Leetcode #2847: Smallest Number With Given Digit Product
In this guide, we solve Leetcode #2847 Smallest Number With Given Digit Product 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 a positive integer n, return a string representing the smallest positive integer such that the product of its digits is equal to n, or "-1" if no such number exists. Example 1: Input: n = 105 Output: "357" Explanation: 3 * 5 * 7 = 105.
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: Greedy, Math
Intuition
A locally optimal choice leads to a globally optimal result for this structure.
That means we can commit to decisions as we scan without backtracking.
Approach
Sort or preprocess if needed, then repeatedly take the best available local choice.
Maintain the minimal state necessary to validate the greedy decision.
Steps:
- Sort or preprocess as needed.
- Iterate and pick the best local option.
- Track the current solution.
Example
Input: n = 105
Output: "357"
Explanation: 3 * 5 * 7 = 105. It can be shown that 357 is the smallest number with a product of digits equal to 105. So the answer would be "357".
Python Solution
class Solution:
def smallestNumber(self, n: int) -> str:
cnt = [0] * 10
for i in range(9, 1, -1):
while n % i == 0:
n //= i
cnt[i] += 1
if n > 1:
return "-1"
ans = "".join(str(i) * cnt[i] for i in range(2, 10))
return ans if ans else "1"
Complexity
The time complexity is , and the space complexity is . The space complexity is .
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.