leetcode 300. Longest Increasing Subsequence

300. Longest Increasing Subsequence

Given an unsorted array of integers, find the length of longest increasing subsequence.

For example,
Given [10, 9, 2, 5, 3, 7, 101, 18],
The longest increasing subsequence is [2, 3, 7, 101], therefore the length is 4. Note that there may be more than one LIS combination, it is only necessary for you to return the length.

Your algorithm should run in O(n2) complexity.

Follow up: Could you improve it to O(n log n) time complexity?

动态规划

• 状态 state[i]表示前i个数字中以第i个结尾的LIS的长度

• 初始化： 以每一位结尾都初始化为1

• 状态转移方程：state[i] = max(state[j] + 1)，其中 j < i && num[j] <= num[i]

• 结果：max(state[i], i从0到n-1)

public class Solution {    public int lengthOfLIS(int[] nums) {        if (nums == null || nums.length == 0) {            return 0;        }        int[] state = new int[nums.length];        int max = 0;        for (int i = 0; i < nums.length; i++) {            state[i] = 1;            for (int j = 0; j < i; j++) {                if (nums[i] > nums[j]) {                    state[i] = state[i] > state[j] + 1 ? state[i] : state[j] + 1;                }            }            if (state[i] > max) {                max = state[i];            }        }        return max;    }}