[LeetCode] 1840. Maximum Building Height

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:

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:

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:

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

最高建筑高度。

在一座城市里，你需要建 n 栋新的建筑。这些新的建筑会从 1 到 n 编号排成一列。

这座城市对这些新建筑有一些规定：

每栋建筑的高度必须是一个非负整数。
第一栋建筑的高度 必须 是 0 。
任意两栋相邻建筑的高度差 不能超过  1 。
除此以外，某些建筑还有额外的最高高度限制。这些限制会以二维整数数组 restrictions 的形式给出，其中 restrictions[i] = [idi, maxHeighti] ，表示建筑 idi 的高度 不能超过 maxHeighti 。

题目保证每栋建筑在 restrictions 中 至多出现一次 ，同时建筑 1 不会 出现在 restrictions 中。

请你返回 最高 建筑能达到的 最高高度 。

来源：力扣（LeetCode）
链接：https://leetcode-cn.com/problems/maximum-building-height
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这道题是 hard。我参考了这个官方题解，写的很好。题目给的是一个一维数组，请你按照数组里给的 restrictions 的要求建造房子，并且房子的高度要按照 restrictions 来。思路和讲解我觉得可以直接参考官方题解，我这里直接贴出代码。

时间O(nlogn)

空间O(1)

Java实现

class Solution {
    public int maxBuilding(int n, int[][] r) {
        // corner case
        if (r == null || r.length == 0) {
            return n - 1;
        }

        // normal case
        // Arrays.sort(r, Comparator.comparingInt(x -> x[0]));
        Arrays.sort(r, (a, b) -> a[0] - b[0]);
        int len = r.length;
        for (int i = len - 2; i >= 0; i--) {
            r[i][1] = Math.min(r[i][1], Math.min(r[i][0] - 1, r[i + 1][1] + r[i + 1][0] - r[i][0]));
        }

        int maxHeight = (0 + r[0][1] + r[0][0] - 1) / 2;
        for (int i = 1; i <= len - 1; i++) {
            r[i][1] = Math.min(r[i][1], Math.min(r[i][0] - 1, r[i - 1][1] + r[i][0] - r[i - 1][0]));
            maxHeight = Math.max(maxHeight, (r[i - 1][1] + r[i][1] + r[i][0] - r[i - 1][0]) / 2);
        }
        maxHeight = Math.max(maxHeight, r[len - 1][1] + n - r[len - 1][0]);
        return maxHeight;
    }
}

LeetCode 题目总结