Longest Increasing Subsequence
Find the length of the longest subsequence of a given sequence such that all elements of the subsequence are sorted in increasing order.
For example, the length of LIS for [50, 3, 10, 7, 40, 80] is 4 and LIS is [3, 7, 40, 80].
Example 1:
| Input | 10 | 9 | 2 | 5 | 3 | 7 | 101 | 18 |
|---|---|---|---|---|---|---|---|---|
LIS | 1 | 2 | 3 | 4 | ||||
| Output | 4 |
Example 2:
| Input | 10 | 22 | 9 | 33 | 21 | 50 | 41 | 60 | 80 |
|---|---|---|---|---|---|---|---|---|---|
LIS | 1 | 2 | 3 | 4 | 5 | 6 | |||
| Output | 6 |
Note:
- There may be more than one LIS combination, it is only necessary for you to return the length.
- Your algorithm should run in
O(n^2)complexity.
Follow up: Could you improve it to O(n*log(n)) time complexity?
Try it yourself
Title
Script
Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book.
Contrary to popular belief, Lorem Ipsum is not simply random text.
>>> a = [1, 2, 3]
>>> a[-1]
3