Given an integer N, the task is to make an array of unique elements of length N such that all subarrays sum modulo N equals to zero.
Examples:
Input: N = 6
Output: 6 12 18 24 30 36
Explanation:
Since all elements are a multiple of 6. Hence all subarrays add up to a sum divisible by 6.
Input: N = 4
Output: 4 8 12 16
Approach:
We can observe that for all subarrays to be divisible by N, the elements of the array need to be a multiple of N.
Illustration:
For N = 4, if we consider the array elements to {4, 8, 12, 16}, All possible subarrays are:
{4}, {8}, {12}, {16}, {4, 8}, {8, 12}, {12, 16}, {4, 8, 12}, {8, 12, 16}, {4, 8, 12, 16}
Hence, all subarrays have a sum divisible by N.
Hence, to solve the problem, we just need to print {N, 2*N, 3*N, ….., N*N} to get the desired array.
Below is the implementation of the above approach:
C++
// C++ implementation of the// above approach#include <bits/stdc++.h>using namespace std;// Function to print the required// arrayvoid makeArray(int a[], int n){ // Print the array for (int i = 1; i <= n; i++) cout << i * n << " ";}// Driver Programint main(){ int N = 6; int arr[N]; makeArray(arr, N);} |
Java
// Java program for the above approachclass GFG{ // Function to print the required// arraystatic void makeArray(int a[], int n){ // Print the array for(int i = 1; i <= n; i++) System.out.print(i * n + " ");}// Driver code public static void main(String[] args) { int N = 6; int arr[] = new int[N]; makeArray(arr, N);} } // This code is contributed by Pratima Pandey |
Python3
# Python3 implementation of the# above approach# Function to print the # required arraydef makeArray(n): # Print Array for i in range(n): print((i + 1) * n, end =" ")# Driver coden = 6;makeArray(n); |
C#
// C# program for the above approachusing System;class GFG{ // Function to print the required// arraystatic void makeArray(int []a, int n){ // Print the array for(int i = 1; i <= n; i++) Console.Write(i * n + " ");}// Driver code public static void Main() { int N = 6; int []arr = new int[N]; makeArray(arr, N);} } // This code is contributed by Code_Mech |
Javascript
<script> // javascript program for the above approach // Function to print the required// arrayfunction makeArray(n){ // Print the array for(var i = 1; i <= n; i++) document.write(i * n + " ");} // Driver code var N = 6; makeArray(N); </script> |
6 12 18 24 30 36
Time Complexity: O(N)
Auxiliary Space: O(1)
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