Python与数据结构[1] -> 栈/Stack[0] -> 链表栈与数组栈的 Python 实现

栈 / Stack

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目录

1. 链表栈
2. 数组栈

 

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：

1. 栈顶元素：栈顶元素即为链表的头结点
2. 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
3. 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

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1. 单链表