implement-rand10-using-rand7

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Algorithms

Given the API <code>rand7()</code> that generates a uniform random integer in the range <code>[1, 7]</code>, write a function <code>rand10()</code> that generates a uniform random integer in the range <code>[1, 10]</code>. You can only call the API <code>rand7()</code>, and you shouldn&#39;t call any other API. Please do not use a language&#39;s built-in random API.

Each test case will have one internal argument <code>n</code>, the number of times that your implemented function <code>rand10()</code> will be called while testing. Note that this is not an argument passed to <code>rand10()</code>.

&nbsp;
Example 1:
<pre>Input: n = 1
Output: [2]
</pre>Example 2:
<pre>Input: n = 2
Output: [2,8]
</pre>Example 3:
<pre>Input: n = 3
Output: [3,8,10]
</pre>
&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n &lt;= 105</code></li>
</ul>

&nbsp;
Follow up:

<ul>
	<li>What is the <a href="https://en.wikipedia.org/wiki/Expected_value" target="_blank">expected value</a> for the number of calls to <code>rand7()</code> function?</li>
	<li>Could you minimize the number of calls to <code>rand7()</code>?</li>
</ul>

rand10

Implement Rand10() Using Rand7()

Math

Rejection Sampling

Probability and Statistics

Randomized

给定方法&nbsp;<code>rand7</code>&nbsp;可生成 <code>[1,7]</code> 范围内的均匀随机整数，试写一个方法&nbsp;<code>rand10</code>&nbsp;生成 <code>[1,10]</code> 范围内的均匀随机整数。

你只能调用&nbsp;<code>rand7()</code>&nbsp;且不能调用其他方法。请不要使用系统的&nbsp;<code>Math.random()</code>&nbsp;方法。

<ol>
</ol>

每个测试用例将有一个内部参数 <code>n</code>，即你实现的函数 <code>rand10()</code> 在测试时将被调用的次数。请注意，这不是传递给 <code>rand10()</code> 的参数。

&nbsp;

示例 1:

<pre>
输入: 1
输出: [2]
</pre>

示例 2:

<pre>
输入: 2
输出: [2,8]
</pre>

示例 3:

<pre>
输入: 3
输出: [3,8,10]
</pre>

&nbsp;

提示:

<ul>
	<li><code>1 &lt;= n &lt;= 105</code></li>
</ul>

&nbsp;

进阶:

<ul>
	<li><code>rand7()</code>调用次数的&nbsp;<a href="https://en.wikipedia.org/wiki/Expected_value" target="_blank">期望值</a>&nbsp;是多少&nbsp;?</li>
	<li>你能否尽量少调用 <code>rand7()</code> ?</li>
</ul>