Smallest Number with Given Digit Product

Given a positive integer 'N', find and return the smallest number 'M', such that the product of all the digits in 'M' is equal to 'N'. If such an 'M' is not possible or if 'M' cannot fit in a 32-bit signed integer, return 0.

Example:

Input:

N = 90

Output:

259

Explanation:

For 'N' = 90, the possible values for 'M' include 259 (2*5*9 = 90), 3352 (3*3*5*2 = 90), 2335 (2*3*3*5 = 90), and 952 (9*5*2 = 90), among others. The smallest possible 'M' is 259, hence, the answer is 259.

Constraints:

1

Question

Smallest Number with Given Digit Product

Given a positive integer 'N', find and return the smallest number 'M', such that the product of all the digits in 'M' is equal to 'N'. If such an 'M' is not possible or if 'M' cannot fit in a 32-bit signed integer, return 0.

Example:

Input:

N = 90

Output:

Explanation:

For 'N' = 90, the possible values for 'M' include 259 (2*5*9 = 90), 3352 (3*3*5*2 = 90), 2335 (2*3*3*5 = 90), and 952 (9*5*2 = 90), among others. The smallest possible 'M' is 259, hence, the answer is 259.

Constraints:

1 <= T <= 1000
1 <= N <= 10⁹
Time limit: 1 sec

Accepted Answer

Find the smallest number whose digits multiply to a given number N.

Iterate through possible digits to form the smallest number with product equal to N
Use a priority queue to keep track of the smallest possible number
Check constraints to ensure the number fits in a 32-bit signed integer