Introduction

In this blog post, we will explore how to solve the LeetCode problem "470" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

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(). Example 1: Input: n = 1 Output: [2] Example 2: Input: n = 2 Output: [2,8] Example 3: Input: n = 3 Output: [3,8,10] Constraints: 1 <= n <= 105 Follow up: What is the expected value for the number of calls to rand7() function? Could you minimize the number of calls to rand7()?

Explanation

Here's a breakdown of the solution:

• Rejection Sampling: The core idea is to generate a larger range using rand7() calls and then reject values that fall outside the desired range (1-10). This ensures uniformity within the 1-10 range.
• Creating a Larger Range: We combine the results of multiple rand7() calls to create a wider range. Specifically, (rand7() - 1) * 7 + rand7() creates a range of 1-49.

• Optimizing Calls: We attempt to minimize rand7() calls. If the generated value is greater than 40, we reject it and repeat. However, each time we reject, we can reuse the "leftover" range. For instance, if we obtain a value between 41 and 49, we can map the value to 1-9, and combined with another rand7 call get the 1-63 range. With this range we can generate a result between 1-60 and map the range 1-60 to 1-10.

• Runtime & Storage Complexity: The runtime complexity is O(1) on average, but can be O(infinity) in the worst case (though highly improbable). The storage complexity is O(1).

Code

    def rand10():
    """
    :rtype: int
    """
    while True:
        # Generate a number in the range 1-49
        num = (rand7() - 1) * 7 + rand7()

        # If the number is in the range 1-40, we can map it to 1-10
        if num <= 40:
            return (num % 10) + 1

        # If the number is in the range 41-49, we can map it to 1-9
        num = num - 40

        #Generate a number in the range 1-63 (9*7)
        num = (num - 1) * 7 + rand7()

        if num <= 60:
            return (num % 10) + 1
        #If the number is in the range 61-63, we can map it to 1-3
        num = num - 60
        num = (num-1)*7 + rand7()
        if num <= 21:
            return (num % 10) + 1
def rand7():
    import random
    return random.randint(1, 7)