Longest Increasing Subsequence

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

You code should return the length of the LIS.

Have you met this question in a real interview? 

Yes

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

中规中矩的动规题，也不难，理解清楚要干什么就可以。嵌套循环，对于内层循环，如果值比当前值要小，更新下当前位置的dp值。感觉可以优化一下。

代码：

public int longestIncreasingSubsequence(int[] nums) {        // write your code here        if(nums == null || nums.length == 0) return 0;        int[] dp = new int[nums.length];        for(int i=0;i<dp.length;i++){            dp[i] = 1;        }        int max = -1;        for(int i=1;i<nums.length;i++){            int temp = -1;            for(int j=i-1;j>=0;j--){                if(nums[j]<nums[i]){                    temp = Math.max(temp, dp[j]);                }            }            if(temp != -1){                dp[i] += temp;            }            max = Math.max(max, dp[i]);        }        return max;    }