Merge Triplets to Form Target Triplet - Solution & Explanation

Problem Overview: You are given multiple triplets and a target triplet. You can merge any number of triplets by taking the maximum value at each index. The task is to determine whether some sequence of merges can produce the exact target triplet.

The merge operation effectively behaves like a coordinate-wise max. If you merge two triplets [a,b,c] and [x,y,z], the result becomes [max(a,x), max(b,y), max(c,z)]. The challenge is deciding whether some subset of the given triplets can combine to reach the target without exceeding any component.

Approach 1: Filter Valid Triplets and Check Feasibility (Greedy) (Time: O(n), Space: O(1))

This approach relies on a simple greedy observation: any triplet containing a value larger than the corresponding value in the target can never be part of a valid merge. Merging it would permanently push that coordinate beyond the target. Start by iterating through the list and ignore any triplet where triplet[i] > target[i] for any index.

For every remaining valid triplet, track whether it helps achieve one of the three target coordinates. If a triplet matches the target value at index 0, 1, or 2, mark that coordinate as achievable. Because merging uses the maximum operation, as long as each coordinate of the target appears in some valid triplet, combining them will eventually produce the exact target.

This method performs a single pass through the input array, using constant extra variables to track progress. The greedy filter ensures that every considered triplet keeps the merge result within the target bounds. This pattern appears frequently in greedy problems where invalid candidates must be discarded early.

Approach 2: Hash Set Tracking for Each Target Element (Time: O(n), Space: O(1))

This variation tracks which indices of the target have already been satisfied using a small hash set. Iterate through the triplets and discard any triplet that exceeds the target in any coordinate. For valid triplets, check each index and insert the index into the set if the value equals the target's value at that position.

The key idea is that you only need one contributing triplet per coordinate. Once indices 0, 1, and 2 appear in the set, the target triplet can be constructed through merges. Hash lookups keep the check constant time while making the logic explicit and easy to reason about.

This approach still runs in linear time because each triplet is processed once. The extra structure is tiny (at most three entries), so space complexity remains constant. It is a clean implementation choice when solving problems involving arrays combined with lightweight hash table tracking.

Recommended for interviews: The greedy filtering approach is typically what interviewers expect. It shows you recognized the key invariant: no triplet may exceed the target. Explaining that observation clearly demonstrates strong problem decomposition. The hash set variation is equally optimal but mostly improves code clarity rather than algorithmic performance.