Ex5.1-3 of Introduction to Algorithms

Question:
Suppose that you want to output 0 with probability 1/2 and 1 with probability 1/2. At your disposal is a procedure BIASED-RANDOM, that outputs either 0 or 1. It outputs 1 with some probability p and 0 with probability 1 - p, where 0 < p < 1, but you do not know what p is. Give an algorithm that uses BIASED-RANDOM as a subroutine, and returns an unbiased answer, returning 0 with probability 1/2 and 1 with probability 1/2. What is the expected running time of your algorithm as a function of p?

Answer:
If we run BIASED-RANDOM twice, we might get of of following result: 00, 01, 10, 11. And the probabilities for getting each of them is: (1-p) square, (1-p)*p, p*(1-p), p square respectively. We can see that the probabilities for getting 01 equals 10. So, if we can constraint the output to either 01 or 10, we have a UNBIASED-RANDOM that can return 01 or 10 with probability of 1/2 each. And we can simply replace 01, 10 with 0 and 1 to get desired function. How can we constraint the result in 01 and 10? We can use the similar idea used in Ex5.1-2, that's abandoning any result that doesn't belong to 01 and 10 till we get one of them.
And there's a risk in this algorithm. If p is very close to 1 or 0, we may need to try a looooot of times to get either 01 or 10 which makes a very poor performance. To get around this, we can invoke BIASED-RANDOM more times. As we know, the probability of getting a full 0 or 1 permutation is p power the number of times invoking BIASED-RANDOM. And because p is between 0 and 1, the more we invoke BIASED-RANDOM, the less will the probability be, consequently the quicker we don't get full 0 or 1.

Code:

#include "iostream"
#include "ctime"
using namespace std;
int p = 50;

int BIASED_RANDOM ()
{
  int rc = 0;
  if((rand() % 100) >= p)
      rc = 1;
  else
      rc = 0;
  return rc;
}  // -----  end of function BIASED_RANDOM  -----

int UNBIASED_RANDOM()
{
  int rc = 0;

  int temp = 0;
  int i = 0;
  while(true)
  {
      temp = 0;
      temp = BIASED_RANDOM() * 10 + BIASED_RANDOM();
      if(temp == 10 || temp == 1)
          break;
  }

  if(temp == 10)
      rc = 1;
  else
      rc = 0;
  return rc;
}

int main ( int argc, char *argv[] )
{
  if(argc > 1)
      p = atoi(argv[1]);
  srand(time(NULL));

  int rc = 0;
  for(int i = 0; i < 100; ++i)
      rc += BIASED_RANDOM();
  cout << "BIASED SUM:" << rc << endl;
  rc = 0;
  for(int i = 0; i < 100; ++i)
      rc += UNBIASED_RANDOM();
  cout << "UNBIASED SUM:" << rc << endl;
  return 0;
}    // ----------  end of function main  ----------