Merge Triplets to Form Target Triplet

Problem Description

You are given a 2D integer array triplets, where triplets[i] describes the i-th triplet, and an integer array target that describes the triplet you want to obtain. You may apply the operation of choosing two indices and updating one triplet to become the maximum values of the chosen triplets. Return true if it is possible to obtain the target triplet as an element of triplets, or false otherwise.

Key Insights

• You can only achieve the target triplet by combining values from the original triplets.
• Each element in the target triplet must be achievable by at least one triplet having a greater than or equal value in the respective position.
• If any value in the target triplet exceeds the maximum value available in the corresponding position across all triplets, it’s impossible to form the target triplet.

Space and Time Complexity

Time Complexity: O(n) where n is the number of triplets, as we need to traverse the list once. Space Complexity: O(1) since we are using a constant amount of extra space.

Solution

To solve the problem, we need to iterate through the list of triplets and check if we can form the target triplet. We will keep track of whether each component of the target triplet can be formed by the maximum values of the triplets. If all components of the target can be formed, we return true, otherwise false.

1. Initialize three boolean flags for each component of the target triplet (x, y, z).
2. Iterate through each triplet in the list.
3. For each triplet, check if it can contribute to forming the target:
   • If the triplet's first element is greater than or equal to x, set the corresponding flag for x.
   • If the triplet's second element is greater than or equal to y, set the corresponding flag for y.
   • If the triplet's third element is greater than or equal to z, set the corresponding flag for z.
4. Finally, check if all three flags are true. If they are, return true; otherwise, return false.

Code Solutions