栈之道：LIFO的简约之美

栈的本质与约束之美

栈是一种遵循**后进先出（LIFO）**原则的线性数据结构。这种看似简单的约束（仅允许在栈顶插入或删除）恰恰是其强大之处。约束简化了操作逻辑，使得栈在编译器、操作系统等场景中成为不可替代的工具。

核心操作仅有两个：

push(x)：将元素x压入栈顶
pop()：弹出并返回栈顶元素

数学表达式可描述为： S.push(x) → S = [..., x] S.pop() → x, S = [...]

栈的底层实现剖析

数组实现（顺序栈）：

class ArrayStack:
    def __init__(self):
        self._data = []

    def push(self, x):
        self._data.append(x)

    def pop(self):
        return self._data.pop()

时间复杂度：push/pop均为O(1)，但可能触发动态数组扩容。

链表实现（链式栈）：

class LinkedStack:
    class _Node:
        __slots__ = 'val', 'next'
        def __init__(self, val, next=None):
            self.val = val
            self.next = next

    def __init__(self):
        self._top = None

    def push(self, x):
        self._top = self._Node(x, self._top)

    def pop(self):
        res = self._top.val
        self._top = self._top.next
        return res

无需考虑扩容问题，每个操作严格O(1)时间复杂度。

栈的典型应用场景

函数调用栈：每次函数调用时，系统栈会压入活动记录（包含参数、返回地址等）。递归的本质就是栈的应用，栈深度限制决定了递归深度。

表达式求值：处理3 + 4 * (2 - 1)这类表达式时：

操作数栈：[3, 4, 2, 1]
遇到)时弹出操作符-计算2-1=1
继续处理*得到4*1=4
最后处理+得到7

浏览器历史记录：前进后退功能通过双栈实现：

栈A存储已访问页面
后退时将栈A顶页面压入栈B
前进时从栈B弹回栈A

栈的约束力量体现

括号匹配校验：遇到左括号压栈，右括号时检查栈顶是否匹配：

def is_valid(s: str) -> bool:
    stack = []
    pairs = {')':'(', '}':'{', ']':'['}
    for ch in s:
        if ch in pairs.values():
            stack.append(ch)
        elif stack and pairs[ch] == stack[-1]:
            stack.pop()
        else:
            return False
    return not stack

单调栈应用：解决"下一个更大元素"类问题。维护栈内元素单调递减，遇到破坏单调性的元素时触发计算：

def next_greater(nums):
    res = [-1] * len(nums)
    stack = []
    for i in range(len(nums)):
        while stack and nums[stack[-1]] < nums[i]:
            res[stack.pop()] = nums[i]
        stack.append(i)
    return res

栈的扩展变体

最小栈：在O(1)时间内获取栈中最小值。辅助栈同步记录当前最小值：

class MinStack:
    def __init__(self):
        self.data = []
        self.min_stack = []

    def push(self, x):
        self.data.append(x)
        if not self.min_stack or x <= self.min_stack[-1]:
            self.min_stack.append(x)

    def pop(self):
        x = self.data.pop()
        if x == self.min_stack[-1]:
            self.min_stack.pop()
        return x

    def getMin(self):
        return self.min_stack[-1]

共享栈：两个栈共享同一数组空间，分别从两端向中间生长。这种设计可有效利用内存空间，适用于内存受限环境。

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