Leetcode #470: Implement Rand10() Using Rand7()
In this guide, we solve Leetcode #470 Implement Rand10() Using Rand7() in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
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.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Math, Rejection Sampling, Probability and Statistics, Randomized
Intuition
There is a mathematical invariant or formula that directly leads to the result.
Using math avoids unnecessary loops and reduces complexity.
Approach
Derive the formula or update rule, then compute the answer directly.
Handle edge cases like overflow or zero carefully.
Steps:
- Identify the math relationship.
- Compute the result with a loop or formula.
- Handle edge cases.
Example
Input: n = 1
Output: [2]
Python Solution
# The rand7() API is already defined for you.
# def rand7():
# @return a random integer in the range 1 to 7
class Solution:
def rand10(self):
"""
:rtype: int
"""
while 1:
i = rand7() - 1
j = rand7()
x = i * 7 + j
if x <= 40:
return x % 10 + 1
Complexity
The time complexity is O(n) or O(1). The space complexity is O(1).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.