DP-Longest Increasing Subsequence

Question 1

300. Longest Increasing Subsequence

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.

TS - N square
SC - N

Answer 1

Pseudo Code:-
1. Define LIS array as same length of input array and initialize it with 1 because each number makes at least LIS of length 1.
2. Run outer loop 0 to n-1 with index i
3. Run inner loop 0 to i-1
4 check if (nums[i] > nums[j]) then
LIS[i] = Math.max(LIS[i], 1 + LIS[j]);

Code:-

class Solution {
    public int lengthOfLIS(int[] nums) {
        int n = nums.length;
        int[] LIS=new int[n];
       for (int i = 0; i < n; i++) {
			LIS[i] = 1;
		}

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

	int ans = 0;
	for (int i = 0; i < n; i++) {
		ans = Math.max(ans, LIS[i]);
	}

	return ans;
}

}