Give an algorithm that gets a positive integer m as input an

Give an algorithm that gets a positive integer m as input and outputs its binary representation. Determine that worst-case time and best-case time complexities of your algorithm. Again, note that the time complexities must be expressed in terms of the size of the input.

Solution

binary(m){
   if(m<=1)
   {
       print(0)
   }
   t = m%2;
   binary(m/2);
   print(t);
}

The time taken for this algorithm is O(log(m)). In each execution of the function we are dividing the number by 2, so the function executes log(m) times.