Solution2.java

/// Source : https://leetcode.com/problems/longest-increasing-subsequence/description/
/// Author : liuyubobobo
/// Time   : 2017-11-19

import java.util.Arrays;

/// Dynamic Programming
/// Time Complexity: O(n^2)
/// Space Complexity: O(n)
public class Solution2 {

    public int lengthOfLIS(int[] nums) {

        if(nums.length == 0)
            return 0;

        // memo[i] is the length of the longest increasing sequence end in nums[i]
        int memo[] = new int[nums.length];
        Arrays.fill(memo, 1);
        for(int i = 1 ; i < nums.length ; i ++)
            for(int j = 0 ; j < i ; j ++)
                if(nums[i] > nums[j])
                    memo[i] = Math.max(memo[i], 1 + memo[j]);

        int res = memo[0];
        for(int i = 1 ; i < nums.length ; i ++)
            res = Math.max(res, memo[i]);

        return res;
    }

    public static void main(String[] args) {

        int nums1[] = {10, 9, 2, 5, 3, 7, 101, 18};
        System.out.println((new Solution2()).lengthOfLIS(nums1));
        // 4

        // ---

        int nums2[] = {4, 10, 4, 3, 8, 9};
        System.out.println((new Solution2()).lengthOfLIS(nums2));
        // 3

        // ---

        int nums3[] = {2, 2};
        System.out.println((new Solution2()).lengthOfLIS(nums3));
        // 1

        // ---

        int nums4[] = {1, 3, 6, 7, 9, 4, 10, 5, 6};
        System.out.println((new Solution2()).lengthOfLIS(nums4));
        // 6
    }
}