0 = 0, cnt1 = 0;
  
        // Counting subarrays of
        // type "01"
        if (S[i] == '0') {
  
            // Count the consecutive
            // 0's
            while (i < n && S[i] == '0') {
                cnt0++;
                i++;
            }
  
            // If consecutive 0's
            // ends then check for
            // consecutive 1's
            int j = i;
  
            // Counting consecutive 1's
            while (j < n && S[j] == '1') {
                cnt1++;
                j++;
            }
        }
  
        // Counting subarrays of
        // type "10"
        else {
  
            // Count consecutive 1's
            while (i < n && S[i] == '1') {
                cnt1++;
                i++;
            }
  
            // If consecutive 1's
            // ends then check for
            // consecutive 0's
            int j = i;
  
            // Count consecutive 0's
            while (j < n && S[j] == '0') {
                cnt0++;
                j++;
            }
        }
  
        // Update the total count
        // of substrings with
        // minimum of (cnt0, cnt1)
        ans += min(cnt0, cnt1);
    }
  
    // Return answer
    return ans;
}
  
// Driver code
int main()
{
    string S = "0001110010";
    int n = S.length();
  
    // Function to print the
    // count of substrings
    cout << countSubstring(S, n);
    return 0;
}

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Java

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// Java implementation of the 
// above approach 
class GFG{
  
    // Function to find the count 
    // of substrings with equal no. 
    // of consecutive 0's and 1's 
    static int countSubstring(String S, int n) 
    
        // To store the total count 
        // of substrings 
        int ans = 0
      
        int i = 0
      
        // Traversing the string 
        while (i < n) { 
      
            // Count of consecutive 
            // 0's & 1's 
            int cnt0 = 0, cnt1 = 0
      
            // Counting subarrays of 
            // type "01" 
            if (S.charAt(i) == '0') { 
      
                // Count the consecutive 
                // 0's 
                while (i < n && S.charAt(i) == '0') { 
                    cnt0++; 
                    i++; 
                
      
                // If consecutive 0's 
                // ends then check for 
                // consecutive 1's 
                int j = i; 
      
                // Counting consecutive 1's 
                while (j < n && S.charAt(j) == '1') { 
                    cnt1++; 
                    j++; 
                
            
      
            // Counting subarrays of 
            // type "10" 
            else
      
                // Count consecutive 1's 
                while (i < n && S.charAt(i) == '1') { 
                    cnt1++; 
                    i++; 
                
      
                // If consecutive 1's 
                // ends then check for 
                // consecutive 0's 
                int j = i; 
      
                // Count consecutive 0's 
                while (j < n && S.charAt(j) == '0') { 
                    cnt0++; 
                    j++; 
                
            
      
            // Update the total count 
            // of substrings with 
            // minimum of (cnt0, cnt1) 
            ans += Math.min(cnt0, cnt1); 
        
      
        // Return answer 
        return ans; 
    
      
    // Driver code 
    static public void main(String args[])
    
        String S = "0001110010"
        int n = S.length(); 
      
        // Function to print the 
        // count of substrings 
        System.out.println(countSubstring(S, n)); 
    
}
  
// This code is contributed by Yash_R

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Python3

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# Python3 implementation of the
# above approach
  
# Function to find the count
# of substrings with equal no.
# of consecutive 0's and 1's
def countSubstring(S, n) :
  
    # To store the total count
    # of substrings
    ans = 0;
  
    i = 0;
  
    # Traversing the string
    while (i < n) :
  
        # Count of consecutive
        # 0's & 1's
        cnt0 = 0; cnt1 = 0;
  
        # Counting subarrays of
        # type "01"
        if (S[i] == '0') :
  
            # Count the consecutive
            # 0's
            while (i < n and S[i] == '0') :
                cnt0 += 1;
                i += 1;
  
            # If consecutive 0's
            # ends then check for
            # consecutive 1's
            j = i;
  
            # Counting consecutive 1's
            while (j < n and S[j] == '1') :
                cnt1 += 1;
                j += 1;
  
        # Counting subarrays of
        # type "10"
        else :
  
            # Count consecutive 1's
            while (i < n and S[i] == '1') :
                cnt1 += 1;
                i += 1;
  
            # If consecutive 1's
            # ends then check for
            # consecutive 0's
            j = i;
  
            # Count consecutive 0's
            while (j < n and S[j] == '0') :
                cnt0 += 1;
                j += 1;
  
        # Update the total count
        # of substrings with
        # minimum of (cnt0, cnt1)
        ans += min(cnt0, cnt1);
  
    # Return answer
    return ans;
  
# Driver code
if __name__ == "__main__" :
    S = "0001110010";
    n = len(S);
  
    # Function to print the
    # count of substrings
    print(countSubstring(S, n));
      
# This code is contributed by Yash_R

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C#

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// C# implementation of the 
// above approach 
using System;
  
class GFG{
  
    // Function to find the count 
    // of substrings with equal no. 
    // of consecutive 0's and 1's 
    static int countSubstring(string S, int n) 
    
        // To store the total count 
        // of substrings 
        int ans = 0; 
      
        int i = 0; 
      
        // Traversing the string 
        while (i < n) { 
      
            // Count of consecutive 
            // 0's & 1's 
            int cnt0 = 0, cnt1 = 0; 
      
            // Counting subarrays of 
            // type "01" 
            if (S[i] == '0') { 
      
                // Count the consecutive 
                // 0's 
                while (i < n && S[i] == '0') { 
                    cnt0++; 
                    i++; 
                
      
                // If consecutive 0's 
                // ends then check for 
                // consecutive 1's 
                int j = i; 
      
                // Counting consecutive 1's 
                while (j < n && S[j] == '1') { 
                    cnt1++; 
                    j++; 
                
            
      
            // Counting subarrays of 
            // type "10" 
            else
      
                // Count consecutive 1's 
                while (i < n && S[i] == '1') { 
                    cnt1++; 
                    i++; 
                
      
                // If consecutive 1's 
                // ends then check for 
                // consecutive 0's 
                int j = i; 
      
                // Count consecutive 0's 
                while (j < n && S[j] == '0') { 
                    cnt0++; 
                    j++; 
                
            
      
            // Update the total count 
            // of substrings with 
            // minimum of (cnt0, cnt1) 
            ans += Math.Min(cnt0, cnt1); 
        
      
        // Return answer 
        return ans; 
    
      
    // Driver code 
    static public void Main ()
    
        string S = "0001110010"
        int n = S.Length; 
      
        // Function to print the 
        // count of substrings 
        Console.WriteLine(countSubstring(S, n)); 
    
}
  
// This code is contributed by Yash_R

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Output:

7

Time Complexity: O(N), where N = length of string.

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