algoadvance

You are given a 0-indexed integer array nums. You have to find the maximum value of the expression nums[i] + nums[j] + nums[k] such that 0 <= i < j < k < nums.length.

Clarifying Questions

1. Input size: How large can the array nums be? This will help in assessing the efficiency requirements.
2. Element values: Are there any constraints on the values of the elements in nums (e.g., can they be negative or are they always positive)?
3. Output: What should be returned if array nums has fewer than 3 elements?

Code

def max_value_ordered_triplet(nums):
    if len(nums) < 3:
        return None  # or some other error value depending on the requirements

    # Initialize the maximum values for the triplet
    max1, max2, max3 = float('-inf'), float('-inf'), float('-inf')

    # Traverse the array from right to left
    for num in reversed(nums):
        if num > max3:
            max1, max2, max3 = max2, max3, num
        elif num > max2:
            max1, max2 = max2, num
        elif num > max1:
            max1 = num

    return max1 + max2 + max3

Strategy

1. Initialization: Start by checking if the length of nums is fewer than 3. If so, return a specific value (None or any other requirement-based value) since no triplet exists.
2. Maximum Values: Use three variables (max1, max2, max3) to keep track of the top three maximum values in the array.
3. Traversal: Iterate through the array in reverse to ensure that we are considering the correct order of indices (i < j < k).
4. Updating Maximums: For each element in the array, appropriately update max1, max2, and max3 to maintain the top three maximum values found so far.

Time Complexity

• Time Complexity: The algorithm runs in O(n), where n is the length of nums, because it involves a single pass through the array.
• Space Complexity: The space complexity is O(1) as we are using a fixed amount of extra space regardless of the input size.

This approach ensures we find the maximum value of an ordered triplet efficiently.

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