php - 兔子和乌龟计算

Question

我有我想比较的 2 个配置文件的数据。

每个配置文件都有一个“总积分”值和一个“每天积分”值，我想计算兔子需要多少天才能超过乌龟。

$hare_points = 10000;
$hare_ppd = 700;

$tortoise_points = 16000;
$tortoise_ppd = 550;

确定兔子需要多少天才能赶上乌龟的最有效方法是什么？我的第一个方法是运行一个循环来计算天数，但很快意识到必须有一个有效的算法，不会破坏它正在运行的服务器，哈哈

Answer 1

It's a simple set of equations to solve.

hare_total = hare_points + hare_ppd * days
tortoise_total = tortoise_points + tortoise_ppd * days

You're trying to find out the day the points are the same, so:

hare_total = tortoise_total
hare_points + hare_ppd * days = tortoise_points + tortoise_ppd * days
hare_points - tortoise_points = (tortoise_ppd - hare_ppd) * days

So there's your answer:

$days = ($hare_points - $tortoise_points) / ($tortoise_ppd - $hare_ppd)

Just plug that into your function and round up / down to an integer depending on how you want to interpret the answer.

Answer 2

假设 ppd 是每天的积分：

<?php
$hare_points = 10000;
$hare_ppd = 700;

$tortoise_points = 16000;
$tortoise_ppd = 550;

$hare_diff = $tortoise_points - $hare_points;
$hare_ppd_diff = abs($tortoise_ppd - $hare_ppd);
$days = $hare_diff/$hare_ppd_diff;
echo $days; // 40

/* Test:
 * 40 * 700 = 28000; hare
 * 40 * 550 = 22000; tortoise
 * 
 * hare_p = 28000 + 10000 = 38 000
 * toit_p = 22000 + 16000 = 38 000
 * 
 * So the math is right. On 40th day, they are equal
 * 
 */