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 <code>tripletsi = a_i, b_i, c_i</code> describes the <code>i^th</code> 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 <code>max(a_i, a_j), max(b_i, b_j), max(c_i, c_j)</code>.

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:

• <code>1 <= triplets.length <= 10⁵</code>

• triplets[i].length == target.length == 3

• <code>1 <= a_i, b_i, c_i, x, y, z <= 1000</code>