算法 - How to prove the expected number of probes in Open addressing
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问题描述
问 题
The outline of my following content
background
question
1.background
theorem 11.6 and Proof process
questions
questions in the background
(1) my first question is why Pr{X>=i} but not Pr{X==i} ?
(2) my second question is Why Pr{A1} = n/m ?
I have some thought for question(2) in my figure.
解决方案
你的第二的问题挺显然的,第一次就撞上被占用格子的概率就是load factor(n/m)啊。
第一个问题把m,n换成具体的数字就好理解了。比如100个格子里面占用了10个,空闲90个:
$$\array{Pr\{X \geq 3\} = Pr\{\text{前两次都撞到占用}\} \\\qquad = \frac{10}{100} \cdot \frac{9}{99}}$$
不同于
$$\matrix{Pr\{X = 3\} = Pr\{\text{前两次都撞到占用,第三次撞到空闲}\} \\= \frac{10}{100} \cdot \frac{9}{99} \cdot \frac{90}{98}}$$
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