Max Sum Increasing Subsequence

JavaView on GFG

Time: O(n^2)

Space: O(n)

Intuition

Find maximum sum of increasing subsequence. LIS-style DP on sums.

Algorithm

1dp[i] = max sum of increasing subsequence ending at i.
2dp[i] = max(dp[j] + nums[i]) for all j < i where nums[j] < nums[i]. Base: dp[i] = nums[i].

Common Pitfalls

•Track sum, not length. O(n^2) DP. Answer = max(dp[]).

Max Sum Increasing Subsequence.java

Java

// Approach: DP similar to LIS but maximize sum. dp[i] = max sum of increasing subsequence ending at i.
// Time: O(n^2) Space: O(n)
class Solution {
    public int maxSumIS(int arr[]) {
        int n = arr.length;
        int[] dp = new int[n];
        for (int i = 0; i < n; i++)
            dp[i] = arr[i];

        int ans = arr[0];
        for (int i = 1; i < n; i++) {
            for (int j = 0; j < i; j++) {
                if (arr[j] < arr[i])
                    dp[i] = Math.max(dp[i], dp[j] + arr[i]);
            }
            ans = Math.max(ans, dp[i]);
        }
        
        return ans;
    }
}

Was this solution helpful?