300. Longest Increasing Subsequence

Medium

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?

Solutin：

1 initial a n length array dp(n). dp(i) means the length of LIS which ends at index i such that the last element of LIS is arr[i].

2 initail 1 for all indexs in dp.

3 dp[i] = dp[j] + 1 if dp[i] > dp[j] and i > j > 0;

4 to find the length of LIS, we should the max value of dp[i] (0<i<n).

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

related issue:

673. Number of Longest Increasing Subsequence

https://leetcode.com/problems/number-of-longest-increasing-subsequence/

Building Brige

https://www.geeksforgeeks.org/dynamic-programming-building-bridges/