Longest Increasing Subsequence
Find the length of the longest strictly increasing subsequence.
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Lesson notes
Try it before you watch
Restate the problem in your own words, list the edge cases, and sketch a solution with its running time. Then play the video and compare.
Reveal the key idea
The O(n²) DP compares each element with all earlier ones. The faster method keeps the smallest tail of every subsequence length and places each number with binary search.
Pattern: Dynamic programming. Define a state, write the recurrence between states, and compute each state only once.
Complexity
| Measure | Bound |
|---|---|
| Time | O(n log n) |
| Extra space | O(n) |
Walkthroughs often start from a simpler approach first; aim to reach these bounds. New to Big-O? Read understanding algorithmic complexity.