354. Russian Doll Envelopes

Hard

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You are given a 2D array of integers envelopes where envelopes[i] = [wi, hi] represents the width and the height of an envelope.

One envelope can fit into another if and only if both the width and height of one envelope are greater than the other envelope's width and height.

Return the maximum number of envelopes you can Russian doll (i.e., put one inside the other).

Note: You cannot rotate an envelope.

Example 1:

Input: envelopes = [[5,4],[6,4],[6,7],[2,3]]
Output: 3
Explanation: The maximum number of envelopes you can Russian doll is 3 ([2,3] => [5,4] => [6,7]).

Example 2:

Input: envelopes = [[1,1],[1,1],[1,1]]
Output: 1

Constraints:

• 1 <= envelopes.length <= 105

• envelopes[i].length == 2

• 1 <= wi, hi <= 105

Solution : Using Same Solution as PB 300 : Longest Increasing Subsequence (Patience Sorting Algorithm) O(nlogn)

class Solution:
    def maxEnvelopes(self, envelopes: List[List[int]]) -> int:
        # Can be done using Patience Sort PB300
        envelopes.sort(key= lambda x : (x[0], -x[1]))
        piles = []
        for _, height in envelopes:
            left, right = 0, len(piles)
            while left < right:
                mid = (right + left) // 2
                if piles[mid] >= height:
                    right = mid
                else:
                    left = mid + 1
            if left == len(piles):
                piles.append(height)
            else:
                piles[left] = height
        return len(piles)