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 <= 10^9

• 0 <= restrictions.length <= min(n - 1, 10^5)

• 2 <= id_i <= n

• idi is unique.

• 0 <= maxHeighti <= 10^9

Solution

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中文版解答Bilibili Link

class Solution {
public:
    int maxBuilding(int n, vector<vector<int>>& restrictions) {
        restrictions.push_back({1, 0});
        restrictions.push_back({n, n - 1});
        sort(restrictions.begin(), restrictions.end());
        
        for (int i = 1; i < restrictions.size(); i++) {
            restrictions[i][1] = min(restrictions[i][1], restrictions[i-1][1] + restrictions[i][0] - restrictions[i-1][0]);
        }
        for (int i = restrictions.size() - 2; i >= 0; --i) {
            restrictions[i][1] = min(restrictions[i][1], restrictions[i+1][1] + restrictions[i+1][0] - restrictions[i][0]);
        }
        
        int res = 0;
        for (int i = 1; i < restrictions.size(); i++) {
            int left_restriction = restrictions[i-1][1];
            int right_restriction = restrictions[i][1];
            res = max(res, max(left_restriction, right_restriction) + (restrictions[i][0] - restrictions[i-1][0] - abs(left_restriction - right_restriction)) / 2);
        }
        
        return res;
    }
};