# 04. Sum-string

The problem can be found at the following link: [Question Link](https://www.geeksforgeeks.org/problems/sum-string3151/1)

![](https://badgen.net/badge/Level/Hard/red)

## My Approach

I checked all possible combinations of substrings to find a valid sum-string. I iterate through the string, considering all possible splits into three substrings (`num1`, `num2`, and `currSum`). I add `num1` and `num2` using a helper function (`add`), and then compare the result with `currSum`. If they match, I continue the process recursively. To solve this, the functions are as follows:

1. **Addition Function (`add`):**
   * Takes two strings representing numbers and performs addition digit by digit.
   * Handles carry during addition.
   * Returns the result as a string.
2. **Solver Function (`solve`):**
   * Takes a string `s` and indices `i`, `j`, and `k`.
   * Extracts three substrings from `s` (num1, num2, currSum).
   * Adds `num1` and `num2` using the `add` function.
   * Compares the result with currSum.
   * Recursively calls itself with updated indices.
   * Returns true if the entire string is a valid sum string.
3. **Main Function (`isSumString`):**
   * Iterates through all possible pairs of indices `(j, k)`.
   * Calls `solve` to check if the string is a valid sum string.
   * Returns true if any valid sum string is found.

## Time and Auxiliary Space Complexity

* **Time Complexity**: `O(N^3)`, where N is the length of the input string.
  * The nested loops iterate over all possible pairs of indices `(j, k)`.
  * In the worst case, the `solve` function has a time complexity of `O(N)` per call.
* **Auxiliary Space Complexity**: `O(N)`, where `N` is the length of the input string.
  * The recursive calls and string manipulations contribute to space complexity.

## Code (C++)

```cpp
class Solution {
public:
    string add(string num1, string num2) {
        int carry = 0;
        int i = num1.size() - 1;
        int j = num2.size() - 1;
        string res;

        while (i >= 0 && j >= 0) {
            int sum = (num1[i] - '0') + (num2[j] - '0') + carry;
            res += (sum % 10) + '0';
            carry = sum / 10;
            --i;
            --j;
        }
        while (i >= 0) {
            int sum = (num1[i] - '0') + carry;
            res += (sum % 10) + '0';
            carry = sum / 10;
            --i;
        }
        while (j >= 0) {
            int sum = (num2[j] - '0') + carry;
            res += (sum % 10) + '0';
            carry = sum / 10;
            --j;
        }
        if (carry)
            res += carry + '0';
            
        reverse(res.begin(), res.end());
        return res;
    }
    
    bool solve(string& s, int i, int j, int k) {
        string num1 = s.substr(i, j - i);
        string num2 = s.substr(j, k - j);
        string sum = add(num1, num2);

        int n = sum.size();
        int len = k + n;

        if (len > s.size())
            return false;

        string currSum = s.substr(k, n);

        if (currSum != sum)
            return false;
        if (len == s.size())
            return true;
        return solve(s, j, k, len);
    }

    int isSumString(string& s) {
        int n = s.size();
    
        for (int j = 1; j < n; ++j) 
            for (int k = j + 1; k < n; ++k) 
                if (solve(s, 0, j, k))
                    return true;

        return false;
    }
};
```

## Contribution and Support

For discussions, questions, or doubts related to this solution, please visit our [discussion section](https://github.com/getlost01/gfg-potd/discussions). We welcome your input and aim to foster a collaborative learning environment.

If you find this solution helpful, consider supporting us by giving a `⭐ star` to the [getlost01/gfg-potd](https://github.com/getlost01/gfg-potd) repository.


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://gl01.gitbook.io/gfg-editorials/2023/12-2023-dec-3/04-sum-string.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.