Multiply two numbers of different base and represent product in another given base

Given two numbers N, M in the bases X, Y and another base P. The task is to find the product of N and M and represent the product in base P.

Examples:

Input: N = 101, M = 110, X = 2, Y = 2, P = 16
Output:1E
Explanation: N_X * M_Y =  (101)₂ * (110)₂  = (11110)₂
(11110)₂ = (1E)₁₆

Input:  N = 101, M = A, X = 2, Y = 20, P = 16
Output:  32
Explanation: N_x = (101)₂ = (5)₂₀ 
N_X  *  M_Y =  (5)₂₀ * (A)₂₀  = (2A)₂₀
(2A)₂₀ = (32)₁₆

Approach: The approach is to convert the given numbers in decimal, perform the product and then turn it back to a number of base p. Follow the steps mentioned below:

1. Convert N_X and M_Y to decimal number.
2. Perform multiplication on the decimal numbers.
3. Convert the result of multiplication from decimal to base P.

Below is the implementation of the above approach. 

C++

// C++ code for the above approach
#include <bits/stdc++.h>
using namespace std;

// Convert Number from a given base
// to decimal
// Return the value of a char.
static int value(char c)
{
  if (c >= '0' && c <= '9')
    return (int)c - '0';
  else
    return (int)c - 'A' + 10;
}

// Function to convert a
// number from given base to decimal
int toDecimal(string s, int base)
{
  int length = s.length();

  // Initialize power of base and result
  int power = 1, ans = 0;

  // Decimal equivalent of s
  for (int i = length - 1; i >= 0; i--)
  {
    ans += value(s[i]) * power;
    power = power * base;
  }

  return ans;
}

// Function to convert decimal
// to any given base
char reverseValue(int n)
{
  if (n >= 0 && n <= 9)
    return (char)(n + 48);
  else
    return (char)(n - 10 + 65);
}

// Function to convert a given
// decimal number to a base 'base'
string toBase(int base, int num)
{
  string s = "";

  // Convert input number is given
  // base by repeatedly dividing it
  // by base and taking remainder
  while (num > 0)
  {
    s += reverseValue(num % base);
    num /= base;
  }
  string sb = "";

  // Append a string into StringBuilder
  sb += (s);

  // Reverse the result
  reverse(sb.begin(), sb.end());
  return sb;
}

// Function to find
// the product of N and M
void findProduct(string N, int X,
                 string M,
                 int Y, int P)
{

  // Convert N to decimal
  int decimalX = toDecimal(N, X);

  // Convert y to decimal
  int decimalY = toDecimal(M, Y);

  // Multiply the decimal numbers
  int product = decimalX * decimalY;

  // Convert product to base
  string result = toBase(P, product);

  // Print the result
  cout << (result);
}

// Driver code
int main()
{
  string N = "101", M = "110";
  int X = 2, Y = 2, P = 16;
  findProduct(N, X, M, Y, P);
  return 0;
}

// This code is contributed by Potta Lokesh

Java

// Java code to implement above approach
import java.io.*;

class GFG {

    // Function to find
    // the product of N and M
    static void findProduct(String N, int X,
                            String M,
                            int Y, int P)
    {

        // Convert N to decimal
        int decimalX = toDecimal(N, X);

        // Convert y to decimal
        int decimalY = toDecimal(M, Y);

        // Multiply the decimal numbers
        int product = decimalX * decimalY;

        // Convert product to base
        String result = toBase(P, product);

        // Print the result
        System.out.println(result);
    }

    // Convert Number from a given base
    // to decimal
    // Return the value of a char.
    static int value(char c)
    {
        if (c >= '0' && c <= '9')
            return (int)c - '0';
        else
            return (int)c - 'A' + 10;
    }

    // Function to convert a
    // number from given base to decimal
    static int toDecimal(String s, int base)
    {
        int length = s.length();

        // Initialize power of base and result
        int power = 1, ans = 0;

        // Decimal equivalent of s
        for (int i = length - 1; i >= 0; i--) {
            ans += value(s.charAt(i)) * power;
            power = power * base;
        }

        return ans;
    }

    // Function to convert decimal
    // to any given base
    static char reverseValue(int n)
    {
        if (n >= 0 && n <= 9)
            return (char)(n + 48);
        else
            return (char)(n - 10 + 65);
    }

    // Function to convert a given
    // decimal number to a base 'base'
    static String toBase(int base, int num)
    {
        String s = "";

        // Convert input number is given
        // base by repeatedly dividing it
        // by base and taking remainder
        while (num > 0) {
            s += reverseValue(num % base);
            num /= base;
        }
        StringBuilder sb = new StringBuilder();

        // Append a string into StringBuilder
        sb.append(s);

        // Reverse the result
        return new String(sb.reverse());
    }

    // Driver code
    public static void main(String[] args)
    {
        String N = "101", M = "110";
        int X = 2, Y = 2, P = 16;
        findProduct(N, X, M, Y, P);
    }
}

Python3

# Python code for the above approach

# Convert Number from a given base
# to decimal
# Return the value of a char.
def value(c):

  if (ord(c[0]) >= ord('0') and ord(c) <= ord('9')):
    return int(c)
  else:
    return ord(c[0]) - ord('A')  + 10

# Function to convert a
# number from given base to decimal
def toDecimal(s,base):

  length = len(s)

  # Initialize power of base and result
  power,ans = 1,0

  # Decimal equivalent of s
  for i in range(length-1,-1,-1):

    ans += value(s[i]) * power
    power = power * base

  return ans

# Function to convert decimal
# to any given base
def reverseValue(n):

  if (n >= 0 and n <= 9):
    return chr(n + 48)
  else:
    return chr(n - 10 + 65)

# Function to convert a given
# decimal number to a base 'base'
def toBase(base, num):

  s = ""

  # Convert input number is given
  # base by repeatedly dividing it
  # by base and taking remainder
  while (num > 0):

    s += reverseValue(num % base)
    num = (num//base)

  sb = ""

  # Append a string into StringBuilder
  sb += (s)

  # Reverse the result
  sb = sb[::-1]
  return sb

# Function to find
# the product of N and M
def findProduct(N, X, M, Y, P):

  # Convert N to decimal
  decimalX = toDecimal(N, X)

  # Convert y to decimal
  decimalY = toDecimal(M, Y)

  # Multiply the decimal numbers
  product = decimalX * decimalY

  # Convert product to base
  result = toBase(P, product)

  # Print the result
  print(result)

# Driver code
N, M = "101", "110"
X, Y, P = 2, 2, 16
findProduct(N, X, M, Y, P)

# This code is contributed by shinjanpatra

C#

// C# code to implement above approach
using System;
class GFG
{

  // Function to find
  // the product of N and M
  static void findProduct(String N, int X,
                          String M,
                          int Y, int P)
  {

    // Convert N to decimal
    int decimalX = toDecimal(N, X);

    // Convert y to decimal
    int decimalY = toDecimal(M, Y);

    // Multiply the decimal numbers
    int product = decimalX * decimalY;

    // Convert product to base
    String result = toBase(P, product);

    // Print the result
    Console.Write(result);
  }

  // Convert Number from a given base
  // to decimal
  // Return the value of a char.
  static int value(char c)
  {
    if (c >= '0' && c <= '9')
      return (int)c - '0';
    else
      return (int)c - 'A' + 10;
  }

  // Function to convert a
  // number from given base to decimal
  static int toDecimal(String s, int _base)
  {
    int length = s.Length;

    // Initialize power of base and result
    int power = 1, ans = 0;

    // Decimal equivalent of s
    for (int i = length - 1; i >= 0; i--)
    {
      ans += value(s[i]) * power;
      power = power * _base;
    }

    return ans;
  }

  // Function to convert decimal
  // to any given base
  static char reverseValue(int n)
  {
    if (n >= 0 && n <= 9)
      return (char)(n + 48);
    else
      return (char)(n - 10 + 65);
  }

  // Function to convert a given
  // decimal number to a base 'base'
  static String toBase(int _base, int num)
  {
    String s = "";

    // Convert input number is given
    // base by repeatedly dividing it
    // by base and taking remainder
    while (num > 0)
    {
      s += reverseValue(num % _base);
      num /= _base;
    }
    String sb = "";

    // Append a string into StringBuilder
    sb += s;

    // Reverse the result
    char[] arr = sb.ToCharArray();
    Array.Reverse(arr);
    return new string(arr);
  }

  // Driver code
  public static void Main()
  {
    String N = "101", M = "110";
    int X = 2, Y = 2, P = 16;
    findProduct(N, X, M, Y, P);
  }
}

// This code is contributed by saurabh_jaiswal.

Javascript

<script>

// JavaScript code for the above approach


// Convert Number from a given base
// to decimal
// Return the value of a char.
function value(c)
{
if (c.charCodeAt(0) >= '0'.charCodeAt(0) && c.charCodeAt(0) <= '9'.charCodeAt(0))
    return parseInt(c);
else
    return c.charCodeAt(0) - 'A'.charCodeAt(0) + 10;
}

// Function to convert a
// number from given base to decimal
function toDecimal(s,base)
{
let length = s.length;

// Initialize power of base and result
let power = 1, ans = 0;

// Decimal equivalent of s
for (let i = length - 1; i >= 0; i--)
{
    ans += value(s[i]) * power;
    power = power * base;
}

return ans;
}

// Function to convert decimal
// to any given base
function reverseValue(n)
{
if (n >= 0 && n <= 9)
    return String.fromCharCode(n + 48);
else
    return String.fromCharCode(n - 10 + 65);
}

// Function to convert a given
// decimal number to a base 'base'
function toBase(base, num)
{
let s = "";

// Convert input number is given
// base by repeatedly dividing it
// by base and taking remainder
while (num > 0)
{
    s += reverseValue(num % base);
    num = Math.floor(num/base);
}
let sb = "";

// Append a string into StringBuilder
sb += (s);

// Reverse the result
sb = sb.split("").reverse().join("");
return sb;
}

// Function to find
// the product of N and M
function findProduct(N, X, M, Y, P)
{

// Convert N to decimal
let decimalX = toDecimal(N, X);

// Convert y to decimal
let decimalY = toDecimal(M, Y);

// Multiply the decimal numbers
let product = decimalX * decimalY;

// Convert product to base
let result = toBase(P, product);

// Print the result
document.write(result,"</br>");
}

// Driver code

let N = "101", M = "110";
let X = 2, Y = 2, P = 16;
findProduct(N, X, M, Y, P);

// This code is contributed by shinjanpatra

</script>

Output

1E

Time Complexity: O(D) where D is the maximum number of digits in N, M and product
Auxiliary Space: O(1)