C语言关于微生物增殖（假设有两种微生物 X 和 Y X出生后每隔3分钟分裂一次…引发的思考

程序之美

题目描述

假设有两种微生物 X 和 Y
X出生后每隔3分钟分裂一次（数目加倍），Y出生后每隔2分钟分裂一次（数目加倍）。
一个新出生的X，半分钟之后吃掉1个Y，并且，从此开始，每隔1分钟吃1个Y。
现在已知有新出生的 X=10, Y=89，求60分钟后Y的数目。
如果X=10，Y=90呢？
本题的要求就是写出这两种初始条件下，60分钟后Y的数目。

输入
没有输入。

输出
两个整数，每个占1行。

有很多朋友拿到这个题目，无从下手，不知道怎么分析，怎么解决问题。这里我就冒充一次长者，带着大家捋顺一下思路。
在解题之前，我们先说下我们的方法，我们的方法叫三点一测法，何为三点一测呢。又是哪三点，哪一测呢。我们详细来讲。
三点一测法精髓：
第一点，提取题目核心点：
第二点，归一化题目分歧点：
第三点，全方位整理解题逻辑点，
一测：及时进行测试，调试，修复逻辑漏洞。

好了，我们就用这个题目开刀，给大伙讲解下具体的实践用法。

提取题目核心点

我们提取题目核心点，本题的核心点，也就是本题能够提供给我们的信息，包括显性的也包括隐形的。从这道题我们可以轻松的看到相关核心点。
比如：
1、生物X每三分钟分裂一次
2、生物Y每两分钟分裂一次
3、新出生X半分钟要吃掉一个Y，之后每一分钟吃掉一个Y。

本题基本上能够提取的信息也就这些。

序号	核心点
1	生物X每三分钟分裂一次
2	生物Y每两分钟分裂一次
3	新出生X半分钟要吃掉一个Y，之后每一分钟吃掉一个Y

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三分钟

两分钟

半分钟

一分钟

生物X

生物Y

生物X

生物Y

看到这三个信息，我相信很多小伙伴蒙了，丈二的和尚，摸不着脑门，说没联系吧，有联系，唯一的联系就X吃Y，说有联系吧，一会二半分钟吃，一会一分钟吃的。

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好了，我们核心点就提取到这里，下一步我们开始归一化分歧点。

归一化分歧点

对于以上核心点，小伙伴们很容易就能想到，我们可以定义两种生物X和Y。然后按分钟执行下去就可以了。如下：

Created with Raphaël 2.3.0 开始输入生物X，Y 相关性操作有60分钟？结束 yes no

其中相关性的操作主要有：
X分裂，Y分裂，X新出生半分钟吃掉一个Y，之后一分钟吃掉一个Y

在这里，对于X分裂，Y分裂，小伙伴们都没有悬念，认为直接写就可以了，比如:
三分钟后：X = X * 2;
两分钟后：Y = Y * 2;
主要分歧点就是X吃Y这一点，因为不是X固定时间去吃Y，而是刚出生半分钟吃掉一个Y，之后每一分钟吃掉一个Y。这时有些小伙伴就有些疑虑了，是不是需要去区分生物X是不是新生的，想到这里，可能整个都乱套了，是不是还要记下来每个生物X是不是新生的，吃过一次Y之后就不是新生的了，就可以一分钟吃一个Y了。但是统计每一生物的新生状态也是一笔不小的开销，既耗费脑细胞，也耗费存储资源。
这个时候，也就是我们感觉到问题的复杂性高，解题难度大时，我们可以想想是不是我们的思路错了，记得曾经有一位伟人说过，任何事情都是有一个最合适，最便捷，最合理的解决方案，如果当你觉得你走的路很累，甚至不通的时候，你可以考虑下是不是你的方向走错了，哈哈，这个伟人就是我。
这时我们在发散下思维，世界万物都一样都是有着宏观和微观的运动方式，当我们宏观难以解决时，我们是否考虑用微观的方式解决问题，当然，如果我们微观难以解决问题时，我们也可以考虑用宏观的方式解决问题。
以下是网上找的一个宏观微观的图片，宏观之中包含微观，微观又透漏着宏观的本质和属性。

从这点出发，我们将操作单位进行扩张，比如之前是一分钟一个操作单位，如果我们将操作单位改为半分钟呢？
这样，六个单位X分裂，4个单位X分裂，X从出生开始一个单位吃掉一个Y，之后每两个单位吃掉一个Y。
这时X吃掉Y的单位分别为：1单位，3单位，5单位，。。。。
看到了正好逢奇数X吃Y。

这时我们很容以的想到X吃Y可以通过判断当前时间单位i，通过i % 2 == 1方式来解决。
这时是不是思路豁然开朗，X生物一个单位吃掉一个Y，之后每逢奇数就吃掉一个Y。

Created with Raphaël 2.3.0 开始输入生物X，Y i % 2 == 1 X生物吃掉一个Y i%4==0 Y分裂 i%6==0 X分裂有60分钟？结束 yes no

至此，是不是小伙伴们已经有了整个逻辑的完整思路了，本来感觉复杂多变，摸不着脑门的问题，经过我们换一个思路，换一种方法，就能用很简单的方法解决掉。

其实所有问题，只要换一个思路，就会有意想不到的效果，解决问题也能变得简单，思路也能变得清晰。
计算机的思路，其实就是由宏观到微观，由微观到宏观的过程，只有具有了这样的大局观，我们遇到问题才能所向披靡，迎刃而解。
其实想想，很多小伙伴们不难理解，计算机就是一个宏观与微观的产物。宏观到其是庞然大物，存储数据量巨大惊人，运算速度更是令人惊叹，百亿次，千亿次的秒级运算量已成为家常之物。微观到，它可以将几千年的历史数据有序的展现，也可以将一张一张的影视图片流式化成电影，可以将细胞分裂，细菌活动等状态一一模拟，展现在人们面前，形成仿真。

遇到问题时只要我们运用计算机的这个有宏观到微观，由微观到宏观的思路，我相信很多问题都可以找到最优解决方案，既省时又省力。

整理解题逻辑点

解题思路：
经过上述流程图，我想信很多小伙伴们已经整理出来了解题逻辑点，对了：
1、输入X生物和Y生物的个数。
2、120个单位，每个单位中，执行如下操作：
逢奇数X吃Y
每四个单位Y分裂
每六个单位X分裂
3，输出最后Y所剩的个数。

具体实现代码如下：

#include<stdio.h>int main()
{int x=10,y=90;for(int i=1;i<=120;i++) //将时间的单位往后延顺到120个单位 {if(i%2==1)//按照题目的条件，正好逢奇数x吃y y=y-x;if(i%4==0)//变成4分钟 y=y*2;if(i%6==0)//变成6分钟 x=x*2;}printf("%d",y);return 0;
}

答案：
0
94371840

好了，今天就说到这里吧，有兴趣的小伙伴可以继续探讨，钻研，看有没有更完美的解法，也欢迎小伙伴们和我联系交流，批评指正。