Longest Increasing Subsequence

Given a sequence of integers, find the longest increasing subsequence (LIS).

You code should return the length of the LIS.

Clarification

What's the definition of longest increasing subsequence?

• The longest increasing subsequence problem is to find a subsequence of a given sequence in which the subsequence's elements are in sorted order, lowest to highest, and in which the subsequence is as long as possible. This subsequence is not necessarily contiguous, or unique.

• https://en.wikipedia.org/wiki/Longest_increasing_subsequence

Example

For[5, 4, 1, 2, 3], the LIS is[1, 2, 3], return3
For[4, 2, 4, 5, 3, 7], the LIS is[2, 4, 5, 7], return4

Solution: DP. State : The longest increasing subsequence in 0 - i

function: dp[i] = Math.max(dp[j] + 1, dp[i])

public int longestIncreasingSubsequence(int[] nums) {
    if(nums == null || nums.length == 0) {
        return 0;
    }
    int[] dp = new int[nums.length];
    int res = 1;
    for(int i = 0; i < nums.length; i++) {
        dp[i] = 1;
        for(int j = 0; j < i; j++) {
            if(nums[j] < nums[i]) {
                //Notice that dp[i] may higher than dp[j] + 1
                dp[i] = Math.max(dp[j] + 1, dp[i]);
            }
        }
        res = Math.max(res, dp[i]);
    }
    return res;
}