Is Minimum Factorization easy or hard?

Minimum Factorization is typically rated Medium difficulty. The implementation is short, but recognizing the greedy factorization idea is the main challenge. Once you identify that digits 2–9 represent factors of the product, the rest of the solution becomes straightforward.

Minimum Factorization Python/Java solution

Most implementations iterate digits from 9 to 2 and repeatedly divide the number while possible. The digits are stored in a list, then reversed to construct the smallest integer. The same logic works across Python, Java, C++, and Go with O(log a) time complexity.

How to solve Minimum Factorization in O(log n)?

Factor the number using digits 9 through 2. For each digit, repeatedly divide the input while it remains divisible and store that digit. After processing all digits, rebuild the number from the collected digits in reverse order. If the remainder is greater than 1 or the result exceeds a 32-bit integer, return 0.

What is the best approach for Minimum Factorization?

The optimal solution uses greedy digit factorization. Divide the number by digits from 9 down to 2 and collect those digits whenever they evenly divide the value. This minimizes the total digit count and guarantees the smallest resulting integer. The approach runs in O(log a) time because the value shrinks with each division.

Is Minimum Factorization asked at Google/Amazon/Meta?

Minimum Factorization represents a typical math and greedy interview problem seen in coding interviews at large tech companies. Variants of digit factorization or greedy decomposition appear in interviews at companies like Google, Amazon, and Meta because they test number reasoning and optimization.

What data structure is used in Minimum Factorization?

The solution mainly uses simple variables and often a list or stack to store the digits extracted during factorization. After collecting digits, they are reversed or appended to build the final integer. No complex data structures are required beyond basic arrays or strings.

What is the time complexity of Minimum Factorization?

The greedy factorization algorithm runs in O(log a) time since each successful division reduces the number. The space complexity is also O(log a) because the resulting digits must be stored before forming the final integer. Brute force alternatives are exponential and impractical.

625. Minimum Factorization - Practice Online

Given a positive integer num, return the smallest positive integer x whose multiplication of each digit equals num. If there is no answer or the answer is not fit in 32-bit signed integer, return 0.

Example 1:

Input: num = 48
Output: 68

Example 2:

Input: num = 15
Output: 35

Constraints:

1 <= num <= 2³¹ - 1