> For the complete documentation index, see [llms.txt](https://docs.1l.lol/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.1l.lol/algorithm-techniques/monotonic.md).

# 单调栈与单调队列

### 单调栈

栈内元素保持单调，常用于求“**下一个更大 / 更小元素**”。

```cpp
// 每个元素右边第一个比它大的位置
stack<int> st;   // 存下标
for (int i = 0; i < n; i++) {
    while (!st.empty() && a[st.top()] < a[i]) {
        ans[st.top()] = i;
        st.pop();
    }
    st.push(i);
}
```

### 单调队列（滑动窗口最值）

用双端队列维护窗口内单调序列，求**定长窗口最大/最小值**，O(n)。

```cpp
deque<int> dq;
for (int i = 0; i < n; i++) {
    while (!dq.empty() && dq.front() <= i - k) dq.pop_front();  // 出窗口
    while (!dq.empty() && a[dq.back()] >= a[i]) dq.pop_back();  // 保持单调
    dq.push_back(i);
    if (i >= k - 1) ans[i] = a[dq.front()];   // 窗口最小值
}
```

### 应用

下一个更大元素、柱状图最大矩形（单调栈）；滑动窗口最值（单调队列）；优化 DP 转移。


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