javascript - 如何在没有 while 循环的情况下重写这段代码？

Question

He drops the ball out of the window. The ball bounces (for example), to two-thirds of its height (a bounce of 0.66).

His mother looks out of a window 1.5 meters from the ground.

How many times will the mother see the ball pass in front of her window (including when it's falling and bouncing?

这是我的解决方案:

function bouncingBall(h, bounce, window) {
  let count = 0;
  if (h < 0 || bounce <= 0 || window >= h) {
    return -1;
  } else {
    count += 2
  }

  let jump = h * bounce

  while (jump > window) {
    jump *= bounce
    count += 2;
  }
  return count - 1;
}

console.log(bouncingBall(3.0, 0.66, 1.5)) //3

我得到的结果是正确的，但显然，它的效率不够，因为它需要一些时间来运行所有内容。关于如何让它“更好”有什么建议吗？

Answer 1

您需要计算出x，即球需要弹跳的次数才能使其峰值低于窗口:

h * (bounce ** x) = window

求解x，我们得到

bounce ** x = window / h
ln(bounce ** x) = ln(window / h)
x * ln(bounce) = ln(window / h)
x = ln(window / h) / ln(bounce)

这将为您提供反弹次数，之后峰值将低于窗口。乘以 2(因为球上来又落下，两次经过 window )，如果第一次球从 window 上方掉落，则加 1:

function bouncingBall(h, bounce, window) {
  const bounces = Math.floor(Math.log(window / h) / Math.log(bounce));
  return bounces * 2 + (h > window ? 1 : 0);
}

console.log(bouncingBall(3.0, 0.66, 1.5))