Write a program in C++ to count the Number of substrings that starts with ‘1’ and ends with ‘1’

We are given the length of a binary string str and the string itself. The task is to count the number of substrings that start with '1' and end with '1'. A binary string contains only '0's and '1's, and a substring is any continuous part of the given string.

Let's look at a few example scenarios to understand the problem clearly:

Scenario 1

<b>Input: </b>N = 5, str = "11101"
<b>Output:</b> 6
<b>Explanation:
</b>In the given binary string, there are 6 substrings that start and end with '1'.
These are: ("11", "111", "1110", "11101", "1101", and "101").

Scenario 2

<b>Input:</b> N = 4, str = "0011"
<b>Output: </b>1
Explanation:
In this binary string, there's only one substring that starts and ends with '1':
("11") So, the total count is 1.

Approach to Solve the Problem

The problem is similar to the well-known Handshake Problem, where we count the number of handshakes in a party of n people. Each person shakes hands with every other person once, so the total number of handshakes is n x (n - 1) / 2.

Similarly, if we count the number of 1's in the given string, we can find the number of substrings that start and end with '1'.

Here are the steps we followed:

• First, we define a function countSubstring(int N, const string& s) that takes the length of the string and the binary string as input, and returns the count of substrings that start and end with '1'.
• Next, we loop through the string and count the number of '1's.
• Then, we apply the formula n x (n - 1) / 2 using the count of '1's.
• Finally, we return the result of that calculation.

C++ Program to Count Substrings Starting and Ending with '1'

Here is a C++ program that uses the above steps to count all substrings that start and end with '1'.

#include<iostream>
using namespace std;

int countSubstring(int N, const string& s) {
   int count = 0;
   for(int i = 0; s[i] != '\0'; ++i) {
      if(s[i] == '1')
         count++;
   }
   // Using the handshake formula to count valid pairs of '1'
   return count * (count - 1) / 2;
}

int main() {
   int N = 5;
   string str = "11101";
   cout << "Input: N = " << N << ", String = " << str << endl;
   int result = countSubstring(N, str);
   cout << "Count of substrings: " << result << endl;
   return 0;
}

Following is the output of the above program:

Input: N = 5, String = 11101
Count of substrings: 6

Time Complexity: O(N), where N is the length of the input string s.

Space Complexity: O(1), no extra space is used.

Conclusion

In this article, we learned how to count the number of substrings that start and end with '1' in a binary string by counting the total number of '1's and applying the formula n x (n - 1) / 2. The program runs with a time complexity of O(n) and a space complexity of O(1).