470. Implement Rand10() Using Rand7()

LeetCode 470. Implement Rand10() Using Rand7()****

Description

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

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

Follow up:

• What is the expected value for the number of calls to rand7() function?

• Could you minimize the number of calls to rand7()?

Example 1:

Input: n = 1
Output: [2]

Example 2:

Input: n = 2
Output: [2,8]

Constraints:

• 1 <= n <= 105

Tags

Math

Solution

We randomly choose a position via (row-1)*7 + (col-1) in the table above, and repeat this procedure until we can obtain a number between 1 and 10 rather than '*'.

Complexity

• Time complexity: $O(1) \rightarrow O(\infty)$

• Space complexity: $O(1)$

Code

func rand10() int {
	t := 40
	for t >= 40 {
		t = (rand7()-1)*7 + (rand7() - 1)
	}
	return t%10 + 1
}

Reference

1. 用 Rand7() 实现 Rand10()