栈 / Stack
目录
栈是一种基本的线性数据结构（先入后出FILO），在 C 语言中有链表和数组两种实现方式，下面用 Python 对这两种栈进行实现。
1 链表栈
链表栈是以单链表为基础实现的栈数据结构，主要有以下几个关键点：
- 栈顶元素：栈顶元素即为链表的头结点
- 压栈：向链表的头结点插进入栈元素，无表头链表则替换插入元素为头结点
- 弹栈：弹出链表头结点，并将链表头结点替换为下一个元素
Stack based on linked list:
| item3 |
| | |
| V |
| item2 |
| | |
| V |
| item1 |
-------
完整代码
class StackEmptyException(Exception): pass class StackFullException(Exception): pass class Node:
def __init__(self, val=None, nxt=None):
self.value = val
self.next = nxt def __str__(self):
return str(self.value) class Stack:
"""
Stack based on linked list:
| item3 |
| | |
| V |
| item2 |
| | |
| V |
| item1 |
-------
"""
def __init__(self, max=0):
self._top = None
self._max = 0
self.max = max @property
def max(self):
return self._max @max.setter
def max(self, m):
m = int(m)
if m < self.length:
raise Exception('Resize stack failed, please pop some elements first.')
self._max = m
if self._max < 0:
self._max = 0 def init(self, iterable=()):
if not iterable:
return
self._top = Node(iterable[0])
for i in iterable[1:]:
node = self._top
self._top = Node(i)
self._top.next = node def show(self):
def _traversal(self):
node = self._top
while node and node.next:
yield node
node = node.next
yield node
print('\n'.join(map(lambda x: '|{:^7}|'.format(str(x)), _traversal(self)))+'\n '+7*'-') @property
def length(self):
if self._top is None:
return 0
node = self._top
i = 1
while node.next:
node = node.next
i += 1
return i @property
def is_empty(self):
return self._top is None @property
def is_full(self):
return bool(self._max and self.length == self._max) def push(self, item):
if self.is_full:
raise StackFullException('Error: trying to push element into a full stack!')
if not self._top:
self._top = Node(item)
return
node = self._top
self._top = Node(item)
self._top.next = node def pop(self):
if self.is_empty:
raise StackEmptyException('Error: trying to pop element from an empty stack!')
node = self._top
self._top = self._top.next
return node.value def top(self):
return self._top.value if self._top else self._top def clear(self):
while self._top:
self.pop() def test(stack):
print('\nShow stack:')
stack.show() print('\nInit linked list:')
stack.init([1, 2, 3, 4, 5])
stack.show() print('\nPush element to stack:')
stack.push(6)
stack.push(7)
stack.push('like')
stack.show() print('\nCheck top element:')
print(stack.top()) print('\nPop element from stack:')
e = stack.pop()
print('Element %s popped,' % e)
stack.show() print('\nSet stack max size:')
try:
stack.max = 1
except Exception as e:
print(e) print('\nSet stack max size:')
stack.max = 7
print(stack.max) print('\nPush full stack:')
try:
stack.push(7)
except StackFullException as e:
print(e) print('\nClear stack:')
stack.clear()
stack.show() print('\nStack is empty:')
print(stack.is_empty) print('\nPop empty stack:')
try:
stack.pop()
except StackEmptyException as e:
print(e) if __name__ == '__main__':
test(Stack())
分段解释
以链表为基础的栈实现，首先需要定义链表结点，以及栈满压栈和栈空弹栈的异常类，
class StackEmptyException(Exception): pass class StackFullException(Exception): pass class Node:
def __init__(self, val=None, nxt=None):
self.value = val
self.next = nxt def __str__(self):
return str(self.value)
定义栈类，主要包括两个属性，即栈顶元素和栈大小，
class Stack:
"""
Stack based on linked list:
| item3 |
| | |
| V |
| item2 |
| | |
| V |
| item1 |
-------
"""
def __init__(self, max=0):
self._top = None
self._max = 0
self.max = max
定义栈最大容量max为属性方法，当设置栈的最大容量值时，若传入的大小小于当前栈大小则提示异常，若传入0或负数大小，则设为无限容量的栈。
@property
def max(self):
return self._max @max.setter
def max(self, m):
m = int(m)
if m < self.length:
raise Exception('Resize stack failed, please pop some elements first.')
self._max = m
if self._max < 0:
self._max = 0
定义栈的init方法，用于初始化一个可迭代对象为栈结构，接受一个可迭代对象，当空栈时以第一个元素为栈顶，随后依次压栈，最后入栈的元素为栈顶元素。
def init(self, iterable=()):
if not iterable:
return
self._top = Node(iterable[0])
for i in iterable[1:]:
node = self._top
self._top = Node(i)
self._top.next = node
定义栈的show方法，用于显示栈，首先遍历栈元素，然后依照格式化输出，当空栈时则栈顶/底元素为None。
def show(self):
def _traversal(self):
node = self._top
while node and node.next:
yield node
node = node.next
yield node
print('\n'.join(map(lambda x: '|{:^7}|'.format(str(x)), _traversal(self)))+'\n '+7*'-')
定义栈的length属性方法，用于返回当前栈内元素数量，通过链表遍历计数实现（类似获取链表长度）。
@property
def length(self):
if self._top is None:
return 0
node = self._top
i = 1
while node.next:
node = node.next
i += 1
return i
定义栈的is_empty属性方法，用于判断栈是否为空栈。
@property
def is_empty(self):
return self._top is None
定义栈的is_full属性方法，用于判断栈容量是否已满。
@property
def is_full(self):
return bool(self._max and self.length == self._max)
定义栈的push方法，用于实现压栈过程，即向栈链前端插入入栈元素，栈满压栈则提示异常。
def push(self, item):
if self.is_full:
raise StackFullException('Error: trying to push element into a full stack!')
if not self._top:
self._top = Node(item)
return
node = self._top
self._top = Node(item)
self._top.next = node
定义栈的pop方法，用于实现弹栈过程，弹出栈顶元素并替换栈顶元素为下一个元素，栈空弹栈则提示异常。
def pop(self):
if self.is_empty:
raise StackEmptyException('Error: trying to pop element from an empty stack!')
node = self._top
self._top = self._top.next
return node.value
定义栈的top方法，用于获取栈顶元素，当栈顶元素为None时，返回None。
def top(self):
return self._top.value if self._top else self._top
定义栈的clear方法，用于清空栈，即依次弹栈至空栈。
def clear(self):
while self._top:
self.pop()
最后定义一个测试函数，用于对栈类进行操作测试。
首先实例化一个栈，并将一个列表元素依次压入栈中，最后显示栈元素
def test(stack):
print('\nShow stack:')
stack.show() print('\nInit linked list:')
stack.init([1, 2, 3, 4, 5])
stack.show()
得到结果
Show stack:
| None |
------- Init linked list:
| 5 |
| 4 |
| 3 |
| 2 |
| 1 |
-------
执行压栈操作，将元素压入栈中，
print('\nPush element to stack:')
stack.push(6)
stack.push(7)
stack.push('like')
stack.show()
得到结果
Push element to stack:
| like |
| 7 |
| 6 |
| 5 |
| 4 |
| 3 |
| 2 |
| 1 |
-------
检测栈顶元素并弹出栈顶元素
print('\nCheck top element:')
print(stack.top())
print('\nPop element from stack:')
e = stack.pop()
print('Element %s popped,' % e)
stack.show()
得到结果
Check top element:
like Pop element from stack:
Element like popped,
| 7 |
| 6 |
| 5 |
| 4 |
| 3 |
| 2 |
| 1 |
-------
尝试修改栈的最大容量，当修改容量小于当前栈内元素数量时，将会触发异常
print('\nSet stack max size:')
try:
stack.max = 1
except Exception as e:
print(e)
print('\nSet stack max size:')
stack.max = 7
print(stack.max)
得到结果
Set stack max size:
Resize stack failed, please pop some elements first. Set stack max size:
7
尝试对一个满元素栈进行压栈操作，将引发异常
print('\nPush full stack:')
try:
stack.push(7)
except StackFullException as e:
print(e)
得到结果
Push full stack:
Error: trying to push element into a full stack!
随后清空栈，并检查栈是否为空，最后尝试对空栈进行弹栈操作，同样会引发一个异常
print('\nClear stack:')
stack.clear()
stack.show()
print('\nStack is empty:')
print(stack.is_empty)
print('\nPop empty stack:')
try:
stack.pop()
except StackEmptyException as e:
print(e)
得到结果
Clear stack:
| None |
------- Stack is empty:
True Pop empty stack:
Error: trying to pop element from an empty stack!
2 数组栈
数组栈是栈的另一种实现方式，在C语言中以数组的形式实现，而在Python中，则可以使用与数组类似的列表进行实现。
Stack based on array/list:
| 4 |
| 3 |
| 2 |
| 1 |
-------
数组栈中需要实现的方法接口与链表栈相同。只是在数据存储时由链表变成了数组/列表。由于Python的列表本身即是一种很方便的线性结构，因此数组栈的实现十分简单。
完整代码
from linked_list_stack import StackEmptyException, StackFullException, test class Stack:
"""
Stack based on array/list:
| 4 |
| 3 |
| 2 |
| 1 |
-------
"""
def __init__(self, max=0):
self._array = []
self._max = 0
self.max = max @property
def max(self):
return self._max @max.setter
def max(self, m):
m = int(m)
if m < self.length:
raise Exception('Resize stack failed, please pop some elements first.')
self._max = m
if self._max < 0:
self._max = 0 def init(self, iterable=()):
if not iterable:
return
for i in iterable:
self._array.append(i) def show(self):
def _traversal(self):
if not self._array:
return [None]
return self._array[::-1]
print('\n'.join(map(lambda x: '|{:^7}|'.format(str(x)), _traversal(self)))+'\n '+7*'-') @property
def length(self):
return len(self._array) @property
def is_empty(self):
return self._array == [] @property
def is_full(self):
return bool(self._max and self.length == self._max) def push(self, item):
if self.is_full:
raise StackFullException('Error: trying to push element into a full stack!')
self._array.append(item) def pop(self):
if self.is_empty:
raise StackEmptyException('Error: trying to pop element from an empty stack!')
return self._array.pop() def top(self):
return self._array[-1] def clear(self):
# self._array = []
while self._array:
self.pop() if __name__ == '__main__':
test(Stack())
分段解释
首先从链表栈中导入两个异常类和测试函数，
from linked_list_stack import StackEmptyException, StackFullException, test
然后定义栈类，与链表栈不同的地方在于，存储数据的方式换成了列表
class Stack:
"""
Stack based on array/list:
| 4 |
| 3 |
| 2 |
| 1 |
-------
"""
def __init__(self, max=0):
self._array = []
self._max = 0
self.max = max
与前面的链表栈一样，定义栈的容量。
@property
def max(self):
return self._max @max.setter
def max(self, m):
m = int(m)
if m < self.length:
raise Exception('Resize stack failed, please pop some elements first.')
self._max = m
if self._max < 0:
self._max = 0
定义栈的init方法，添加入栈元素时只需要在列表末尾加入元素即可，
def init(self, iterable=()):
if not iterable:
return
for i in iterable:
self._array.append(i)
下面的几个方法与链表栈类似，只是操作时换成了对数组列表的检测，
def show(self):
def _traversal(self):
if not self._array:
return [None]
return self._array[::-1]
print('\n'.join(map(lambda x: '|{:^7}|'.format(str(x)), _traversal(self)))+'\n '+7*'-') @property
def length(self):
return len(self._array) @property
def is_empty(self):
return self._array == [] @property
def is_full(self):
return bool(self._max and self.length == self._max)
定义栈的push方法，实现压栈操作，压栈只需要对列表进行append即可，
def push(self, item):
if self.is_full:
raise StackFullException('Error: trying to push element into a full stack!')
self._array.append(item)
定义栈的pop方法，实现弹栈操作，弹栈只需要对列表进行pop即可，
def pop(self):
if self.is_empty:
raise StackEmptyException('Error: trying to pop element from an empty stack!')
return self._array.pop()
定义栈的top方法，实现栈顶元素获取，返回列表最后一位元素即可，
def top(self):
return self._array[-1]
定义栈的clear方法，实现栈的清空操作，可以直接清空数组列表或依次将栈内元素弹出栈，
def clear(self):
# self._array = []
while self._array:
self.pop()
最后，利用测试函数对数组栈进行测试
if __name__ == '__main__':
test(Stack())
得到结果与链表栈相同
Show stack:
| None |
------- Init linked list:
| 5 |
| 4 |
| 3 |
| 2 |
| 1 |
------- Push element to stack:
| like |
| 7 |
| 6 |
| 5 |
| 4 |
| 3 |
| 2 |
| 1 |
------- Check top element:
like Pop element from stack:
Element like popped,
| 7 |
| 6 |
| 5 |
| 4 |
| 3 |
| 2 |
| 1 |
------- Set stack max size:
Resize stack failed, please pop some elements first. Set stack max size:
7 Push full stack:
Error: trying to push element into a full stack! Clear stack:
| None |
------- Stack is empty:
True Pop empty stack:
Error: trying to pop element from an empty stack!
相关阅读
1. 单链表