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Maximum Value of an Ordered Triplet I

Difficulty: Easy

Problem 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].

Key Insights

  • You need to evaluate all triplets (i, j, k) where i < j < k.
  • The value calculation depends on the difference nums[i] - nums[j] and the multiplication by nums[k].
  • If all calculated values are negative, the answer should be 0.

Space and Time Complexity

Time Complexity: O(n^3) - due to the nested loops iterating through the array to form triplets.
Space Complexity: O(1) - no additional data structures are used that grow with input size.

Solution

To solve the problem, we will use a triple nested loop to iterate over all possible triplets (i, j, k). For each triplet, we will compute the value (nums[i] - nums[j]) * nums[k] and keep track of the maximum value found. If the maximum value remains negative, we will return 0.

Code Solutions

def maxValueOfTriplet(nums):
    max_value = float('-inf')  # Initialize maximum value to negative infinity
    n = len(nums)
    
    # Iterate through all triplets (i, j, k)
    for i in range(n):
        for j in range(i + 1, n):
            for k in range(j + 1, n):
                # Calculate the value of the triplet
                value = (nums[i] - nums[j]) * nums[k]
                max_value = max(max_value, value)  # Update maximum value if needed

    return max(max_value, 0)  # Return max value or 0 if negative
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