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3152. Maximum Value of an Ordered Triplet II

Medium
Array
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Description

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 <= 105
  • 1 <= nums[i] <= 106

Hints

Hint 1
Preprocess the prefix maximum array, <code>prefix_max[i] = max(nums[0], nums[1], …, nums[i])</code> and the suffix maximum array, <code>suffix_max[i] = max(nums[i], nums[i + 1], …, nums[n - 1])</code>.
Hint 2
For each index <code>j</code>, find two indices <code>i</code> and <code>k</code> such that <code>i < j < k</code> and <code>(nums[i] - nums[j]) * nums[k]</code> is the maximum, using the prefix and suffix maximum arrays.
Hint 3
For index <code>j</code>, the maximum triplet value is <code>(prefix_max[j - 1] - nums[j]) * suffix_max[j + 1]</code>.

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