Norway


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

Examples:

;
Input : x = 5, n = 20;
Output : 956741640625;
;
Input : x = 2, n = 100;
Output : 12676506002282294014967020576;

In the above example, 2^100 has 31 digits and it is not possible to these digits even if we use long long int which can maximum 18 digits. The idea behind is that multiply x, n times and result in res[] array.
Here is the algorithm for finding 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++ 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) {
  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 = 2;
  power(base, exponent);
  return 0;
}

Output:

2^100 = 1267650600228229401496703205376

- avatar - Writing power function for large numbers

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



Source link

LEAVE A REPLY

Please enter your comment!
Please enter your name here