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Maximum Sum Decreasing Subsequence in C++
In this problem, we are given an array arr[] of N integers. Our task is to find the Maximum Sum Decreasing Subsequence in C++.
Problem Description
We will find the maximum sum of elements from the array such that the subsequence is strictly decreasing.
Let’s take an example to understand the problem,
Input
arr[] = {3, 1, 6, 10, 5, 2, 9}
Output
17
Explanation
Decreasing subsequence with max sum is {10, 5, 2} = 10 + 5 + 2 = 17
Solution Approach
Here, we will use the dynamic programming approach to find the solution. Here, we will create a maxSum[] array which will store the maxSum till the index i. The follow formula is employed to find array values,
maxSum[i] = arr[i] + max(maxSum[0 … (*i-1)])
The maximum sum is given by the maximum element of the array maxSum[].
Example
Program to illustrate the working of our solution,
#include <iostream> using namespace std; int findMaxSumDecSubSeq(int arr[], int N){ int maximumSum = 0; int maxSum[N]; for (int i = 0; i < N; i++) maxSum[i] = arr[i]; for (int i = 1; i < N; i++) for (int j = 0; j < i; j++) if (arr[i] < arr[j] && maxSum[i] < maxSum[j] + arr[i]) maxSum[i] = maxSum[j] + arr[i]; for (int i = 0; i < N; i++) if (maximumSum < maxSum[i]) maximumSum = maxSum[i]; return maximumSum; } int main(){ int arr[] = { 5, 4, 100, 3, 2, 101, 1 }; int N= sizeof(arr) / sizeof(arr[0]); cout<<"The maximum sum of decreasing subsequence is "<<findMaxSumDecSubSeq(arr, N); return 0; }
Output
The maximum sum of decreasing subsequence is 106
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