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Given a numeric string **str**, the task is to calculate the number of substrings with the sum of digits equal to their length.

**Examples:**

_Input: __str = “112112” _

_Output: __6 _

Explanation:

Substrings “1”, “1”, “11”, “1”, “1”, “11” satisfy the given condition.

_ str = “1101112” _Input:

_Output: _12

**Recommended: Please try your approach on _ {IDE}_ first, before moving on to the solution.**

**Naive Approach: **The simplest solution is to generate all substrings of the given string and for each substring, check if its sum is equal to its length or not. For each substring found to be true, increase count.

**_Time Complexity: _**_O(N3) _

** Auxiliary Space:**_ O(1)_

**Efficient Approach: * The above approach can be optimized using a Hashmap and keep updating the count of substrings in the *Hashmap** and print the required count at the end.

Below is the implementation of the above approach:

- C++
- Java
- Python3

`// C++ Program to implement`

`// the above approach`

`#include <bits/stdc++.h>`

`**using**`

`**namespace**`

`std;`

`// Function to count the number of`

`// substrings with sum equal to length`

`**int**`

`countSubstrings(string s,`

`**int**`

`n)`

`{`

`**int**`

`count = 0, sum = 0;`

`// Stores the count of substrings`

`unordered_map<``**int**``,`

`**int**``> mp;`

`mp[0]++;`

`**for**`

`(``**int**`

`i = 0; i < n; ++i) {`

`// Add character to sum`

`sum += (s[i] -`

`'0'``);`

`// Add count of substrings to result`

`count += mp[sum - (i + 1)];`

`// Increase count of subarrays`

`++mp[sum - (i + 1)];`

`}`

`// Return count`

`**return**`

`count;`

`}`

`// Driver Code`

`**int**`

`main()`

`{`

`string str =`

`"112112"``;`

`**int**`

`n = str.length();`

`cout << countSubstrings(str, n) << endl;`

`**return**`

`0;`

`}`

**Output:**

`6`

**Time Complexity: **O(N)

**Auxiliary Space:** O(N)

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greedy hash mathematical searching strings cpp-map frequency-counting substring

A Computer Science portal for geeks. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions.