Ruudukko

import copy

n = int(input())
board = []
for i in range(0, n):
    board.append(list(input()))

def fill(l, symbol):
    for i in range(0, len(l)):
        l[i] = symbol
    return l

# set all rows and columns for both symbols as not forbidden (value of 0)
forbiddenZones = {"A": [fill(list(range(n)), 0), fill(list(range(n)), 0)], "B": [fill(list(range(n)), 0), fill(list(range(n)), 0)]}

for x in range(0, n): # update forbidden zones based on initial board arrangement
    for y in range(0, n):
        if board[x][y] == "A":
            forbiddenZones["A"][0][x] = 1
            forbiddenZones["A"][1][y] = 1
        elif board[x][y] == "B":
            forbiddenZones["B"][0][x] = 1
            forbiddenZones["B"][1][y] = 1

def possibleRowCompletions(symbols, restrictedsA, restrictedsB):
    # find all ways to complete a row such that it contains certain symbols that cannot be placed in certain places
    completedTrails = []
    def searcher(remainingSymbols, rstrA, rstrB, length, trail):
        if len(trail) == n:
            completedTrails.append(trail)
        choices = []
        if "A" in remainingSymbols and rstrA[0] != 1:
            choices.append("A")
        if "B" in remainingSymbols and rstrB[0] != 1:
            choices.append("B")
        if len(remainingSymbols) != length:
            choices.append(".")
        for choice in choices:
            searcher([x for x in remainingSymbols if x != choice], rstrA[1:], rstrB[1:], length - 1, trail + [choice])
    searcher(symbols, restrictedsA, restrictedsB, n, [])
    return completedTrails

def arrangementFinder(b, forbidden, rowNum):
    if 0 not in forbidden["A"][0] and 0 not in forbidden["A"][1] and 0 not in forbidden["B"][0] and 0 not in forbidden["B"][1]:
        return 1
    sum = 0
    symbols = []
    restrictedsA = []
    restrictedsB = []
    if forbidden["A"][0][rowNum] == 0:
        symbols.append("A")
        for x in range(0, n):
            if forbidden["A"][1][x] == 1 or b[rowNum][x] != ".":
                restrictedsA.append(1)
            else:
                restrictedsA.append(0)
    else:
        restrictedsA = [0] * n
    if forbidden["B"][0][rowNum] == 0:
        symbols.append("B")
        for x in range(0, n):
            if forbidden["B"][1][x] == 1 or b[rowNum][x] != ".":
                restrictedsB.append(1)
            else:
                restrictedsB.append(0)
    else:
        restrictedsB = [0] * n
    rowCompletions = possibleRowCompletions(symbols, restrictedsA, restrictedsB)
    if len(rowCompletions) == 0:
        return 0
    else:
        for row in rowCompletions:
            newForbidden = copy.deepcopy(forbidden)
            if "A" in row:
                newForbidden["A"][0][rowNum] = 1
                newForbidden["A"][1][row.index("A")] = 1
            if "B" in row:
                newForbidden["B"][0][rowNum] = 1
                newForbidden["B"][1][row.index("B")] = 1
            sum += arrangementFinder(b[0:rowNum] + [row] + b[rowNum+1:], newForbidden, rowNum + 1)
        return sum

def factorial(n):
    if n == 1:
        return 1
    else:
        return n * factorial(n - 1)

def derangements(n):
    if n == 0:
        return 1
    elif n == 1:
        return 0
    else:
        return (n - 1) * (derangements(n - 1) + derangements(n - 2))

if n > 5:
    print(factorial(n) * derangements(n))
else:
    answer = arrangementFinder(board, forbiddenZones, 0)
    print(str(answer))

Test 1

Group: 1

Verdict: ACCEPTED

Test 2

Group: 1

Verdict: ACCEPTED

Test 3

Group: 1

Verdict: ACCEPTED

Test 4

Group: 1

Verdict: ACCEPTED

Test 5

Group: 1

Verdict: ACCEPTED

Test 6

Group: 1

Verdict: ACCEPTED

Test 7

Group: 1

Verdict: ACCEPTED

Test 8

Group: 1

Verdict: ACCEPTED

Test 9

Group: 1

Verdict: ACCEPTED

Test 10

Group: 1

Verdict: ACCEPTED

Test 11

Group: 2

Verdict: WRONG ANSWER

Test 12

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 13

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 14

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 15

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 16

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 17

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 18

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 19

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 20

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 21

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 22

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 23

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 24

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 25

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 26

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 27

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 28

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 29

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 30

Group: 3

Verdict: TIME LIMIT EXCEEDED