Description

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

You code should return the length of the LIS.

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

public class Solution {
    /*
     * @param nums: An integer array
     * @return: The length of LIS (longest increasing subsequence)
     */
    public int longestIncreasingSubsequence(int[] nums) {
        // write your code here
        if (nums == null || nums.length == 0) {
            return 0;
        }

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

            max = Math.max(max, dp[i]);
        }

        return max;
    }
}