1def maxSumOfThreeSubarrays(nums, k):
2    n = len(nums)
3    prefix = [0] * (n + 1)
4    for i in range(1, n + 1):
5        prefix[i] = prefix[i - 1] + nums[i - 1]
6    left = [0] * n
7    right = [0] * n
8    for i in range(k, n):
9        if prefix[i + 1] - prefix[i + 1 - k] > prefix[left[i - 1] + k] - prefix[left[i - 1]]:
10            left[i] = i + 1 - k
11        else:
12            left[i] = left[i - 1]
13    for i in range(n - k - 1, -1, -1):
14        if prefix[i + k] - prefix[i] >= prefix[right[i + 1] + k] - prefix[right[i + 1]]:
15            right[i] = i
16        else:
17            right[i] = right[i + 1]
18    max_sum = 0
19    ans = [-1, -1, -1]
20    for mid in range(k, n - 2 * k + 1):
21        l, r = left[mid - 1], right[mid + k]
22        total_sum = (prefix[l + k] - prefix[l]) + (prefix[mid + k] - prefix[mid]) + (prefix[r + k] - prefix[r])
23        if total_sum > max_sum:
24            max_sum = total_sum
25            ans = [l, mid, r]
26    return ans
27
28# Example usage
29nums = [1, 2, 1, 2, 6, 7, 5, 1]
30k = 2
31print(maxSumOfThreeSubarrays(nums, k))

1
public class Solution {
    public int[] MaxSumOfThreeSubarraysDP(int[] nums, int k) {
        int n = nums.Length;
        int[] prefix = new int[n + 1];
        int[] dp = new int[n];
        int[] left = new int[n];
        int[] right = new int[n];

        for (int i = 0; i < n; ++i) {
            prefix[i + 1] = prefix[i] + nums[i];
        }

        for (int i = k; i < n; ++i) {
            if (prefix[i + 1] - prefix[i + 1 - k] > (dp[i - 1] if i - 1 >= 0 else 0)) {
                dp[i] = prefix[i + 1] - prefix[i + 1 - k];
                left[i] = i + 1 - k;
            } else {
                dp[i] = dp[i - 1];
                left[i] = left[i - 1];
            }
        }

        right[n - k] = n - k;
        for (int i = n - k - 1; i >= 0; --i) {
            if (prefix[i + k] - prefix[i] >= prefix[right[i + 1] + k] - prefix[right[i + 1]]) {
                right[i] = i;
            } else {
                right[i] = right[i + 1];
            }
        }

        int maxSum = 0;
        int[] result = new int[3];
        for (int i = k; i <= n - 2 * k; ++i) {
            int l = left[i - 1];
            int r = right[i + k];
            int totalSum = (prefix[i + k] - prefix[i]) + (prefix[l + k] - prefix[l]) + (prefix[r + k] - prefix[r]);
            if (totalSum > maxSum) {
                maxSum = totalSum;
                result[0] = l;
                result[1] = i;
                result[2] = r;
            }
        }
        return result;
    }

    public static void Main(string[] args) {
        Solution solution = new Solution();
        int[] nums = {1, 2, 1, 2, 6, 7, 5, 1};
        int k = 2;
        int[] result = solution.MaxSumOfThreeSubarraysDP(nums, k);
        Console.WriteLine(string.Join(", ", result));
    }
}