Russian Doll Envelopes

LeetCode 354. Maximum chain of envelopes that strictly fit inside each other. Sort + LIS reduction. Requirements Input: list of (width, height) envelopes. Output: longest chain where each envelope strictly fits in the next. Trick: sort by width ascending, height descending (when widths tie); run LIS (Longest Increasing Subsequence) on heights. LIS with patience-sort gives O(n log n). Examples [[5,4],[6,4],[6,7],[2,3]] → 3. Notes Sorting heights descending on width-ties prevents same-width envelopes from chaining — easy to miss. LIS via bisect_left on a tails array is the standard O(n log n) implementation. Preparation Write LIS O(n log n) from memory in under 8 min. Justify the descending-height-on-tie trick out loud. Plain LIS and the mountain-LIS variant make good drill partners.