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一、什么是单调栈？先打破 “栈” 的常规认知
提到栈，大家首先想到的是 “先进后出” 的线性结构，而单调栈，顾名思义，就是在普通栈的基础上，给元素加上了 “单调性” 的约束 —— 栈内的元素必须严格保持递增或递减（也可根据需求调整为非严格递增 / 递减）。

1.1 单调栈的核心特性
本质还是栈：完全遵循栈的 “先进后出” 规则，只是多了 “维护单调性” 的操作；
单调性可控：可维护单调递增栈（栈底到栈顶元素从小到大），也可维护单调递减栈（栈底到栈顶元素从大到小）；
操作高效：每个元素最多入栈一次、出栈一次，整体时间复杂度稳定在 O (n)。
1.2 如何实现一个单调栈？
话不多说，先看基础代码实现。我们以 C++ 为例，分别实现单调递增栈和单调递减栈：

1.3 核心操作解析：为什么要 “弹出元素”？
大家可能会疑惑：“为什么要先弹出元素再入栈？” 其实这正是单调栈的核心 ——为了保证栈的单调性不被破坏。

比如维护单调递增栈时，若当前元素a[i]比栈顶元素小，说明栈顶元素 “挡路” 了：如果直接入栈，栈就会出现 “大元素在前、小元素在后” 的情况，违背递增规则。因此需要先弹出所有≥a[i]的元素，直到栈顶元素＜a[i]（或栈为空），再将a[i]入栈。

举个直观的例子：假设数组a = [5, 3, 7, 2]，维护单调递增栈的过程：

i=1，a [i]=5：栈空，直接入栈 → 栈：[5]
i=2，a [i]=3：栈顶 5≥3，弹出 5；栈空，入栈 3 → 栈：[3]
i=3，a [i]=7：栈顶 3＜7，直接入栈 → 栈：[3,7]
i=4，a [i]=2：栈顶 7≥2，弹出 7；栈顶 3≥2，弹出 3；栈空，入栈 2 → 栈：[2]
最终栈内元素为 [2]，完美保持递增特性。

二、单调栈能解决什么问题？四大核心场景全覆盖
单调栈的核心应用场景，总结起来就是 “找最近最值”—— 给定一个元素，找到它左侧 / 右侧最近的、比它大 / 小的元素的位置。这四类问题看似不同，实则原理相通，掌握一种就能举一反三。

先记住一句 “口诀”：找左侧，正遍历；找右侧，逆遍历；比它大，单调减；比它小，单调增。这句话能帮你快速确定遍历方向和栈的单调性，下文会反复验证。

2.1 场景 1：找左侧最近的 “更大元素”
问题描述
给定数组a，对于每个元素a[i]，找到其左侧第一个比它大的元素的下标；若不存在，返回 0。
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