Formatted question description: https://leetcode.ca/all/1793.html

1793. Maximum Score of a Good Subarray

Level

Hard

Description

You are given an array of integers nums (0-indexed) and an integer k.

The score of a subarray (i, j) is defined as min(nums[i], nums[i+1], ..., nums[j]) * (j - i + 1). A good subarray is a subarray where i <= k <= j.

Return the maximum possible score of a good subarray.

Example 1:

Input: nums = [1,4,3,7,4,5], k = 3

Output: 15

Explanation: The optimal subarray is (1, 5) with a score of min(4,3,7,4,5) * (5-1+1) = 3 * 5 = 15.

Example 2:

Input: nums = [5,5,4,5,4,1,1,1], k = 0

Output: 20

Explanation: The optimal subarray is (0, 4) with a score of min(5,5,4,5,4) * (4-0+1) = 4 * 5 = 20.

Constraints:

  • 1 <= nums.length <= 10^5
  • 1 <= nums[i] <= 2 * 10^4
  • 0 <= k < nums.length

Solution

Loop over nums and use a monotonic stack to store each element’s edges, where the elements increase from botton to top of the monotonic stack.

For each 0 <= i < nums.length, use left[i] to store the maximum j such that j < i and nums[j] < nums[i], and use right[i] to store the minimum j such that j > i and nums[j] < nums[i]. Suppose nums[-1] = nums[nums.length] = -1.

For each 0 <= i < nums.length, if right[i] > k and left[i] < k, calculate the score at index i as nums[i] * (right[i] - left[i] - 1). Maintain the maximum score and return the maximum score.

class Solution {
    public int maximumScore(int[] nums, int k) {
        int length = nums.length;
        int[] left = new int[length];
        int[] right = new int[length];
        Arrays.fill(right, length);
        Deque<Integer> stack = new LinkedList<Integer>();
        for (int i = 0; i < length; i++) {
            while (!stack.isEmpty() && nums[stack.peek()] >= nums[i])
                right[stack.pop()] = i;
            left[i] = stack.isEmpty() ? -1 : stack.peek();
            stack.push(i);
        }
        int score = 0;
        for (int i = 0; i < length; i++) {
            if (left[i] < k && right[i] > k)
                score = Math.max(score, nums[i] * (right[i] - left[i] - 1));
        }
        return score;
    }
}

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