Submission #188384

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Source Code Expand

n, d = gets.chomp.split.map(&:to_i)
x, y = gets.chomp.split.map(&:to_i)

grid_x = x / d
grid_y = y / d

if grid_x * d != x || grid_y * d != y
  puts "0"; exit
end

redundant = n - grid_x - grid_y
if redundant < 0 || redundant % 2 != 0
  puts "0"; exit
end

whole = 4 ** n
patterns = 0

def comb(a, b)
  a.times.inject(1){|prod, i|prod * (b - i) / (i + 1)}
end

redundant /= 2
(0..redundant).each do |grid_xr|
  grid_yr = redundant - grid_xr
  # +x: grid_x + grid_xr times
  # -x: grid_xr times
  # +y: grid_y + grid_yr times
  # -y: grid_yr times
  grid_xp = grid_x + grid_xr
  grid_yp = grid_y + grid_yr

  patterns += comb(grid_xr, grid_xp + grid_xr) *
      comb(grid_yp, grid_xp + grid_xr + grid_yp) *
      comb(grid_yr, grid_xp + grid_xr + grid_yp + grid_yr)
end

puts Rational(patterns, whole).to_f

Submission Info

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