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Find any K distinct odd integers such that their sum is equal to N

  • Last Updated : 08 Apr, 2021

Given two integers N and K, the task is to find any K distinct odd integers such that their sum is equal to N. If no such integers exists, print -1.
Examples: 
 

Input: N = 10, K = 2 
Output: 1, 9 
Explanation: 
There are two possible distinct odd integers, such that their sum is equal to N. 
Possible K integers can be – {(1, 9), (3, 7)}
Input: N = 5, K = 4 
Output: -1 
Explanation: 
There are no such 4 distinct odd integers such that their sum is 5. 
 

 

Approach: 
 

  • The key observation in this problem is if N and K have different parity then it is not possible to find K such distinct integers such that their sum is equal to N,
  • Otherwise such K – 1 integers will consist of first K-1 odd positive integers
  • The Kth odd number will be equal to (N – the sum of first (K-1) odd integers) 
     
Kth Odd number  = N - sum of first K-1 integer
  •  

Below is the implementation of the above approach:
 



C++




// C++ implementation to find k
// odd integers such that their sum is N
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find K odd integers
// such that their sum is N
void oddIntegers(int n, int k)
{
    // Condition to check if there
    // exist such K integers
    if (n % 2 != k % 2) {
        cout << "-1"
             << "\n";
        return;
    }
 
    int sum = 0;
    int i = 1;
    int j = 1;
 
    // Loop to find first K-1
    // distinct odd integers
    while (j < k) {
        sum = sum + i;
        cout << i << " ";
        i = i + 2;
        j++;
    }
 
    // Final Kth odd number
    int finalOdd = n - sum;
 
    cout << finalOdd << "\n";
}
 
// Driver code
int main()
{
    int n = 10;
    int k = 2;
 
    oddIntegers(n, k);
 
    return 0;
}

Java




// Java implementation to find k
// odd integers such that their sum is N
class GFG
{
 
// Function to find K odd integers
// such that their sum is N
static void oddIntegers(int n, int k)
{
    // Condition to check if there
    // exist such K integers
    if (n % 2 != k % 2) {
        System.out.println("-1");
        return;
    }
 
    int sum = 0;
    int i = 1;
    int j = 1;
 
    // Loop to find first K-1
    // distinct odd integers
    while (j < k) {
        sum = sum + i;
        System.out.print(i+" ");
        i = i + 2;
        j++;
    }
 
    // Final Kth odd number
    int finalOdd = n - sum;
     
    System.out.println(finalOdd);
}
 
// Driver code
public static void main (String[] args)
{
    int n = 10;
    int k = 2;
 
    oddIntegers(n, k);
}
}
 
// This code is contributed by shubhamsingh

Python3




# Python3 implementation to find k
# odd integers such that their sum is N
 
# Function to find K odd integers
# such that their sum is N
def oddIntegers(n, k) :
 
    # Condition to check if there
    # exist such K integers
    if (n % 2 != k % 2) :
        print("-1");
         
        return;
 
    sum = 0;
    i = 1;
    j = 1;
 
    # Loop to find first K-1
    # distinct odd integers
    while (j < k) :
        sum += i;
        print(i,end= " ");
        i += 2;
        j += 1;
 
    # Final Kth odd number
    finalOdd = n - sum;
 
    print(finalOdd);
 
# Driver code
if __name__ == "__main__" :
 
    n = 10;
    k = 2;
 
    oddIntegers(n, k);
     
# This code is contributed by AnkitRai01

C#




// C# implementation to find k
// odd integers such that their sum is N
using System;
 
class GFG
{
  
// Function to find K odd integers
// such that their sum is N
static void oddints(int n, int k)
{
    // Condition to check if there
    // exist such K integers
    if (n % 2 != k % 2) {
        Console.WriteLine("-1");
        return;
    }
  
    int sum = 0;
    int i = 1;
    int j = 1;
  
    // Loop to find first K-1
    // distinct odd integers
    while (j < k) {
        sum = sum + i;
        Console.Write(i+" ");
        i = i + 2;
        j++;
    }
  
    // Final Kth odd number
    int finalOdd = n - sum;
      
    Console.WriteLine(finalOdd);
}
  
// Driver code
public static void Main(String[] args)
{
    int n = 10;
    int k = 2;
  
    oddints(n, k);
}
}
 
// This code is contributed by PrinciRaj1992

Javascript




<script>
 
// JavaScript implementation to find k
// odd integers such that their sum is N   
 
// Function to find K odd integers
// such that their sum is N
    function oddIntegers(n , k)
    {
        // Condition to check if there
        // exist such K integers
        if (n % 2 != k % 2) {
            document.write("-1");
            return;
        }
 
        var sum = 0;
        var i = 1;
        var j = 1;
 
        // Loop to find first K-1
        // distinct odd integers
        while (j < k) {
            sum = sum + i;
            document.write(i + " ");
            i = i + 2;
            j++;
        }
 
        // Final Kth odd number
        var finalOdd = n - sum;
 
        document.write(finalOdd);
    }
 
    // Driver code
     
        var n = 10;
        var k = 2;
 
        oddIntegers(n, k);
 
// This code contributed by Rajput-Ji
 
</script>
Output: 
1 9

 

Performance Analysis: 
 

  • Time Complexity: As in the above approach, There is a loop to find such K odd integers which takes O(K) time in worst case. Hence the Time Complexity will be O(K).
  • Auxiliary Space Complexity: As in the above approach, There is no extra space used. Hence the auxiliary space complexity will be O(1).

 

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