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.

Example

For [5, 4, 1, 2, 3], the LIS is [1, 2, 3], return 3

For [4, 2, 4, 5, 3, 7], the LIS is [2, 4, 5, 7], return 4

Notes:

Coordinate DP

1. State: f[i], the longest increasing subsequence to i
2. initialize: f[i] = 1
3. function: Max(f[j]+1) when nums[i] > nums[j], j from 0 to i-1
4. answer: max f[i]

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

        // state
        int[] f = new int[nums.length];

        // initialize
        f[0] = 1;

        // function
        int max = 1;
        for (int i = 1; i < nums.length; ++i) {
            f[i] = 1;
            for (int j = i-1; j >= 0; --j) {
                if (nums[i] > nums[j]) {
                    f[i] = Math.max(f[i], f[j] + 1);
                }
            }
            max = Math.max(max, f[i]);
        }

        // answer
        return max;
    }