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354. Russian Doll Envelopes

Array Binary Search Dynamic Programming Sorting

Problem - Russian Doll Envelopes

Hard

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

Solutions

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class Solution:
    def maxEnvelopes(self, envelopes: List[List[int]]) -> int:
        envelopes.sort(key=(lambda x: (x[0], -x[1])))
        dp = [envelopes[0][1]]

        for _, height in envelopes[1:]:
            if height > dp[-1]:
                dp.append(height)
            else:
                index = bisect_left(dp, height)
                dp[index] = height

        return len(dp)

Submission Stats:

  • Runtime: 116 ms (95.43%)
  • Memory: 52.7 MB (91.73%)