Python實現的帕斯卡三角形

帶有緩存的迭代器

# 帕斯卡三角形

mCache = {}
def pascalWithDict(n,k):
  if n==k or k==0 or n==1:
    return 1
  if k==1:
    return n
  if mCache.has_key((n,k)):
    return mCache[(n,k)]
  else:
    mCache[n,k] = pascalWithDict(n-1,k-1)+pascalWithDict(n-1,k)
    return mCache[n,k]

## 得到每行pascal列表
def generatePascal(depth):
  lines = []
  for row in range(depth):
    line = []
    for col in range(row+1):
      line.append(pascal(row, col))
    lines.append(line)
  return lines

if __name__ == "__main__":
  high = int(raw_input("pls enter the height of pascal:"))
  lines = generatePascal(high)
  for i in range(high):
    print lines[i]

結果以下：

pls enter the height of pascal:6
[1]
[1, 1]
[1, 2, 1]
[1, 3, 3, 1]
[1, 4, 6, 4, 1]
[1, 5, 10, 10, 5, 1]

使用裝飾器的迭代器

from functools import wraps

def memo(func):
  cache={}
  @wraps(func)
  def wrap(*args):
    if args not in cache:
      cache[args]=func(*args)
    return cache[args]
  return wrap

@memo
def pascal(n,k):
  if n==k or k==0 or n==1:
    return 1
  if k==1:
    return n
  return pascal(n-1,k-1)+pascal(n-1,k)

跳舞的數字[Just for fun]

if __name__ == "__main__":
  #depth = int(raw_input("pls enter the depth of pascal:"))
  for depth in range(100):
    lines = generatePascal(depth)
    for i in range(depth):
      print lines[i]