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Writing power function for large numbers
  • Difficulty Level : Medium
  • Last Updated : 28 May, 2021

We have given two numbers x and n which are base and exponent respectively. Write a function to compute x^n where 1 <= x, n <= 10000 and overflow may happen
Examples: 
 

Input : x = 5, n = 20
Output : 95367431640625

Input : x = 2, n = 100
Output : 1267650600228229401496703205376

 

In the above example, 2^100 has 31 digits and it is not possible to store these digits even if we use long long int which can store maximum 18 digits. The idea behind is that multiply x, n times and store result in res[] array. 
Here is the algorithm for finding power of a number.
Power(n) 
1. Create an array res[] of MAX size and store x in res[] array and initialize res_size as the number of digits in x. 
2. Do following for all numbers from i=2 to n 
…..Multiply x with res[] and update res[] and res_size to store the multiplication result.
Multiply(res[], x) 
1. Initialize carry as 0. 
2. Do following for i=0 to res_size-1 
….a. Find prod = res[i]*x+carry. 
….b. Store last digit of prod in res[i] and remaining digits in carry. 
3. Store all digits of carry in res[] and increase res_size by number of digits. 
 

 

C++




// C++ program to compute
// factorial of big numbers
#include <iostream>
using namespace std;
 
// Maximum number of digits in
// output
#define MAX 100000
 
// This function multiplies x
// with the number represented by res[].
// res_size is size of res[] or
// number of digits in the number
// represented by res[]. This function
// uses simple school mathematics
// for multiplication.
// This function may value of res_size
// and returns the new value of res_size
int multiply(int x, int res[], int res_size) {
 
// Initialize carry
int carry = 0;
 
// One by one multiply n with
// individual digits of res[]
for (int i = 0; i < res_size; i++) {
    int prod = res[i] * x + carry;
 
    // Store last digit of
    // 'prod' in res[]
    res[i] = prod % 10;
 
    // Put rest in carry
    carry = prod / 10;
}
 
// Put carry in res and
// increase result size
while (carry) {
    res[res_size] = carry % 10;
    carry = carry / 10;
    res_size++;
}
return res_size;
}
 
// This function finds
// power of a number x
void power(int x, int n)
{
 
//printing value "1" for power = 0
if(n == 0 ){
    cout<<"1";
    return;
}
 
 
int res[MAX];
int res_size = 0;
int temp = x;
 
// Initialize result
while (temp != 0) {
    res[res_size++] = temp % 10;
    temp = temp / 10;
}
 
// Multiply x n times
// (x^n = x*x*x....n times)
for (int i = 2; i <= n; i++)
    res_size = multiply(x, res, res_size);
 
cout << x << "^" << n << " = ";
for (int i = res_size - 1; i >= 0; i--)
    cout << res[i];
}
 
// Driver program
int main() {
int exponent = 100;
int base = 20;
power(base, exponent);
return 0;
}

Java




// Java program to compute
// factorial of big numbers
class GFG {
// Maximum number of digits in
// output
static final int MAX = 100000;
 
// This function multiplies x
// with the number represented by res[].
// res_size is size of res[] or
// number of digits in the number
// represented by res[]. This function
// uses simple school mathematics
// for multiplication.
// This function may value of res_size
// and returns the new value of res_size
static int multiply(int x, int res[], int res_size) {
 
    // Initialize carry
    int carry = 0;
 
    // One by one multiply n with
    // individual digits of res[]
    for (int i = 0; i < res_size; i++) {
    int prod = res[i] * x + carry;
 
    // Store last digit of
    // 'prod' in res[]
    res[i] = prod % 10;
 
    // Put rest in carry
    carry = prod / 10;
    }
 
    // Put carry in res and
    // increase result size
    while (carry > 0) {
    res[res_size] = carry % 10;
    carry = carry / 10;
    res_size++;
    }
    return res_size;
}
 
// This function finds
// power of a number x
static void power(int x, int n) {
     
    //printing value "1" for power = 0
    if(n == 0 ){
    System.out.print("1");
    return;
}
    int res[] = new int[MAX];
    int res_size = 0;
    int temp = x;
 
    // Initialize result
    while (temp != 0) {
    res[res_size++] = temp % 10;
    temp = temp / 10;
    }
 
    // Multiply x n times
    // (x^n = x*x*x....n times)
    for (int i = 2; i <= n; i++)
    res_size = multiply(x, res, res_size);
 
    System.out.print(x + "^" + n + " = ");
    for (int i = res_size - 1; i >= 0; i--)
    System.out.print(res[i]);
}
// Driver code
public static void main(String[] args) {
    int exponent = 100;
    int base = 2;
    power(base, exponent);
}
}
// This code is contributed by Anant Agarwal.

Python3




# Python program to compute
# factorial of big numbers
 
# Maximum number of digits in
# output
MAX=100000
 
# This function multiplies x
# with the number represented by res[].
# res_size is size of res[] or
# number of digits in the number
# represented by res[]. This function
# uses simple school mathematics
# for multiplication.
# This function may value of res_size
# and returns the new value of res_size
def multiply(x, res, res_size):
 
    # Initialize carry
    carry = 0
 
    # One by one multiply n with
    # individual digits of res[]
    for i in range(res_size):
        prod = res[i] * x + carry
 
        # Store last digit of
        # 'prod' in res[]
        res[i] = prod % 10
 
        # Put rest in carry
        carry = prod // 10
 
    # Put carry in res and
    # increase result size
    while (carry):
        res[res_size] = carry % 10
        carry = carry // 10
        res_size+=1
 
    return res_size
 
 
# This function finds
# power of a number x
def power(x,n):
     
    # printing value "1" for power = 0
     if (n == 0) :
        print("1")
        return
     
    res=[0 for i in range(MAX)]
    res_size = 0
    temp = x
 
    # Initialize result
    while (temp != 0):
        res[res_size] = temp % 10;
        res_size+=1
        temp = temp // 10
 
 
    # Multiply x n times
    # (x^n = x*x*x....n times)
    for i in range(2, n + 1):
        res_size = multiply(x, res, res_size)
 
    print(x , "^" , n , " = ",end="")
    for i in range(res_size - 1, -1, -1):
        print(res[i], end="")
 
 
# Driver program
 
exponent = 100
base = 2
power(base, exponent)
 
# This code is contributed
# by Anant Agarwal.

C#




// C# program to compute
// factorial of big numbers
using System;
 
class GFG {
     
    // Maximum number of digits in
    // output
    static int MAX = 100000;
     
    // This function multiplies x
    // with the number represented by res[].
    // res_size is size of res[] or
    // number of digits in the number
    // represented by res[]. This function
    // uses simple school mathematics
    // for multiplication.
    // This function may value of res_size
    // and returns the new value of res_size
    static int multiply(int x, int []res,
                            int res_size)
    {
     
        // Initialize carry
        int carry = 0;
     
        // One by one multiply n with
        // individual digits of res[]
        for (int i = 0; i < res_size; i++)
        {
            int prod = res[i] * x + carry;
         
            // Store last digit of
            // 'prod' in res[]
            res[i] = prod % 10;
         
            // Put rest in carry
            carry = prod / 10;
        }
     
        // Put carry in res and
        // increase result size
        while (carry > 0)
        {
            res[res_size] = carry % 10;
            carry = carry / 10;
            res_size++;
        }
         
        return res_size;
    }
     
    // This function finds
    // power of a number x
    static void power(int x, int n)
    {
        //printing value "1" for power = 0
    if(n == 0 ){
    Console.Write("1");
    return;
    }
        int []res = new int[MAX];
        int res_size = 0;
        int temp = x;
     
        // Initialize result
        while (temp != 0) {
            res[res_size++] = temp % 10;
            temp = temp / 10;
        }
     
        // Multiply x n times
        // (x^n = x*x*x....n times)
        for (int i = 2; i <= n; i++)
            res_size = multiply(x, res, res_size);
     
        Console.Write(x + "^" + n + " = ");
         
        for (int i = res_size - 1; i >= 0; i--)
            Console.Write(res[i]);
    }
     
    // Driver code
    public static void Main()
    {
        int exponent = 100;
        int b_ase = 2;
        power(b_ase, exponent);
    }
}
 
// This code is contributed by vt_m.

PHP




<?php
// PHP program to compute
// factorial of big numbers
 
// Maximum number of
// digits in output
 
// This function multiplies
// x with the number represented
// by res[]. res_size is size of
// res[] or number of digits in
// the number represented by res[].
// This function uses simple school
// mathematics for multiplication.
// This function may value of
// res_size and returns the new
// value of res_size
function multiply($x, $res)
{
     
// Initialize carry
$carry = 0;
$res_size = count($res);
 
// One by one multiply
// n with individual
// digits of res[]
for ($i = 0;
    $i < $res_size; $i++)
{
    $prod = $res[$i] *
            $x + $carry;
 
    // Store last digit of
    // 'prod' in res[]
    $res[$i] = $prod % 10;
     
    // Put rest in carry
    $carry = (int)($prod / 10);
}
 
// Put carry in res and
// increase result size
while ($carry)
{
    if($carry % 10)
    $res[$res_size++] = $carry % 10;
    $carry = (int)($carry / 10);
}
return $res;
}
 
// This function finds
// power of a number x
function power($x, $n)
{
     //printing value "1" for power = 0
    if($n == 0 ){
    echo "1";
    return;
    }
$res_size = 0;
$res = array();
$temp = $x;
 
// Initialize result
while ($temp != 0)
{
    $res[$res_size++] = $temp % 10;
    $temp = $temp / 10;
}
 
// Multiply x n times
// (x^n = x*x*x....n times)
for ($i = 2; $i <= $n; $i++)
    $res = multiply($x, $res);
 
echo $x . "^" .
    $n . " = ";
$O = 0;
for ($i = count($res) - 1;
    $i >= 0; $i--, $O++)
if($res[$i])
break;
for ($i = count($res) - $O - 1;
            $i >= 0; $i--)
    echo $res[$i];
}
 
// Driver Code
$exponent = 100;
$base = 2;
power($base, $exponent);
 
// This code is contributed
// by mits
?>

Javascript




<script>
 
// Javascript program to compute
// factorial of big numbers
 
// Maximum number of digits in
// output
let MAX = 100000
 
// This function multiplies x
// with the number represented by res[].
// res_size is size of res[] or
// number of digits in the number
// represented by res[]. This function
// uses simple school mathematics
// for multiplication.
// This function may value of res_size
// and returns the new value of res_size
function multiply( x,  res, res_size) {
 
// Initialize carry
let carry = 0;
 
// One by one multiply n with
// individual digits of res[]
for (let i = 0; i < res_size; i++) {
    let prod = res[i] * x + carry;
 
    // Store last digit of
    // 'prod' in res[]
    res[i] = prod % 10;
 
    // Put rest in carry
    carry = Math.floor(prod / 10);
}
 
// Put carry in res and
// increase result size
while (carry) {
    res[res_size] = carry % 10;
    carry =  Math.floor(carry / 10);
    res_size++;
}
return res_size;
}
 
// This function finds
// power of a number x
function power( x, n)
{
 
//printing value "1" for power = 0
if(n == 0 ){
    document.write("1");
    return;
}
 
 
 
let res = new Array(MAX);
let res_size = 0;
let temp = x;
 
// Initialize result
while (temp != 0) {
    res[res_size++] = temp % 10;
    temp =  Math.floor(temp / 10);
}
 
// Multiply x n times
// (x^n = x*x*x....n times)
for (let i = 2; i <= n; i++)
    res_size = multiply(x, res, res_size);
 
document.write( x + "^" + n + " = ");
for (let i = res_size - 1; i >= 0; i--)
    document.write(res[i]);
}
 
 
// Driver Code
 
let exponent = 100;
let base = 2;
power(base, exponent);
 
</script>

Output: 
 

2^100 = 1267650600228229401496703205376

 

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