Q8 Longest Increasing Subsequence - LeetCode 300

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Thu Mar 02 2023 08:00:48 GMT+0000 (Coordinated Universal Time)

Saved by @Ayush_dabas07

class Solution {
    public int lengthOfLIS(int[] nums) {
        /* 1D array
        storage- every cell denotes LIS till that cell ,mandatory that LIS ends at 
        that cell

        moving fromt left to right(small problem to large problem)
        */

        int n = nums.length;

        //base case
        if(n == 1)return 1;
        int dp[] = new int[n];
        dp[0] = 1;  //LIS for 1 length will be of length 1 
        
        int ans = 1 ;
        for(int i = 1 ; i < n ; i++){

/*finding max LIS in previous elements in dp and also ensuring that current element
is greater than last element of previous LIS , as we have already assigned storage 
ensuring that LIS will end at that element so we already know that last element will 
be previous element only  */


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

            ans = Math.max(ans , dp[i]);
        }        
        return ans;
/*we are returning ans and not dp[n-1] as dp[n-1] will just store LIS which the and 
will end at arr[n-1] but we need maximum length so we will store max as we traverse 
put in values in dp */

    }
}

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

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