Solution: Russian Doll Envelopes

Explore how to find the maximum number of envelopes that can be nested within each other by sorting them and using binary search to efficiently track the longest increasing subsequence of heights. Understand the combined use of sorting and search techniques to solve this problem with an optimized time complexity.

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Statement
Solution
- Time complexity
- Space complexity

Statement

You are given a 2D array of integers, envelopes, where each element envelopes[i] = [w_i, h_i] represents the width and height of an envelope. An envelope can fit inside another if and only if its width and height are strictly smaller than the width and height of the other envelope. The task is to determine the maximum number of envelopes that can be nested inside each other, similar to Russian dollsRussian dolls, also known as stacking dolls or nesting dolls, are a set of wooden dolls of decreasing size placed one inside another. .

Constraints:

$1\leq$ envelopes.length $\leq 10^3$ ...