# Longest sub-sequence with non-negative sum

• Last Updated : 24 Aug, 2022

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:
The complete array has a non-negative sum.
Input: arr[] = {1, 2, -4}
Output:
{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 their 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:

## C++

 `// C++ implementation of the approach` `#include ` `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;` `}`

## Java

 `// Java implementation of the approach` `import` `java.util.*;`   `class` `GFG ` `{`   `// Function to return the length of` `// the largest subsequence` `// with non-negative sum` `static` `int` `maxLen(``int``[] arr, ``int` `n)` `{` `    ``// To store the current sum` `    ``int` `c_sum = ``0``;`   `    ``// Sort the input array in` `    ``// non-increasing order` `    ``Arrays.sort(arr);`   `    ``// Traverse through the array` `    ``for` `(``int` `i = n-``1``; i >=``0``; 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` `public` `static` `void` `main(String []args)` `{` `    ``int` `arr[] = { ``3``, ``5``, -``6` `};` `    ``int` `n = arr.length;`   `    ``System.out.println(maxLen(arr, n));` `}` `}`   `// This code is contributed by Rajput-Ji`

## Python3

 `# Python3 implementation of the approach `   `# Function to return the length of ` `# the largest subsequence ` `# with non-negative sum ` `def` `maxLen(arr, n) : `   `    ``# To store the current sum ` `    ``c_sum ``=` `0``; `   `    ``# Sort the input array in ` `    ``# non-increasing order ` `    ``arr.sort(reverse ``=` `True``); `   `    ``# Traverse through the array ` `    ``for` `i ``in` `range``(n) :`   `        ``# 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 ` `if` `__name__ ``=``=` `"__main__"` `: `   `    ``arr ``=` `[ ``3``, ``5``, ``-``6` `]; ` `    ``n ``=` `len``(arr); `   `    ``print``(maxLen(arr, n)); `   `# This code is contributed by AnkitRai01`

## C#

 `// C# implementation of the approach` `using` `System; `   `class` `GFG ` `{`   `// Function to return the length of` `// the largest subsequence` `// with non-negative sum` `static` `int` `maxLen(``int``[] arr, ``int` `n)` `{` `    ``// To store the current sum` `    ``int` `c_sum = 0;`   `    ``// Sort the input array in` `    ``// non-increasing order` `    ``Array.Sort(arr);`   `    ``// Traverse through the array` `    ``for` `(``int` `i = n - 1; i >= 0; 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` `public` `static` `void` `Main(String []args)` `{` `    ``int` `[]arr = { 3, 5, -6 };` `    ``int` `n = arr.Length;`   `    ``Console.WriteLine(maxLen(arr, n));` `}` `}`   `// This code is contributed by PrinciRaj1992`

## Javascript

 ``

Output:

`3`

Time Complexity: O(n*log(n))
Auxiliary Space: O(1)

My Personal Notes arrow_drop_up
Recommended Articles
Page :