Given two integers N and K, the task is to represent N as the sum of K even number. If it is not possible to represent the number, print -1.
Note: The representation may contain duplicate even numbers.
Examples:
Input: N = 6, K = 3
Output: 2 2 2
Explanation:
The given number 6 can be represented as 2 + 2 + 2 = 6
Input: N = 8, K = 2
Output: 2 6
Explanation:
The given number 3 can be represented as 2 + 6 = 8
Approach: To solve the problem mentioned above a simple solution is to maximize the occurrence of 2 which is the smallest even number. The necessary condition to represent N as the sum of K numbers are:
- (K – 1) * 2 must be less than N.
- N – (K – 1) * 2 must be Even.
Below is the implementation of the above approach:
C++
// C++ implementation to represent// N as sum of K even numbers#include <bits/stdc++.h>using namespace std;// Function to print the representationvoid sumEvenNumbers(int N, int K){ int check = N - 2 * (K - 1); // N must be greater than equal to 2*K // and must be even if (check > 0 && check % 2 == 0) { for (int i = 0; i < K - 1; i++) { cout << "2 "; } cout << check; } else { cout << "-1"; }}// Driver Codeint main(){ int N = 8; int K = 2; sumEvenNumbers(N, K); return 0;} |
Java
// Java implementation to represent// N as sum of K even numbersimport java.util.*;class GFG{ // Function to print the representationstatic void sumEvenNumbers(int N, int K){ int check = N - 2 * (K - 1); // N must be greater than equal to 2 * K // and must be even if (check > 0 && check % 2 == 0) { for(int i = 0; i < K - 1; i++) { System.out.print("2 "); } System.out.println(check); } else { System.out.println("-1"); }}// Driver Codepublic static void main(String args[]){ int N = 8; int K = 2; sumEvenNumbers(N, K);}}// This code is contributed by ANKITKUMAR34 |
Python3
# Python3 implementation to represent# N as sum of K even numbers# Function to print the representationdef sumEvenNumbers(N, K): check = N - 2 * (K - 1) # N must be greater than equal to 2 * K # and must be even if (check > 0 and check % 2 == 0): for i in range(K - 1): print("2 ", end = "") print(check) else: print("-1")# Driver CodeN = 8K = 2sumEvenNumbers(N, K)# This code is contributed by ANKITKUMAR34 |
C#
// C# implementation to represent// N as sum of K even numbersusing System;class GFG{ // Function to print the representationstatic void sumEvenNumbers(int N, int K){ int check = N - 2 * (K - 1); // N must be greater than equal to // 2 * K and must be even if (check > 0 && check % 2 == 0) { for(int i = 0; i < K - 1; i++) { Console.Write("2 "); } Console.WriteLine(check); } else { Console.WriteLine("-1"); }}// Driver Codestatic public void Main(String []args){ int N = 8; int K = 2; sumEvenNumbers(N, K);}}// This code is contributed by 29AjayKumar |
Javascript
<script>// Javascript implementation to represent// N as sum of K even numbers // Function to print the representationfunction sumEvenNumbers(N, K){ let check = N - 2 * (K - 1); // N must be greater than equal to 2 * K // and must be even if (check > 0 && check % 2 == 0) { for(let i = 0; i < K - 1; i++) { document.write("2 "); } document.write(check); } else { document.write("-1"); }}// Driver Code let N = 8; let K = 2; sumEvenNumbers(N, K); </script> |
Output:
2 6
Time Complexity: O(K)
Auxiliary Space: O(1)
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