Given the base and exponent, how do we implement the pow(base,exp) function efficiently?

For example

pow(2.0,5) = 32

pow(0.4,2) = 0.16

pow(2.0,-2) = 0.25

For simplicity, let us assume that the base can be a decimal number and exponent can be any integer. A straight forward implementation that comes to mind is simply multiplying the base with itself for ‘e’ times where e is the exponent.

There is one more efficient way to calculate this value using

*divide and conquer technique*. If we have to calculate a^{n}, we can divide the computation into two similar tasks i.e we can calculate a^{n/2}once, and multiplying it with itself gives the required valuea

^{n}= a^{n/2}*a^{n/2}Here is the C++ implementation of the above algorithm. This reduces the number of multiplications required for calculating the power. Observe how different test cases are handled in the program.