Objective : Given two numbers ‘k’ and ‘n’. Write an algorithm to calculate k^{n} .
Example :

k = 4, n = 5
k^{n} = 4^{5} = 1024
k = 2, n = 3
k^{n} = 2^{3} = 8
Approach :

Method 1: Brute Force

Use for loop to iterate from 1 to n and do k*k for each iteration.

Time Complexity: O(n)

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Method 2: Only if ‘k’ and ‘n’ are positive .

1. Use recursion.

2. Divide the problem into sub problems with size n/2 and solve it recursively.

3. Handle the case if n is odd. Multiply the final result with k.

Time Complexity: O(logn)

Example :

2^{4} = 2^{2} * 2^{2} = 4*4 = 16.
So instead of doing it 2*2*2*2, we have divided into two parts = 2^{2} * 2^{2}
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Method 3: Handle the case if n is negative

1. Same as Method 2 above.

2. Instead of multiplying with k, divide with k.

3. See the code for more understanding.

Time Complexity: O(logn)

Code :Run Code

Output :

4 power -2 : Result: 0.0625
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If you find anything incorrect or you feel that there is any better approach to solve the above problem, please write comment.
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