Time complexity of power() [duplicate]

Question

I implemented this function power() which takes two arguments a and b and computes a^b.

typedef long long int LL;

LL power(int a,int b)
{
   int i = 1;
   LL pow = 1; 
   for( ; i <= b ; ++i )
     pow *= a;
   return pow;
}

Given : a^b falls in the range of long long int.
Problem : How to reduce the time complexity of my algorithm?

Answer 1

Exponentiation by Squaring.

A non-recursive implementation

LL power(int a, int b)
{
  LL pow = 1;
  while ( b ) 
  {
         if ( b & 1 ) 
         {
           pow = pow * a;
           --b;
         }
         a = a*a;
         b = b/2;
  }
  return pow;
}

This algorithm requires log₂b squarings and at most log₂b multiplications.

The running time is O(log b)

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Answer 2

Use Exponentiation by squaring