[leetcode]300. Longest Increasing Subsequence最长递增子序列

Given an unsorted array of integers, find the length of longest increasing subsequence.

Example:

Input: [10,9,2,5,3,7,101,18]
Output: 4 
Explanation: The longest increasing subsequence is [2,3,7,101], therefore the length is 4. 

Note:

• There may be more than one LIS combination, it is only necessary for you to return the length.
• Your algorithm should run in O(n2) complexity.

Follow up: Could you improve it to O(n log n) time complexity?

Solution: DP

dp[i] stands for the length of LIS ends with nums[i] (nums[i] must be used)

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code

class Solution {
    public int lengthOfLIS(int[] nums) {
        if(nums.length < 2)   return nums.length;
        
        int result = 1;
        int[] dp = new int[nums.length];
      
        for(int i = 0; i < nums.length; i++){
            dp[i] = 1;
        }
        
        for(int i = 1; i< nums.length; i++){
            for(int j = 0; j < i; j++){
                if(nums[j] < nums[i]){
                    dp[i] = Math.max(dp[i], dp[j]+1);
                } 
            }
            result = Math.max(result, dp[i]);     
        }
        return result;
    }
}