PROBLEM DESCRIPTION
Given an array of n positive integers. Find the sum of the maximum sum subsequence of the given array such that the integers in the subsequence are sorted in strictly increasing order i.e. a strictly increasing subsequence.
SOLUTION
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class Solution
{
// Method to find the maximum sum of an increasing subsequence
public int maxSumIS(int arr[], int n)
{
int maxSum = 0;
// dp[i] represents the maximum sum of an increasing subsequence ending with arr[i]
int[] dp = new int[n];
// dp[i] will be at least equal to that element itself
for(int i = 0; i < n; i++)
dp[i] = arr[i];
// Initialize maxSum with the first element of dp
maxSum = dp[0];
// Loop over the array to find the maximum sum increasing subsequence
for(int i = 1; i < n; i++){
// Check all previous elements to find subsequences that can be extended by arr[i]
for(int j = 0; j < i; j++){
// If arr[i] is greater than arr[j], we can extend the subsequence ending at j
if(arr[i] > arr[j]){
// Update dp[i] to reflect the maximum possible sum ending at arr[i]
dp[i] = Math.max(dp[i], dp[j] + arr[i]);
}
}
// Update maxSum with the maximum value found so far
maxSum = Math.max(maxSum, dp[i]);
}
return maxSum;
}
}