你是如何解决这个游戏的？

Question

我知道答案是B，但我不明白为什么会这样。如果有人能够解释找到答案或可能展示模拟的过程，那就太棒了。

谢谢。

Answer 1

你可以沿着桌子上的球路走。使这一点变得简单的一点是球以45°的方向开始。因此，所有碰撞角度都是45°。因此，您只需要反转球的方向向量的一个分量。

这是一些C＃示例代码。坐标系的原点位于表格的左下角。球位置在其左下角的边界框处测量：

int ballX = 0;
int ballY = 0;
int ballWidth = 5;
int tableWidth = 230;
int tableHeight = 130;

int directionX = 1;
int directionY = 1;

while(true)
{
    //the distances that the ball could travel until it collides with a vertical or horizontal border, respectively
    int travelDistanceX, travelDistanceY;
    if (directionX > 0)
        travelDistanceX = tableWidth - ballWidth - ballX;
    else
        travelDistanceX = ballX;

    if (directionY > 0)
        travelDistanceY = tableHeight - ballWidth - ballY;
    else
        travelDistanceY = ballY;

    if(travelDistanceX == travelDistanceY)
    {
        //we found the target pocket:
        Console.WriteLine("Target is located at {0}/{1}.", ballX + travelDistanceX * directionX, ballY + travelDistanceY * directionY);
        break;
    }

    if(travelDistanceX < travelDistanceY)
    {
        //collision with the vertical borders
        ballX += travelDistanceX * directionX;
        ballY += travelDistanceX * directionY;
        directionX *= -1;
    }
    else
    {
        //collision with the horizontal borders
        ballX += travelDistanceY * directionX;
        ballY += travelDistanceY * directionY;
        directionY *= -1;
    }
    Console.WriteLine("Collision at {0}/{1}.", ballX, ballY);
}

代码产生以下路径：

Collision at 125/125.
Collision at 225/25.
Collision at 200/0.
Collision at 75/125.
Collision at 0/50.
Collision at 50/0.
Collision at 175/125.
Collision at 225/75.
Collision at 150/0.
Collision at 25/125.
Collision at 0/100.
Collision at 100/0.
Target is located at 225/125.

(225/125)处的口袋（加上球宽以获得实际位置）为B。