0470. Implement Rand10() Using Rand7() (M)

Implement Rand10() Using Rand7() (M)

题目

Given a function rand7 which generates a uniform random integer in the range 1 to 7, write a function rand10 which generates a uniform random integer in the range 1 to 10.

Do NOT use system's Math.random().

Example 1:

Input: 1
Output: [7]

Example 2:

Input: 2
Output: [8,4]

Example 3:

Input: 3
Output: [8,1,10]

Note:

1. rand7 is predefined.
2. Each testcase has one argument: n, the number of times that rand10 is called.

Follow up:

1. What is the expected value for the number of calls to rand7() function?
2. Could you minimize the number of calls to rand7()?

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题意

使用能够随机生成整数1-7的函数rand7()，来写一个新的函数rand10()，使其能够随机生成整数1-10。

思路

1. \(rand7()-1\) 生成整数 0-6
2. \((rand7()-1)\times7\) 生成整数 [0, 7, 14, ..., 42]
3. \((rand7()-1)\times7+rand7()\) 生成整数 1-49，即得到 rand49()
4. 利用拒绝采样来得到 1-40 范围内的随机整数num：通过rand49()得到一个数，如果大于40，则重新运行rand49()，否则赋值给num
5. \(num\ \%\ 10+1\) 得到 1-10 范围内的整数

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代码实现

Java

/**
 * The rand7() API is already defined in the parent class SolBase. public int
 * rand7();
 * 
 * @return a random integer in the range 1 to 7
 */
class Solution extends SolBase {
    public int rand10() {
        int num = (rand7() - 1) * 7 + rand7();
        return num <= 40 ? num % 10 + 1 : rand10();
    }
}