Kortit II

mod_by = 10**9 + 7

def factorial(n)
  (1..n).reduce(1, :*)
end

def choose(a, b)
  # a choose b
  (factorial(a) / (factorial(b) * factorial(a-b))).to_i
end

def slow_ass_recursive_function(played_moves, moves_left, p1_wins)
  if moves_left.length == 0
    p1_wins_calc = 0
    played_moves.each_with_index do |move, idx|
      if move < idx + 1
        p1_wins_calc += 1
      end
      if p1_wins_calc > p1_wins
        return 0
      end
    end
    if p1_wins_calc < p1_wins
      return 0
    else
      return 1
    end
  end

  total = 0
  played_moves_len = played_moves.length + 1
  moves_left.each do |move|
    if move == played_moves_len
      next
    end
    total += slow_ass_recursive_function(played_moves + [move], moves_left - [move], p1_wins)
  end
  return total
end

row_count = gets.chomp.to_i
rows = []
row_count.times do
  rows.append(gets.chomp.split(" ").map(&:to_i))
end

rows.each do |row|
  n = row[0]
  original_n = n
  p1_wins = row[1]
  p2_wins = row[2]
  p1_moves = []
  p2_moves = []

  if p1_wins + p2_wins > n
    puts(0)
    next
  end

  draws = n - p1_wins - p2_wins
  
  # we need to choose "draws" from n
  # ways_to_draw = n choose draws
  # this gives us the number of possible choices of numbers to draw with
  # in the end you should multiply this with ways_to_choose_other_numbers and multiply it by its factorial (unique orderings of the solution)
  ways_to_choose_drawing_numbers = choose(n, draws)
  
  n -= draws
  
  if (p1_wins + p2_wins > 0) && (p1_wins == 0 || p2_wins == 0)
    puts(0)
    next
  end

  ways_to_choose_other_numbers = slow_ass_recursive_function([], (1..n).to_a, p1_wins)

  # code here
  # note: we can fix p1 moves to be [0...n] since the permutations of the final moves are already accounted for
  
  # start => n! * draws * other
  # 3 1 2 => 3! * 1 * 1
  # 2 0 1 => 0
  # 5 2 2 => 5! * 5 * 7
  # note: f(2, 2) => 7
  # 9 3 5 => 9! * 9 * 3361
  # note: f(3, 5) => 3361
  # 4 4 1 => 0

  puts(
    (ways_to_choose_drawing_numbers * ways_to_choose_other_numbers * factorial(original_n)) % (mod_by)
  )
end

Test 1

Group: 1, 2, 3, 4, 5

Verdict: ACCEPTED

Test 2

Group: 2, 3, 4, 5

Verdict: ACCEPTED

Test 3

Group: 3, 4, 5

Verdict: TIME LIMIT EXCEEDED

Test 4

Group: 4, 5

Verdict: TIME LIMIT EXCEEDED

Test 5

Group: 5

Verdict: TIME LIMIT EXCEEDED

Test 6

Group: 5

Verdict: TIME LIMIT EXCEEDED