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++

// 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;
}

Java

// 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

Python3

# 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

C#

// 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

Javascript

<script>

// Javascript implementation of the approach

var CHARS = "0123456789ABCDEF";
var DIGITS = 16;

// Function that returns true
// if s is divisible by m
function isDivisible(s, m)
{
    // Map to map characters to real values
    var mp = new Map();

    for (var i = 0; i < DIGITS; i++) {
        mp.set(CHARS[i], i);
    }

    // To store the remainder at any stage
    var r = 0;

    // Find the remainder
    for (var i = 0; i < s.length; i++) {
        r = (r * 16 + mp.get(s[i])) % m;
    }

    // Check the value of remainder
    if (!r)
        return true;
    return false;
}

// Driver code
var s = "10";
var m = 3;
if (isDivisible(s, m))
    document.write( "Yes");
else
    document.write( "No");

</script>

Time complexity: O(n)

Auxiliary Space: O(logn)