> For the complete documentation index, see [llms.txt](https://jaywin.gitbook.io/leetcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jaywin.gitbook.io/leetcode/solutions/1840-maximum-building-height.md).

# 1840. Maximum Building Height

<https://leetcode.com/problems/maximum-building-height>

## Description

You want to build `n` new buildings in a city. The new buildings will be built in a line and are labeled from `1` to `n`.

However, there are city restrictions on the heights of the new buildings:

* The height of each building must be a non-negative integer.
* The height of the first building **must** be `0`.
* The height difference between any two adjacent buildings **cannot exceed** `1`.

Additionally, there are city restrictions on the maximum height of specific buildings. These restrictions are given as a 2D integer array `restrictions` where `restrictions[i] = [idi, maxHeighti]` indicates that building `idi` must have a height **less than or equal to** `maxHeighti`.

It is guaranteed that each building will appear **at most once** in `restrictions`, and building `1` will **not** be in `restrictions`.

Return *the **maximum possible height** of the **tallest** building*.

**Example 1:**

![](https://assets.leetcode.com/uploads/2021/04/08/ic236-q4-ex1-1.png)

```
**Input:** n = 5, restrictions = [[2,1],[4,1]]
**Output:** 2
**Explanation:** The green area in the image indicates the maximum allowed height for each building.
We can build the buildings with heights [0,1,2,1,2], and the tallest building has a height of 2.
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2021/04/08/ic236-q4-ex2.png)

```
**Input:** n = 6, restrictions = []
**Output:** 5
**Explanation:** The green area in the image indicates the maximum allowed height for each building.
We can build the buildings with heights [0,1,2,3,4,5], and the tallest building has a height of 5.
```

**Example 3:**

![](https://assets.leetcode.com/uploads/2021/04/08/ic236-q4-ex3.png)

```
**Input:** n = 10, restrictions = [[5,3],[2,5],[7,4],[10,3]]
**Output:** 5
**Explanation:** The green area in the image indicates the maximum allowed height for each building.
We can build the buildings with heights [0,1,2,3,3,4,4,5,4,3], and the tallest building has a height of 5.
```

**Constraints:**

* `2 <= n <= 109`
* `0 <= restrictions.length <= min(n - 1, 105)`
* `2 <= idi <= n`
* `idi` is **unique**.
* `0 <= maxHeighti <= 109`

## ac

```java
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://jaywin.gitbook.io/leetcode/solutions/1840-maximum-building-height.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.