# Write a program to calculate pow(x,n)

Given two integers x and n, write a function to compute xn. We may assume that x and n are small and overflow doesn’t happen.

Examples :

```Input : x = 2, n = 3
Output : 8

Input : x = 7, n = 2
Output : 49
```

## Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

Below solution divides the problem into subproblems of size y/2 and call the subproblems recursively.

## C

 `#include ` ` `  `/* Function to calculate x raised to the power y */` `int` `power(``int` `x, unsigned ``int` `y) ` `{ ` `    ``if` `(y == 0) ` `        ``return` `1; ` `    ``else` `if` `(y%2 == 0) ` `        ``return` `power(x, y/2)*power(x, y/2); ` `    ``else` `        ``return` `x*power(x, y/2)*power(x, y/2); ` `} ` ` `  `/* Program to test function power */` `int` `main() ` `{ ` `    ``int` `x = 2; ` `    ``unsigned ``int` `y = 3; ` ` `  `    ``printf``(``"%d"``, power(x, y)); ` `    ``return` `0; ` `} `

## Java

 `class` `GFG { ` `    ``/* Function to calculate x raised to the power y */` `    ``static` `int` `power(``int` `x, ``int` `y) ` `    ``{ ` `        ``if` `(y == ``0``) ` `            ``return` `1``; ` `        ``else` `if` `(y % ``2` `== ``0``) ` `            ``return` `power(x, y / ``2``) * power(x, y / ``2``); ` `        ``else` `            ``return` `x * power(x, y / ``2``) * power(x, y / ``2``); ` `    ``} ` ` `  `    ``/* Program to test function power */` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int` `x = ``2``; ` `        ``int` `y = ``3``; ` ` `  `        ``System.out.printf(``"%d"``, power(x, y)); ` `    ``} ` `} ` ` `  `// This code is contributed by Smitha Dinesh Semwal `

## Python3

 `# Python3 program to calculate pow(x,n) ` ` `  `# Function to calculate x ` `# raised to the power y  ` `def` `power(x, y): ` ` `  `    ``if` `(y ``=``=` `0``): ``return` `1` `    ``elif` `(``int``(y ``%` `2``) ``=``=` `0``): ` `        ``return` `(power(x, ``int``(y ``/` `2``)) ``*` `               ``power(x, ``int``(y ``/` `2``))) ` `    ``else``: ` `        ``return` `(x ``*` `power(x, ``int``(y ``/` `2``)) ``*` `                   ``power(x, ``int``(y ``/` `2``))) ` ` `  `# Driver Code ` `x ``=` `2``; y ``=` `3` `print``(power(x, y)) ` ` `  `# This code is contributed by Smitha Dinesh Semwal. `

## C#

 `using` `System; ` ` `  `public` `class` `GFG { ` `     `  `    ``// Function to calculate x raised to the power y ` `    ``static` `int` `power(``int` `x, ``int` `y) ` `    ``{ ` `        ``if` `(y == 0) ` `            ``return` `1; ` `        ``else` `if` `(y % 2 == 0) ` `            ``return` `power(x, y / 2) * power(x, y / 2); ` `        ``else` `            ``return` `x * power(x, y / 2) * power(x, y / 2); ` `    ``} ` ` `  `    ``// Program to test function power ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `x = 2; ` `        ``int` `y = 3; ` ` `  `        ``Console.Write(power(x, y)); ` `    ``} ` `} ` ` `  `// This code is contributed by shiv_bhakt. `

## PHP

 ` `

Output :

`8`

Time Complexity: O(n)
Space Complexity: O(1)

Above function can be optimized to O(logn) by calculating power(x, y/2) only once and storing it.

 `/* Function to calculate x raised to the power y in O(logn)*/` `int` `power(``int` `x, unsigned ``int` `y) ` `{ ` `    ``int` `temp; ` `    ``if``( y == 0) ` `        ``return` `1; ` `    ``temp = power(x, y/2); ` `    ``if` `(y%2 == 0) ` `        ``return` `temp*temp; ` `    ``else` `        ``return` `x*temp*temp; ` `} `

Time Complexity of optimized solution: O(logn)
Let us extend the pow function to work for negative y and float x.

## C

 `/* Extended version of power function that can work ` ` ``for float x and negative y*/` `#include ` ` `  `float` `power(``float` `x, ``int` `y) ` `{ ` `    ``float` `temp; ` `    ``if``( y == 0) ` `       ``return` `1; ` `    ``temp = power(x, y/2);        ` `    ``if` `(y%2 == 0) ` `        ``return` `temp*temp; ` `    ``else` `    ``{ ` `        ``if``(y > 0) ` `            ``return` `x*temp*temp; ` `        ``else` `            ``return` `(temp*temp)/x; ` `    ``} ` `}   ` ` `  `/* Program to test function power */` `int` `main() ` `{ ` `    ``float` `x = 2; ` `    ``int` `y = -3; ` `    ``printf``(``"%f"``, power(x, y)); ` `    ``return` `0; ` `} `

## Java

 `/* Java code for extended version of power function ` `that can work for float x and negative y */` `class` `GFG { ` `     `  `    ``static` `float` `power(``float` `x, ``int` `y) ` `    ``{ ` `        ``float` `temp; ` `        ``if``( y == ``0``) ` `            ``return` `1``; ` `        ``temp = power(x, y/``2``);  ` `         `  `        ``if` `(y%``2` `== ``0``) ` `            ``return` `temp*temp; ` `        ``else` `        ``{ ` `            ``if``(y > ``0``) ` `                ``return` `x * temp * temp; ` `            ``else` `                ``return` `(temp * temp) / x; ` `        ``} ` `    ``}  ` `     `  `    ``/* Program to test function power */` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``float` `x = ``2``; ` `        ``int` `y = -``3``; ` `        ``System.out.printf(``"%f"``, power(x, y)); ` `    ``} ` `} ` ` `  `// This code is contributed by  Smitha Dinesh Semwal. `

## Python3

 `# Python3 code for extended version ` `# of power function that can work ` `# for float x and negative y ` ` `  `def` `power(x, y): ` ` `  `    ``if``(y ``=``=` `0``): ``return` `1` `    ``temp ``=` `power(x, ``int``(y ``/` `2``))  ` `     `  `    ``if` `(y ``%` `2` `=``=` `0``): ` `        ``return` `temp ``*` `temp ` `    ``else``: ` `        ``if``(y > ``0``): ``return` `x ``*` `temp ``*` `temp ` `        ``else``: ``return` `(temp ``*` `temp) ``/` `x ` `     `  `# Driver Code ` `x, y ``=` `2``, ``-``3` `print``(``'%.6f'` `%``(power(x, y))) ` ` `  `# This code is contributed by Smitha Dinesh Semwal.  `

## C#

 `// C# code for extended version of power function ` `// that can work for float x and negative y ` ` `  `using` `System; ` ` `  `public` `class` `GFG{ ` `     `  `    ``static` `float` `power(``float` `x, ``int` `y) ` `    ``{ ` `        ``float` `temp; ` `         `  `        ``if``( y == 0) ` `            ``return` `1; ` `        ``temp = power(x, y/2);  ` `         `  `        ``if` `(y % 2 == 0) ` `            ``return` `temp * temp; ` `        ``else` `        ``{ ` `            ``if``(y > 0) ` `                ``return` `x * temp * temp; ` `            ``else` `                ``return` `(temp * temp) / x; ` `        ``} ` `    ``}  ` `     `  `    ``// Program to test function power  ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``float` `x = 2; ` `        ``int` `y = -3; ` `         `  `        ``Console.Write(power(x, y)); ` `    ``} ` `} ` ` `  `// This code is contributed by shiv_bhakt. `

## PHP

 ` 0) ` `            ``return` `\$x` `*  ` `                   ``\$temp` `* ``\$temp``; ` `        ``else` `            ``return` `(``\$temp` `*  ` `                    ``\$temp``) / ``\$x``; ` `    ``} ` `}  ` ` `  `// Driver Code ` `\$x` `= 2; ` `\$y` `= -3; ` `echo` `power(``\$x``, ``\$y``); ` ` `  `// This code is contributed by ajit ` `?> `

Output :

`0.125000`

Write an iterative O(Log y) function for pow(x, y)
Modular Exponentiation (Power in Modular Arithmetic)

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