300 Longest Increasing Subsequence

300. Longest Increasing Subsequence

1. Question

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 is4. 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(nlogn) time complexity?

2. Implementation

(1) DP

class Solution {
    public int lengthOfLIS(int[] nums) {
        if (nums == null || nums.length == 0) {
            return 0;
        }

        int n = nums.length;
        int[] LIS = new int[n];
        Arrays.fill(LIS, 1);

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < i; j++) {
                if (nums[j] < nums[i] && (LIS[j] + 1 > LIS[i])) {
                    LIS[i] = LIS[j] + 1;
                }
            }
        }

        int res = 0;
        for (int e : LIS) {
            res = Math.max(e, res);
        }
        return res;
    }
}

(2) Binary Search优化

3. Time & Space Complexity

DP: 时间复杂度O(n^2), 空间复杂度O(n)