Multiple of x closest to n

Given two numbers n and x, we need to calculate the smallest value of x that is closest to given number n.

Examples:

Input : n = 9, x = 4
Output : 8

Input  : n = 2855, x = 13
Output : 2860

Input  :  n = 46426171, x = 43
Output :  46426154

Input  :  n = 1, x = 3
Output :  3



We need to find a k such that x*k is closest to n. If we do k = n/x, we get a value of k that may not lead to maximum. We can get closest by comparing the values floor(n/x) * x and ceil(n/x) * x.

Below is an interesting solution that doesn’t require computations of floor(n/x) and ceil(n/x). The idea is to do following two steps.

    n = n + x/2;
    n = n - (n%x);
    result = n

Let us consider below example

  n = 2855 
  x = 13

  n = 2855 + 13/2
    = 2861
  n = 2861 - (2861 % 13)
    = 2861 - 1
    = 2860 

Below are implementations of above steps.

C++

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// CPP program to calculate the smallest multiple
// of x closest to a given number
#include <bits/stdc++.h>
using namespace std;
  
// Function to calculate the smallest multiple
int closestMultiple(int n, int x)
{   
    if(x>n)
       return x;
  
    n = n + x/2;
    n = n - (n%x);
    return n;
}
  
// driver program
int main()
{
    int n = 9, x = 4;
    printf("%d", closestMultiple(n, x));
    return 0;
}

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Java

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// Java program to calculate the smallest 
// multiple of x closest to a given number
import java.io.*;
class Solution
{
    // Function to calculate the smallest multiple
    static int closestMultiple(int n, int x)
    {   
        if(x>n)
           return x;
        n = n + x/2;
        n = n - (n%x);
        return n;
    }
  
    // driver program
    public static void main (String[] args) 
    {
        int n = 56287, x = 27;
        System.out.println(closestMultiple(n, x));
    }
}

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Python3

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# Python3 program to calculate 
# the smallest multiple of x 
# closest to a given number
  
# Function to calculate
# the smallest multiple
def closestMultiple(n, x):
    if x > n:
        return x;
    z = (int)(x / 2);
    n = n + z;
    n = n - (n % x);
    return n;
  
# Driver Code
n = 56287;
x = 27;
print(closestMultiple(n, x));
  
# This code is contributed
# by mits

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C#

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// C# program to calculate smallest
// multiple of x closest to a
// given number
using System;
  
class Solution {
    // Function to calculate the
    // smallest multiple
    static int closestMultiple(int n, int x)
    {
  
        if (x > n)
            return x;
        n = n + x / 2;
        n = n - (n % x);
        return n;
    }
  
    // Driver program
    public static void Main()
    {
        int n = 56287, x = 27;
        Console.WriteLine(closestMultiple(n, x));
    }
}
  
// This code is contributed by Anant Agarwal.

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PHP

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<?php
// PHP program to calculate 
// the smallest multiple
// of x closest to a 
// given number
  
// Function to calculate 
// the smallest multiple
function closestMultiple($n, $x)
    if($x > $n)
    return $x;
  
    $n = $n + $x / 2;
    $n = $n - ($n % $x);
    return $n;
}
  
    // Driver Code
    $n = 9;
    $x = 4;
    echo closestMultiple($n, $x);
      
// This code is contributed by ajit
?>

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Output:

 56295

This article is contributed by Pramod Kumar. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



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Improved By : jit_t, Mithun Kumar