1899. Merge Triplets to Form Target Triplet

1899. Merge Triplets to Form Target Triplet

Description

A triplet is an array of three integers. You are given a 2D integer array triplets, where triplets[i] = [a_i, b_i, c_i] describes the i^th triplet . You are also given an integer array target = [x, y, z] that describes the triplet you want to obtain.

To obtain target, you may apply the following operation on triplets any number of times (possibly zero ):

• Choose two indices (0-indexed ) i and j (i != j) and update triplets[j] to become [max(a_i, a_j), max(b_i, b_j), max(c_i, c_j)].

• For example, if triplets[i] = [2, 5, 3] and triplets[j] = [1, 7, 5], triplets[j] will be updated to [max(2, 1), max(5, 7), max(3, 5)] = [2, 7, 5].

Return true if it is possible to obtain the target triplet [x, y, z] as an element of triplets, or false otherwise.

Example 1:

Input: triplets = [[2,5,3],[1,8,4],[1,7,5]], target = [2,7,5]
Output: true
Explanation: Perform the following operations:
- Choose the first and last triplets [[2,5,3],[1,8,4],[1,7,5]]. Update the last triplet to be [max(2,1), max(5,7), max(3,5)] = [2,7,5]. triplets = [[2,5,3],[1,8,4],[2,7,5]]
The target triplet [2,7,5] is now an element of triplets.

Example 2:

Input: triplets = [[3,4,5],[4,5,6]], target = [3,2,5]
Output: false
Explanation: It is impossible to have [3,2,5] as an element because there is no 2 in any of the triplets.

Example 3:

Input: triplets = [[2,5,3],[2,3,4],[1,2,5],[5,2,3]], target = [5,5,5]
Output: true
Explanation: Perform the following operations:
- Choose the first and third triplets [[2,5,3],[2,3,4],[1,2,5],[5,2,3]]. Update the third triplet to be [max(2,1), max(5,2), max(3,5)] = [2,5,5]. triplets = [[2,5,3],[2,3,4],[2,5,5],[5,2,3]].
- Choose the third and fourth triplets [[2,5,3],[2,3,4],[2,5,5],[5,2,3]]. Update the fourth triplet to be [max(2,5), max(5,2), max(5,3)] = [5,5,5]. triplets = [[2,5,3],[2,3,4],[2,5,5],[5,5,5]].
The target triplet [5,5,5] is now an element of triplets.

Constraints:

• 1 <= triplets.length <= 10^5
• triplets[i].length == target.length == 3
• 1 <= a_i, b_i, c_i, x, y, z <= 1000

Hints/Notes

• 2025/01/08
• greedy
• 0x3F’s solution(checked)

Solution

Language: C++

class Solution {
public:
    bool mergeTriplets(vector<vector<int>>& triplets, vector<int>& target) {
        vector<int> res = {0, 0, 0};
        for (auto& tri : triplets) {
            if (tri[0] <= target[0] && tri[1] <= target[1] && tri[2] <= target[2]) {
                res[0] = max(res[0], tri[0]);
                res[1] = max(res[1], tri[1]);
                res[2] = max(res[2], tri[2]);
            }
            if (res == target) {
                return true;
            }
        }
        return false;
    }
};