C++ Primer Plus

Both of these implementations have advantages and disadvantages. Storing the data means that the object occupies more memory and that code has to be careful to update both rectangular and polar representations each time a Vector object is changed. But data look-up is faster. If an application often needs to access both representations of a vector, the implementation used in this example would be preferable; if polar data were needed only infrequently, the other implementation would be better. You could choose to use one implementation in one program and the second implementation in another, yet retain the same user interface for both.

Taking the Vector Class on a Random Walk

Listing 11.15 provides a short program that uses the revised Vector class. It simulates the famous Drunkard’s Walk problem. Actually, now that drunks are recognized as people with a serious health problem rather than as a source of amusement, it’s usually called the Random Walk problem. The idea is that you place someone at a lamppost. The person begins walking, but the direction of each step varies randomly from the direction of the preceding step. One way of phrasing the problem is this: How many steps does it take the random walker to travel, say, 50 feet away from the post? In terms of vectors, this amounts to adding a bunch of randomly oriented vectors until the sum exceeds 50 feet.

Listing 11.15 lets you select the target distance to be traveled and the length of the wanderer’s step. It maintains a running total that represents the position after each step (represented as a vector) and reports the number of steps needed to reach the target distance, along with the walker’s location (in both formats). As you’ll see, the walker’s progress is quite inefficient. A journey of 1,000 steps, each 2 feet long, may carry the walker only 50 feet from the starting point. The program divides the net distance traveled (50 feet, in this case) by the number of steps to provide a measure of the walker’s inefficiency. All the random direction changes make this average much smaller than the length of a single step. To select directions randomly, the program uses the standard library functions rand(), srand(), and time(), described in the following “Program Notes” section. Be sure to compile Listing 11.14 along with Listing 11.15.

Listing 11.15. randwalk.cpp

// randwalk.cpp -- using the Vector class

// compile with the vect.cpp file

#include

#include       // rand(), srand() prototypes

#include         // time() prototype

#include "vect.h"

int main()

{

    using namespace std;

    using VECTOR::Vector;

    srand(time(0));     // seed random-number generator

    double direction;

    Vector step;

    Vector result(0.0, 0.0);

    unsigned long steps = 0;

    double target;

    double dstep;

    cout << "Enter target distance (q to quit): ";

    while (cin >> target)

    {

        cout << "Enter step length: ";

        if (!(cin >> dstep))

            break;

        while (result.magval() < target)

        {

            direction = rand() % 360;

            step.reset(dstep, direction, Vector::POL);

            result = result + step;

            steps++;

        }

        cout << "After " << steps << " steps, the subject "

            "has the following location:\n";

        cout << result << endl;

        result.polar_mode();

        cout << " or\n" << result << endl;

        cout << "Average outward distance per step = "

            << result.magval()/steps << endl;

        steps = 0;

        result.reset(0.0, 0.0);

        cout << "Enter target distance (q to quit): ";

    }

    cout << "Bye!\n";

    cin.clear();

    while (cin.get() != '\n')

        continue;

    return 0;

}

Because the program has a using declaration bringing Vector into scope, the program can use Vector::POL instead of VECTOR::Vector::POL.

Here is a sample run of the program in Listings 11.13, 11.14, and 11.15:

Enter target distance (q to quit): 50

Enter step length: 2

After 253 steps, the subject has the following location:

(x,y) = (46.1512, 20.4902)

 or

(m,a) = (50.495, 23.9402)

Average outward distance per step = 0.199587

Enter target distance (q to quit): 50

Enter step length: 2

After 951 steps, the subject has the following location:

(x,y) = (-21.9577, 45.3019)

 or

(m,a) = (50.3429, 115.8593)

Average outward distance per step = 0.0529362

Enter target distance (q to quit): 50

Enter step length: 1

After 1716 steps, the subject has the following location:

(x,y) = (40.0164, 31.1244)

 or

(m,a) = (50.6956, 37.8755)

Average outward distance per step = 0.0295429

Enter target distance (q to quit): q

Bye!

The random nature of the process produces considerable variation from trial to trial, even if the initial conditions are the same. On average, however, halving the step size quadruples the number of steps needed to cover a given distance. Probability theory suggests that, on average, the number of steps (N) of length s needed to reach a net distance of D is given by the following equation:

N = (D/s)²