1899

1899. Merge Triplets to Form Target Triplet (Medium)

A triplet is an array of three integers. You are given a 2D integer array triplets, where triplets[i] = [ai, bi, ci] describes the ith 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(ai, aj), max(bi, bj), max(ci, cj)].

  <ul>
  	<li>For example, if <code>triplets[i] = [2, 5, 3]</code> and <code>triplets[j] = [1, 7, 5]</code>, <code>triplets[j]</code> will be updated to <code>[max(2, 1), max(5, 7), max(3, 5)] = [2, 7, 5]</code>.</li>
  </ul>
  </li>
  

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 = [[1,3,4],[2,5,8]], target = [2,5,8]
Output: true
Explanation: The target triplet [2,5,8] is already an element of 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.

Example 4:

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.

 

Constraints:

• 1 <= triplets.length <= 105
• triplets[i].length == target.length == 3
• 1 <= ai, bi, ci, x, y, z <= 1000

Companies:
Google

Related Topics:
Greedy

Solution 1.

// OJ: https://leetcode.com/problems/merge-triplets-to-form-target-triplet/
// Author: github.com/lzl124631x
// Time: O(N)
// Space: O(1)
class Solution {
public:
    bool mergeTriplets(vector<vector<int>>& A, vector<int>& T) {
        int cnt[3] = {};
        for (int i = 0; i < A.size(); ++i) {
            if (A[i][0] > T[0] || A[i][1] > T[1] || A[i][2] > T[2]) continue;
            for (int t = 0; t < 3; ++t)
                if (A[i][t] == T[t]) cnt[t] = 1;
        }
        for (int t = 0; t < 3; ++t) {
            if (cnt[t] == 0) return false;
        }
        return true;
    }
};

Or

// OJ: https://leetcode.com/problems/merge-triplets-to-form-target-triplet/
// Author: github.com/lzl124631x
// Time: O(N)
// Space: O(1)
class Solution {
public:
    bool mergeTriplets(vector<vector<int>>& A, vector<int>& T) {
        vector<int> v(3);
        for (int i = 0; i < A.size(); ++i) {
            if (A[i][0] > T[0] || A[i][1] > T[1] || A[i][2] > T[2]) continue;
            v = {max(v[0], A[i][0]), max(v[1], A[i][1]), max(v[2], A[i][2])};
        }
        return v == T;
    }
};