Solution: Russian Doll Envelopes

Explore how to determine the maximum number of envelopes that can be nested inside each other by sorting envelopes by width and height, then applying binary search to find the longest increasing subsequence based on height. Understand the combined strategy of sorting and searching to handle multi-dimensional comparisons and optimize time complexity for efficient solutions.

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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 $\leq 10^3$
envelopes[i].length $== 2$
$1\leq$ ...