def encode(n, m)
  str = []
  for i in 1..n
    if m % 2 == 0
      m = m / 2
      str.unshift('0')
    else
      m = (m - 1) / 2
      str.unshift('1')
    end
  end
  return str.join
end
 
for i in 0..7
  printf "%s %d\n", encode(3, i), i
end

def decode(n, vrtta)
  if vrtta.kind_of?(String)
    if vrtta.length != n
      raise TypeError
    else
      a = 1; sum = 0
      for i in 0...n
        if vrtta[n-1-i].chr == '1'
          sum += a
        end
        a <<= 1
      end
      return sum
    end
  else
    raise TypeError
  end
end
 
table = ["000","001","010","011","100","101","110","111"]
for vrtta in table
  printf "%s %d\n", vrtta, decode(3, vrtta)
end

# 算術三角形の作成
# C[k][j] : 二項係数
max = 10
C = Array.new(max) { Array.new(max) { 0 } }
C[0][0] = 1
for k in 1...max
  C[k][0] = C[k-1][0]
  for j in 1..k
    C[k][j] = C[k-1][j-1] + C[k-1][j]
  end
end
 
# 算術三角形の印字
for k in 0...max
  for j in 0..k
    printf " %3d", C[k][j]
  end
  print "\n\n"
end