Longest Increasing Subsequence Show result

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], return 3

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

state: dp[i]表示前i个数中以第i个为结尾的LIS长度

function： dp[i] = max{dp[j] + 1}--> if (A[j] <= A[i])

initial: dp[0] = 1; dp[i] = 1;//如果不初始化dp[i] 例如数组【5,1】dp[1]就为0了

return max{dp[i]}

public class Solution {
    /**
     * @param nums: The integer array
     * @return: The length of LIS (longest increasing subsequence)
     */
    public int longestIncreasingSubsequence(int[] nums) {
        int n = nums.length; 
        if (nums == null || n == 0) {
            return 0;
        }
        int[] dp = new int[n];
        int max = 0;
        dp[0] = 1;
        for (int i = 1; i < n; i++) {
            dp[i] = 1;
            for (int j = 0; j < i; j++) {
                if (nums[i] >= nums[j]) {
                    dp[i] = Math.max(dp[i], dp[j] + 1);
                }
            }
            max = Math.max(dp[i], max);
        }
        return max;
    }
}