Longest sub-sequence with non-negative sum
source link: https://www.geeksforgeeks.org/longest-sub-sequence-with-non-negative-sum/
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- Last Updated : 06 Nov, 2019
Given an array arr[] of length N, the task is to find the length of the largest sub-sequence with non-negative sum.
Examples:
Input: arr[] = {1, 2, -3}
Output: 3
The complete array has a non-negative sum.Input: arr[] = {1, 2, -4}
Output: 2
{1, 2} is the required subsequence.
Approach: The idea is that all the non-negative numbers must be included in the sub-sequence because such numbers will only increase the value of the total sum.
Now, it’s not hard to see among negative numbers, the larger ones must be chosen first. So, keep adding the negative numbers in non-increasing order of there values as long as they don’t decrease the value of the total sum below 0. This can be done after sorting the array.
Below is the implementation of the above approach:
- Python3
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// C++ implementation of the approach #include <bits/stdc++.h> using namespace std; // Function to return the length of // the largest subsequence // with non-negative sum int maxLen(int* arr, int n) { // To store the current sum int c_sum = 0; // Sort the input array in // non-increasing order sort(arr, arr + n, greater<int>()); // Traverse through the array for (int i = 0; i < n; i++) { // Add the current element to the sum c_sum += arr[i]; // Condition when c_sum falls // below zero if (c_sum < 0) return i; } // Complete array has a non-negative sum return n; } // Driver code int main() { int arr[] = { 3, 5, -6 }; int n = sizeof(arr) / sizeof(int); cout << maxLen(arr, n); return 0; } 3
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