# 354 Russian Doll Envelopes

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`
 `````` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 `````` ``````from bisect import bisect_left class Solution: def maxEnvelopes(self, envelopes: List[List[int]]) -> int: ''' E.g. ---------------> incr 1, 2, 5, 5, 6, 6 8, 3, 4, 2, 7, 4 ---> ---> decr ^ ^ ^ longest incr subseq ''' envelopes.sort(key=lambda x: (x, -x)) dp = [] ''' dp is an array such that dp[i] is the smallest element that ends an increasing subsequence of length i + 1. Whenever we encounter a new element e, we binary search inside dp to find the largest index i such that e can end that subsequence. We then update dp[i] with e. The length of the LIS is the same as the length of dp, as if dp has an index i, then it must have a subsequence of length i+1. ''' arr = [e for e in envelopes] for num in arr: idx = bisect_left(dp, num) if idx == len(dp): dp.append(num) else: dp[idx] = num return len(dp)``````