Count of substrings of a string containing another given string as a substring

Given two strings S and T, the task is to count the number of substrings of S that contains string T in it as a substring.

Examples:

Input: S = "dabc", T = "ab"
Output: 4
Explanation: Substrings of S containing T as a substring are: 
 

1. S[0, 2] = “dab”
2. S[1, 2] = “ab”
3. S[1, 3] = “abc”
4. S[0, 3] = “dabc”

Input: S = "hshshshs" T = "hs"
Output: 25

Approach: The idea is to generate all the substrings of S and check for each substring if it contains T in it or not. Follow the steps below to solve the problem:

• Initialize a variable, say count, with 0 to store the number of required substrings.
• Find all the substrings of the given string S and store them in an auxiliary array arr[].
• Traverse the given array arr[] and for every string in it, check if the string T is present in that string. If T occurs, increment the count by 1.
• After completing the above steps, the value of count is the resultant count.

Below is the implementation of the above approach:

4

Time Complexity: O(N²)
Auxiliary Space: O(N²)