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Find N distinct integers with zero sum

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  • Difficulty Level : Basic
  • Last Updated : 28 May, 2022

Given an integer N, our task is to print N distinct numbers such that their sum is 0.
Examples:
 

Input: N = 3 
Output: 1, -1, 0 
Explanation: 
On adding the numbers that is 1 + (-1) + 0 the sum is 0.
Input: N = 4 
Output: 1, -1, 2, -2 
Explanation: 
On adding the numbers that is 1 + (-1) + 2 + (-2) the sum is 0. 
 

 

Approach: To solve the problem mentioned above the main idea is to print Symmetric Pairs like (+x, -x) so that the sum will always be 0. The edge case to the problem is to observe that if integer N is odd, then print one 0 along with the numbers so that sum is not affected.
Below is the implementation of the above approach: 
 

C++




// C++ implementation to Print N distinct
// numbers such that their sum is 0
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to print distinct n
// numbers such that their sum is 0
void findNumbers(int N)
{
    for (int i = 1; i <= N / 2; i++) {
 
        // Print 2 symmetric numbers
        cout << i << ", " << -i << ", ";
    }
 
    // print a extra 0 if N is odd
    if (N % 2 == 1)
        cout << 0;
}
 
// Driver code
int main()
{
    int N = 10;
 
    findNumbers(N);
}

Java




// Java implementation to Print N distinct
// numbers such that their sum is 0
 
class GFG{
 
// Function to print distinct n
// numbers such that their sum is 0
static void findNumbers(int N)
{
    for (int i = 1; i <= N / 2; i++)
    {
        // Print 2 symmetric numbers
        System.out.print(i + ", " + -i + ", ");
    }
 
    // Print a extra 0 if N is odd
    if (N % 2 == 1)
        System.out.print(0);
}
 
// Driver code
public static void main(String[] args)
{
    int N = 10;
    findNumbers(N);
}
}
 
// This code is contributed by 29AjayKumar

Python3




# Python3 implementation to print N distinct
# numbers such that their sum is 0
 
# Function to print distinct n
# numbers such that their sum is 0
def findNumbers(N):
     
    for i in range(1, N // 2 + 1):
         
        # Print 2 symmetric numbers
        print(i, end = ', ')
        print(-i, end = ', ')
         
    # Print a extra 0 if N is odd
    if N % 2 == 1:
        print(0, end = '')
     
# Driver code
if __name__=='__main__':
     
    N = 10
    findNumbers(N)
 
# This code is contributed by rutvik_56

C#




// C# implementation to print N distinct
// numbers such that their sum is 0
using System;
 
class GFG {
 
// Function to print distinct n
// numbers such that their sum is 0
static void findNumbers(int N)
{
    for(int i = 1; i <= (N / 2); i++)
    {
 
       // Print 2 symmetric numbers
       Console.Write(i + ", " + -i + ", ");
    }
     
    // Print a extra 0 if N is odd
    if (N % 2 == 1)
        Console.Write(0);
}
 
// Driver code
static void Main()
{
    int N = 10;
     
    findNumbers(N);
}
}
 
// This code is contributed by divyeshrabadiya07   

Javascript




<script>
 
// Javascript implementation to Print N distinct
// numbers such that their sum is 0
 
// Function to print distinct n
// numbers such that their sum is 0
function findNumbers(N)
{
    for (var i = 1; i <= N / 2; i++) {
 
        // Print 2 symmetric numbers
        document.write( i + ", " + -i + ", ");
    }
 
    // print a extra 0 if N is odd
    if (N % 2 == 1)
        document.write( 0);
}
 
// Driver code
var N = 10;
findNumbers(N);
 
</script>

Output: 

1, -1, 2, -2, 3, -3, 4, -4, 5, -5,

 

Time Complexity: O(N)

Auxiliary Space: O(1)
 


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