Kertoma

import math
 
# 0 0 1 => 2
# 1 1 1 0 0 0 0 0 0 0 => 5
# 42 25 24 16 15 16 21 14 17 16 => 123
# 2 0 1 1 0 0 1 0 2 0 => 10
def main():
    input_array = get_input()
    INPUT_DIGIT_COUNT = sum(input_array)
 
    # magic number that represents the maximum amount of digits, if you calculate (10*10^5)! 
    # 10*10^5 means the maxkimum amount of input digits in subtask 3
    UPPER_X_BOUND = 210000      
    min_guess = 2
    max_guess = UPPER_X_BOUND
    while(True):
        average = round((max_guess - min_guess) / 2) + min_guess
        guess_digit_count = get_factorial_digit_count(average)
        if (guess_digit_count < INPUT_DIGIT_COUNT):
            min_guess = average
        elif (guess_digit_count > INPUT_DIGIT_COUNT):
            max_guess = average
        else:
            result = increase_accuracy(average, input_array, INPUT_DIGIT_COUNT)
            print(result)
            break
 
def get_input():
    x = input().split()
    return [eval(i) for i in x]
 
def get_factorial_digit_count(number : int) -> int:
    # if negative or less than 2 => automatically has only 1 digit
    if (number < 2): return 1   
    return math.floor(math.log10(math.factorial(number))) + 1
 
def count_specific_digit(number : int, digit : str) -> int:
    return str(number).count(str(digit))
 
# check if number matches input array
def try_match(guess : int, input_array) -> bool:
    factorial = math.factorial(guess)
    for i in range(len(input_array)):
        count = count_specific_digit(factorial, i)
        if (input_array[i] != count):
            return -1
        if (i == len(input_array) - 1):
            return guess
 
def increase_accuracy(guess : int, input_array, input_digit_count : int) -> int:
    # digit count should not match even the close numbers
    if (guess > 200): return guess
    if (try_match(guess, input_array) != -1): 
        return guess
 
    wannabe_guess = guess - 1
    while (get_factorial_digit_count(wannabe_guess) == input_digit_count):
        if (try_match(wannabe_guess, input_array)): 
            return wannabe_guess
        wannabe_guess -= 1
 
    wannabe_guess = guess + 1
    while (get_factorial_digit_count(wannabe_guess) == input_digit_count):
        if (try_match(wannabe_guess, input_array)): 
            return wannabe_guess
        wannabe_guess += 1
 
    raise ValueError(f"Cannot find value for input array {input_array}")
 
 
 
 
main()

Test 1

Group: 1, 2, 3

Verdict: ACCEPTED

Test 2

Group: 1, 2, 3

Verdict: ACCEPTED

Test 3

Group: 1, 2, 3

Verdict: ACCEPTED

Test 4

Group: 1, 2, 3

Verdict: ACCEPTED

Test 5

Group: 1, 2, 3

Verdict: ACCEPTED

Test 6

Group: 1, 2, 3

Verdict: ACCEPTED

Test 7

Group: 2, 3

Verdict: ACCEPTED

Test 8

Group: 2, 3

Verdict: ACCEPTED

Test 9

Group: 2, 3

Verdict: ACCEPTED

Test 10

Group: 2, 3

Verdict: ACCEPTED

Test 11

Group: 3

Verdict: ACCEPTED

Test 12

Group: 3

Verdict: ACCEPTED

Test 13

Group: 3

Verdict: ACCEPTED

Test 14

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 15

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 16

Group: 3

Verdict: TIME LIMIT EXCEEDED