2873. Maximum Value of an Ordered Triplet I

Problem Link

Description

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You are given a 0-indexed integer array nums.

Return the maximum value over all triplets of indices (i, j, k) such that i < j < k. If all such triplets have a negative value, return 0.

The value of a triplet of indices (i, j, k) is equal to (nums[i] - nums[j]) * nums[k].

 

Example 1:

Input: nums = [12,6,1,2,7]
Output: 77
Explanation: The value of the triplet (0, 2, 4) is (nums[0] - nums[2]) * nums[4] = 77.
It can be shown that there are no ordered triplets of indices with a value greater than 77. 

Example 2:

Input: nums = [1,10,3,4,19]
Output: 133
Explanation: The value of the triplet (1, 2, 4) is (nums[1] - nums[2]) * nums[4] = 133.
It can be shown that there are no ordered triplets of indices with a value greater than 133.

Example 3:

Input: nums = [1,2,3]
Output: 0
Explanation: The only ordered triplet of indices (0, 1, 2) has a negative value of (nums[0] - nums[1]) * nums[2] = -3. Hence, the answer would be 0.

 

Constraints:

• 3 <= nums.length <= 100
• 1 <= nums[i] <= 106

Solution

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Python3

class Solution:
    def maximumTripletValue(self, nums: List[int]) -> int:
        N = len(nums)
        res = 0
        leftMax = [0] * N
        rightMax = [0] * N
 
        for i in range(N):
            leftMax[i] = max(leftMax[max(i - 1, 0)], nums[i])
        
        for i in range(N - 1, -1, -1):
            rightMax[i] = max(rightMax[min(i + 1, N - 1)], nums[i])
        
        for i in range(1, N - 1):
            res = max(res, (leftMax[i - 1] - nums[i]) * rightMax[i + 1])
        
        return res