# 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
```