砸蛋问题

 2 Egg Problem

* You are given 2 eggs.

* You have access to a 100-storey building.

* Eggs can be very hard or very fragile means it may break if dropped from the first floor or may not even break if dropped from 100^th floor. Both eggs are identical.

* You need to figure out the highest floor of a 100-storey building an egg can be dropped without breaking.

Now the question is how many drops you need to make. You are allowed to break 2 eggs in the process

100层楼，2个鸡蛋。某层之上扔鸡蛋就会碎。问至少要测试多少次才能试出这个层数。

答：

p1. 如果只有1个鸡蛋，那我们只能从一楼开始一层一层的测，否则砸烂了就没得测了。

现在有2个鸡蛋，有个鸡蛋可以浪费了，用一号鸡蛋来缩小范围，二号鸡蛋在一号鸡蛋缩小的范围内一层一层的测试。

比如一号鸡蛋每十层扔一下，10,20,30...... 如果在30层碎了，二号鸡蛋可以从21层开始测试。

 

现在的问题是如何确定一号鸡蛋每多少层测试一下，才能平衡1号2号鸡蛋的测试次数，使之最小。

设x层测试一下,最坏情况下需要测试

n =100/x+x  >=2(100/x *x) ^ (1/2)

n>=20

为了使得n最小 x = 100^(1/2) = 10

 

扩展： 3个鸡蛋的情况

设一号鸡蛋x层测试一下，总次数

100/x+x^(1/2)

可得 x=22 最小

 

 

(数学忘的差不多了，不完整，有空再补充)