阶乘：
# 循环实现阶乘
def factorial_iteration(n):
result = 1
for i in range(1, n + 1):
result *= i
return result
# d递归实现阶乘
def factorial_recursion(n):
if n == 1:
return 1
else:
return n * factorial_recursion(n - 1)
print(factorial_recursion(3))
print(factorial_iteration(3))
斐波那契：
# 循环实现斐波那契
def fibonacci_iteration(n):
n1 = 1
n2 = 1
n3 = 1
if n < 1: # 斐波那契数列必须从2开始
return -1
while (n - 2) > 0:
n3 = n2 + n1
n1 = n2
n2 = n3
n -= 1
return n3
print(list(map(fibonacci_iteration, range(1, 12))))
# 递归实现斐波那契
def fibonacci_recursion(n):
if n < 1:
return -1
if n == 1 or n == 2:
return 1
else:
return fibonacci_recursion(n - 1) + fibonacci_recursion(n - 2)
print(list(map(fibonacci_recursion, range(1, 12))))
汉诺塔：
# 递归实现汉诺塔
def hanoi_recursion(n, x, y, z):
if n == 1:
print(x, "-->", z)
else:
# 将前 n-1 个物体从x移动到y上
hanoi_recursion(n - 1, x, z, y)
print(x, "-->", z) # 将最底下的最后一个盘子从x移动到z上
hanoi_recursion(n - 1, y, x, z)
hanoi_recursion(6, "x", "y", "z")
# Python 循环实现汉诺塔
class Disk:
def __init__(self, name, disk=0):
self.name = name
if disk:
self.p = [i for i in range(disk, 0, -1)]
else:
self.p = []
def name(self):
return self.name
def get_disk_counts(self):
return len(self.p)
def get_top_disk(self):
disk_counts = self.get_disk_counts()
if disk_counts:
return self.p[disk_counts - 1]
return None
def move_disk(self):
self.p.pop()
def add_disk(self, new_disk):
self.p.append(new_disk)
class Hanoi:
def __init__(self, x, y, z, disk=1):
self.disk = disk
self.X = Disk(x, disk)
self.Y = Disk(y)
self.Z = Disk(z)
def get_move_obj(self, box):
move_obj = box[0].get_top_disk(), box[0].name
if move_obj[0]:
if box[1].get_top_disk() and move_obj[0] > box[1].get_top_disk():
move_obj = box[1].get_top_disk(), box[1].name
box[1].move_disk()
else:
box[0].move_disk()
else:
move_obj = box[1].get_top_disk(), box[1].name
box[1].move_disk()
return move_obj
def to_next(self, num, x):
if self.disk % 2 == 0:
sequence = {'x': 'y', 'y': 'z', 'z': 'x'}
else:
sequence = {'x': 'z', 'z': 'y', 'y': 'x'}
for i in [self.X, self.Y, self.Z]:
if i.name == sequence[x]:
if not i.get_top_disk():
return i
if num < i.get_top_disk():
return i
return self.name2obj(sequence[i.name])
def name2obj(self, x):
for i in [self.X, self.Y, self.Z]:
if i.name == x:
return i
def move(self):
seq = [self.X, self.Y]
while self.Z.get_disk_counts() < self.disk:
move_obj = self.get_move_obj(seq)
next_obj = self.to_next(move_obj[0], move_obj[1])
next_obj.add_disk(move_obj[0])
seq = [self.X, self.Y, self.Z]
seq.remove(next_obj)
print('%c --> %c' % (move_obj[1], next_obj.name))
if __name__ == '__main__':
hanoi = Hanoi("x", "y", "z", disk=5)
hanoi.move()
