简单二维随机游动

Question

我在这个练习中的平均距离有问题。它应该接近N步的sqrt，但它更低。你能帮我找出我的错误在哪里吗？

二维随机游动。二维随机游动模拟了一个粒子在点网格中运动的行为。在每一步中，随机步行者以1/4的概率向北、向南、向东或向西移动，与之前的移动无关。确定N步后随机步行者离起点有多远（平均）。（理论答案：按sqrt(N)的顺序）

public class RandomWalk{
    public static void main(String[] args){

    int N = Integer.parseInt(args[0]);

    double nextStep = 0;
    double averageDistance = 0;
    int COUNT = 1000;

    for (int j = 0; j < COUNT; j++){
        int moveWest = 0;
        int moveEast = 0;
        int moveSouth = 0;
        int moveNorth = 0;
        double distance = 0;

        for (int i = 0; i < N; i++){
        nextStep = Math.random()*4;
        if (nextStep <= 1) ++moveWest;
          else if (nextStep <= 2) ++moveEast;
            else if (nextStep <= 3) ++moveSouth;
              else if (nextStep <= 4)++moveNorth;       
        }

        moveEast = moveEast - moveWest;
        moveNorth = moveNorth - moveSouth;
        distance = Math.sqrt((moveEast * moveEast) + (moveNorth * moveNorth));
        averageDistance += distance; 

        System.out.println("Walker is " + distance + "\t steps away of from the starting point");
        //System.out.println("Sqrt of N is " + Math.sqrt(N));

    }
    System.out.println("Average distance is " + averageDistance/COUNT + " steps away of from the starting point");
    }
}

Answer 1

我在您的代码上运行了几个测试，上面提到的范围变化为<0,1)，<1,2)，<2,3)，<3,4)，使它们相等。

你是这样做的：

if (nextStep < 1) ++moveWest;
          else if (nextStep < 2) ++moveEast;
            else if (nextStep < 3) ++moveSouth;
              else if (nextStep < 4)++moveNorth;

注意<=变成<。

Average distance is 8.873435509749317 steps away of from the starting point
W=2498906
E=2501447
N=2500022
S=2499625