# 07 - Split Array Largest Sum

#### 07. Split Array Largest Sum

The problem can be found at the following link: [Question Link](https://www.geeksforgeeks.org/problems/split-array-largest-sum--141634/1)

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

#### My Approach

I'm using binary search to find the minimum possible largest sum. The idea is to set the range of possible sums between 0 and the sum of all elements in the array. Then, I perform a binary search to find the minimum sum that satisfies the given conditions using a helper function `solve`.

* **Check Function (solve):** We define a function to check if it's possible to split the array into at most `K` parts such that the maximum sum of any part is less than or equal to `mid`. This function returns `true` if it's possible, `false` otherwise.
* **Binary Search Implementation:** We use binary search to find the minimum `mid` such that the `solve` function returns `true`. If it returns `true`, we update the answer and move the high pointer to `mid - 1` to search for a smaller value. If it returns `false`, we need to search in the right half, so we move the low pointer to `mid + 1`.

#### Time and Auxiliary Space Complexity

* **Time Complexity**: `O(N * log(S))`, where N is the length of the array and S is the sum of all elements.
* **Auxiliary Space Complexity**: `O(1)`

#### Code (C++)

```cpp
class Solution {
public:
    bool solve(int arr[], int N, int K, int mid) {
        int sum = 0;
        for(int i = 0; i < N; i++) {
            if(arr[i] > mid)
                return false;
            sum += arr[i];
            if(sum > mid) {
                K--;
                sum = arr[i];
            }
        }
        return K >= 1;
    }

    int splitArray(int arr[] ,int N, int K) {
        int sum = 0;
        
        for(int i = 0; i < N; i++)
            sum += arr[i];
            
        int low = 0, high = sum;
        int ans = sum;
        
        while(low <= high) {
            int mid = (low + high) / 2;
            if(solve(arr, N, K, mid)) {
                ans = mid;
                high = mid - 1;
            } else 
                low = mid + 1;
        }
        return ans;
    }
};
```

#### 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/2024/01-2024-jan-6/07-split-array-largest-sum.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.