2874. Maximum Value of an Ordered Triplet II
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
Solutions
Solution 1: Maintain Maximum Prefix Value and Maximum Difference
We can use two variables $mx$ and $mx_diff$ to maintain the maximum prefix value and maximum difference, respectively. When traversing the array, we update these two variables, and the answer is the maximum value of all $mx_diff \times nums[i]$.
The time complexity is $O(n)$, where $n$ is the length of the array. The space complexity is $O(1)$.
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