Writing power function for large numbers

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 happenExamples:  
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++
Java
Python3
C#
PHP
Javascript
// 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_sizeint multiply(int x, int res[], int res_size) { // Initialize carryint 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 sizewhile (carry) {    res[res_size] = carry % 10;    carry = carry / 10;    res_size++;}return res_size;} // This function finds// power of a number xvoid power(int x, int n){ //printing value "1" for power = 0if(n == 0 ){    cout<<"1";    return;}  int res[MAX];int res_size = 0;int temp = x; // Initialize resultwhile (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 programint main() {int exponent = 100;int base = 20;power(base, exponent);return 0;}
// Java program to compute// factorial of big numbersclass GFG {// Maximum number of digits in// outputstatic 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_sizestatic 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 xstatic 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 codepublic static void main(String[] args) {    int exponent = 100;    int base = 2;    power(base, exponent);}}// This code is contributed by Anant Agarwal.
# Python program to compute# factorial of big numbers # Maximum number of digits in# outputMAX=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_sizedef 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 xdef 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 = 100base = 2power(base, exponent) # This code is contributed# by Anant Agarwal.
// C# program to compute// factorial of big numbersusing 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 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_sizefunction 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 sizewhile ($carry){    if($carry % 10)    $res[$res_size++] = $carry % 10;    $carry = (int)($carry / 10);}return $res;} // This function finds// power of a number xfunction power($x, $n){     //printing value "1" for power = 0    if($n == 0 ){    echo "1";    return;    }$res_size = 0;$res = array();$temp = $x; // Initialize resultwhile ($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?>
<script> // Javascript program to compute// factorial of big numbers // Maximum number of digits in// outputlet 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_sizefunction multiply( x,  res, res_size) { // Initialize carrylet 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 sizewhile (carry) {    res[res_size] = carry % 10;    carry =  Math.floor(carry / 10);    res_size++;}return res_size;} // This function finds// power of a number xfunction power( x, n){ //printing value "1" for power = 0if(n == 0 ){    document.write("1");    return;}   let res = new Array(MAX);let res_size = 0;let temp = x; // Initialize resultwhile (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
 
Mithun Kumar
AmanBhagat
arorapranav23
jana_sayantan
large-numbers
maths-power
Mathematical
Mathematical
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