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Longest sub-sequence with non-negative sum

  • Last Updated : 12 May, 2021

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 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: 
 

C++




// 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;
}

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




<script>
 
// Javascript implementation of the approach
 
// Function to return the length of
// the largest subsequence
// with non-negative sum
function maxLen(arr, n)
{
    // To store the current sum
    var c_sum = 0;
 
    // Sort the input array in
    // non-increasing order
    arr.sort((a,b)=> b-a)
 
    // Traverse through the array
    for (var 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
var arr = [3, 5, -6];
var n = arr.length;
document.write( maxLen(arr, n));
 
</script>
Output: 
3

 

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