// Oldham, Jeffrey D.
// 2000Feb01
// CS3352

// Number of Times the Net Total Crosses the Axis

// We repeatedly toss fair coins, adding +1 for heads and adding -1
// for tails.  We keep track of the number of times the cumulative sum
// changes from positive to negative or vice versa.  Touching zero and
// but returning to the same side does not count.  Given the number of
// coin tosses, the program prints the number of crossings to standard
// output.

// Command-Line Argument
// 1. number of trials

#include <iostream>
#include <stdlib.h>		// has EXIT_SUCCESS
#include "rng.h"
#include <time.h>		// has time()
#include <unistd.h>		// for getpid()
#include <sys/types.h>		// for getpid()
#include <limits.h>		// has ULONG_MAX


// Equilikely(a,b) returns a random integer in the range a, a+1, ..., b.
template <class LONG>
LONG Equilikely(const LONG & a, const LONG & b) {
  return a + static_cast<LONG>((b-a+1)* Random());
}


int main(int argc, char *argv[]) {
  if (argc != 2) {
    cerr << argv[0] << ": number-of-trials\n";
    throw "illegal command line argument list";
  }

  unsigned long nuTrials = strtoul(argv[1], static_cast<char **>(0), 0);
  if (nuTrials == ULONG_MAX) {
    cerr << argv[0] << ": number-of-trials out of range\n";
    throw "illegal number of trials";
  }

  // Prepare the random number generator.
  // erroneous code: PutSeed(time(static_cast<time_t *>(0)) ^ (getpid() << 15 + getpid()));
  PutSeed(time(static_cast<time_t *>(0)) ^ ((getpid() << 15) + getpid()));

  // Toss the coins.
  long sum = 0;
  unsigned long nuCrossings = 0;
  enum sign { negative, zero, positive };
  sign s = zero;
  for (; nuTrials > 0; --nuTrials) {
    if (Equilikely(0,1) == 1) {
      ++sum;
#ifdef DEBUG
      //      cout << "tail\n";
#endif // DEBUG
    }
    else {
      --sum;
#ifdef DEBUG
      //      cout << "head\n";
#endif // DEBUG
    }
#ifdef DEBUG
    cout << "sum = " << sum << endl;
#endif // DEBUG
    if (sum < 0 && s == positive) {
      s = negative;
      ++nuCrossings;
#ifdef DEBUG
      cout << "positive->negative crossing\n";
#endif // DEBUG
    }
    else if (sum > 0 && s == negative) {
      s = positive;
      ++nuCrossings;
#ifdef DEBUG
      cout << "negative->positive crossing\n";
#endif // DEBUG
    }
    else if (s == zero)
      s = (sum < 0) ? negative : positive;
  }

  // Print the results.
  cout << nuCrossings << endl;

  return EXIT_SUCCESS;
}