> For the complete documentation index, see [llms.txt](https://gl01.gitbook.io/gfg-editorials/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://gl01.gitbook.io/gfg-editorials/2024/01-2024-jan-1/02-largest-sum-subarray-of-size-at-least-k.md).

# 02. Largest Sum Subarray of Size at least K

The problem can be found at the following link: [Question Link](https://www.geeksforgeeks.org/problems/largest-sum-subarray-of-size-at-least-k3121/1)

![](https://badgen.net/badge/Level/Medium/yellow)

## My Approach

I solve the problem using a sliding window approach.

* Initialize a vector `pre` of length `n` to store the prefix sum of the input array.
* Calculate the prefix sum and store it in the `pre` vector.
* Initialize sum with the sum of the first `k` elements and ans with the same value.
* Iterate from `k to n`, and in each iteration:
  * Calculate the sum of the subarray ending at index i.
  * Update sum with the maximum of the current sum and the sum of the previous k elements plus the current element.
  * Update ans with the maximum of the current sum and the previous ans.
* Return the final value of ans as the result.

## Time and Auxiliary Space Complexity

* **Time Complexity** : `O(n)`, where n is the size of the input vector.
* **Auxiliary Space Complexity** : `O(n)`, where n is the size of the pre vector.

## Code (C++)

```cpp
class Solution {
public:
    long long int maxSumWithK(long long int a[], long long int n, long long int k) 
    {
        vector<long long int> pre(n, 0);
        pre[0] = a[0];

        for (int i = 1; i < n; ++i)
            pre[i] = pre[i - 1] + a[i];

        long long int sum = pre[k - 1];
        long long int ans = sum;

        for (int i = k; i < n; i++) 
        {
            long long int cur = pre[i] - pre[i - k];
            sum = max(cur, sum + a[i]);
            ans = max(ans, sum);
        }

        return ans;
    }
};
```

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