Given a positive integer N, the task is to find the smallest multiple of N with exactly N digits in its binary number representation.
Example:
Input: N = 3
Output: 6
Explanation:
6 is the smallest multiple of 3 and has length also 3(110) in binary.
Input: N = 5
Output: 20
Explanation:
6 is the smallest multiple of 5 and has length also 5(10100) in binary.
Approach: The idea is to make an observation.
- If we observe carefully a series will be formed as 1, 2, 6, 8, 20, …
- The N-th term in the series would be:
- Therefore, the number N is taken as the input and the above formula is implemented.
Below is the implementation of the above approach:
C++
// C++ program to find smallest// multiple of n with exactly N// digits in Binary number System.#include <iostream>#include <math.h>using namespace std;// Function to find smallest multiple// of n with exactly n digits// in Binary number representation.void smallestNumber(int N){ cout << N * ceil(pow(2, (N - 1)) / N);}// Driver codeint main(){ int N = 3; smallestNumber(N); return 0;} |
Java
// Java program to find smallest // multiple of n with exactly N // digits in Binary Number System. class GFG{ // Function to find smallest // multiple of n with exactly N // digits in Binary Number System. static void smallestNumber(int N) { System.out.print(N * Math.ceil (Math.pow(2, (N - 1)) / N)); } // Driver code public static void main(String[] args) { int N = 3; smallestNumber(N);} } // This code is contributed by shubham |
Python3
# Python3 program to find smallest# multiple of n with exactly N# digits in Binary number System.from math import ceil# Function to find smallest multiple# of n with exactly n digits# in Binary number representation.def smallestNumber(N): print(N * ceil(pow(2, (N - 1)) / N))# Driver codeN = 3smallestNumber(N)# This code is contributed by Mohit Kumar |
C#
// C# program to find smallest // multiple of n with exactly N // digits in Binary Number System.using System;class GFG{ // Function to find smallest // multiple of n with exactly N // digits in Binary Number System. static void smallestNumber(int N) { Console.Write(N * Math.Ceiling( Math.Pow(2, (N - 1)) / N)); } // Driver code public static void Main(string[] args) { int N = 3; smallestNumber(N);} } // This code is contributed by AnkitRai01 |
Javascript
<script>// Javascript program to find smallest// multiple of n with exactly N// digits in Binary number System.// Function to find smallest multiple// of n with exactly n digits// in Binary number representation.function smallestNumber(N){ document.write(N * parseInt(Math.ceil(Math.pow(2, (N - 1)) / N)));}// Driver codelet N = 3;smallestNumber(N);// This code is contributed by rishavmahato348.</script> |
Output:
6
Time Complexity: O(n)
Auxiliary Space: O(1)
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