Check the divisibility of Hexadecimal numbers

Given a string S consisting of a large hexadecimal number, the task is to check its divisibility by a given decimal number M. If divisible then print Yes else print No.

Examples:

Input: S = “10”, M = 4
Output: Yes
10 is 16 in decimal and (16 % 4) = 0



Input: S = “10”, M = 5
Output: No

Approach: An approach used in this article will be used to avoid overflow. Iterate the entire string from the back-side.
If the remainder of the sub-string S[0…i] is known on division with M. Let’s call this remainder as R. This can be used to get the remainder when the substring S[0…i+1] is divided. To do that, first left shift the string S[0…i] by 1. This will be equivalent to multiplying the string by 16. Then, add S[i+1] to this and take its mod with M. With a little bit of modular arithmetic it boils down to

S[0…i+1] % M = (S[0…i] * 16 + S[i+1]) % M = ((S[0…i] % M * 16) + S[i+1]) % M

Thus, continue the above steps till the end of the string. If the final remainder is 0 then the string is divisible otherwise it is not.

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
const string CHARS = "0123456789ABCDEF";
const int DIGITS = 16;
  
// Function that returns true
// if s is divisible by m
bool isDivisible(string s, int m)
{
    // Map to map characters to real values
    unordered_map<char, int> mp;
  
    for (int i = 0; i < DIGITS; i++) {
        mp[CHARS[i]] = i;
    }
  
    // To store the remainder at any stage
    int r = 0;
  
    // Find the remainder
    for (int i = 0; i < s.size(); i++) {
        r = (r * 16 + mp[s[i]]) % m;
    }
  
    // Check the value of remainder
    if (!r)
        return true;
    return false;
}
  
// Driver code
int main()
{
    string s = "10";
    int m = 3;
  
    if (isDivisible(s, m))
        cout << "Yes";
    else
        cout << "No";
  
    return 0;
}

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Java

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// Java implementation of the approach
import java.util.*;
  
class GFG 
{
  
static char []CHARS = "0123456789ABCDEF".toCharArray();
static int DIGITS = 16;
  
// Function that returns true
// if s is divisible by m
static boolean isDivisible(String s, int m)
{
    // Map to map characters to real values
    Map<Character, Integer> mp = new HashMap<>();
  
    for (int i = 0; i < DIGITS; i++)
    {         
        mp. put(CHARS[i], i);
    }
  
    // To store the remainder at any stage
    int r = 0;
  
    // Find the remainder
    for (int i = 0; i < s.length(); i++) 
    {
        r = (r * 16 + mp.get(s.charAt(i))) % m;
    }
  
    // Check the value of remainder
    if (r == 0)
        return true;
    return false;
}
  
// Driver code
public static void main(String []args) 
{
    String s = "10";
    int m = 3;
  
    if (isDivisible(s, m))
        System.out.println("Yes");
    else
        System.out.println("No");
}
}
  
// This code is contributed by 29AjayKumar

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Python3

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# Python3 implementation of the approach
CHARS = "0123456789ABCDEF"
DIGITS = 16
  
# Function that returns true 
# if s is divisible by m 
def isDivisible(s, m) :
  
    # Map to map characters to real value
    mp = dict.fromkeys(CHARS, 0); 
  
    for i in range( DIGITS) :
        mp[CHARS[i]] = i; 
  
    # To store the remainder at any stage 
    r = 0
  
    # Find the remainder 
    for i in range(len(s)) :
        r = (r * 16 + mp[s[i]]) % m; 
  
    # Check the value of remainder 
    if (not r) :
        return True
          
    return False
  
# Driver code 
if __name__ == "__main__"
      
    s = "10"
    m = 3
  
    if (isDivisible(s, m)) :
        print("Yes"); 
    else :
        print("No"); 
  
# This code is contributed by AnkitRai01

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C#

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// C# implementation of the approach
using System;
using System.Collections.Generic;
  
class GFG
{
  
static char []CHARS = "0123456789ABCDEF".ToCharArray();
static int DIGITS = 16;
  
// Function that returns true
// if s is divisible by m
static bool isDivisible(String s, int m)
{
    // Map to map characters to real values
    Dictionary<char, int> mp = new Dictionary<char, int>();
  
    for (int i = 0; i < DIGITS; i++)
    {        
        if(mp.ContainsKey(CHARS[i]))
            mp[CHARS[i]] = i;
        else
            mp.Add(CHARS[i], i);
    }
  
    // To store the remainder at any stage
    int r = 0;
  
    // Find the remainder
    for (int i = 0; i < s.Length; i++) 
    {
        r = (r * 16 + mp[s[i]]) % m;
    }
  
    // Check the value of remainder
    if (r == 0)
        return true;
    return false;
}
  
// Driver code
public static void Main(String []args) 
{
    String s = "10";
    int m = 3;
  
    if (isDivisible(s, m))
        Console.WriteLine("Yes");
    else
        Console.WriteLine("No");
}
}
  
// This code is contributed by 29AjayKumar

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Output:

No


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Improved By : AnkitRai01, 29AjayKumar