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feat: add solutions to lc problem: No.1840
No.1840.Maximum Building Height
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‎solution/1800-1899/1840.Maximum Building Height/README.md

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@@ -66,22 +66,144 @@
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<!-- 这里可写通用的实现逻辑 -->
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**方法一：排序 + 数学**
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首先，我们将所有的限制条件按照建筑物的编号从小到大排序。
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然后我们从左到右遍历所有的限制条件，对于每个限制条件，我们可以得到一个最高高度的上界，即 $r_i[1] = min(r_i[1], r_{i-1}[1] + r_i[0] - r_{i-1}[0])$，其中 $r_i$ 表示第 $i$ 个限制条件，而 $r_i[0]$ 和 $r_i[1]$ 分别表示建筑物的编号以及建筑物的最高高度的上界。
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然后我们从右到左遍历所有的限制条件，对于每个限制条件，我们可以得到一个最高高度的上界，即 $r_i[1] = min(r_i[1], r_{i+1}[1] + r_{i+1}[0] - r_i[0])$。
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这样，我们就得到了每个限制建筑物的最高高度的上界。
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题目求的是最高建筑物的高度，我们可以枚举相邻两个限制条件之间的建筑物 $i$ 和 $i+1$，要使得高度最大，那么高度应该是先增大后减小，假设最大高度为 $t$，那么 $t - r_i[1] + t - r_{i+1}[1] \leq r_{i+1}[0] - r_i[0]$，即 $t \leq \frac{r_i[1] + r_{i+1}[1] + r_{i+1}[0] - r_{i}[0]}{2}$，我们取所有的 $t$ 中的最大值即可。
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时间复杂度 $O(n \times \log n)$，空间复杂度 $O(n)$。其中 $n$ 为建筑物的数量。
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<!-- tabs:start -->
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### **Python3**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```python
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class Solution:
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def maxBuilding(self, n: int, restrictions: List[List[int]]) -> int:
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r = restrictions
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r.append([1, 0])
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r.sort()
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if r[-1][0] != n:
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r.append([n, n - 1])
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m = len(r)
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for i in range(1, m):
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r[i][1] = min(r[i][1], r[i - 1][1] + r[i][0] - r[i - 1][0])
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for i in range(m - 2, 0, -1):
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r[i][1] = min(r[i][1], r[i + 1][1] + r[i + 1][0] - r[i][0])
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ans = 0
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for i in range(m - 1):
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t = (r[i][1] + r[i + 1][1] + r[i + 1][0] - r[i][0]) // 2
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ans = max(ans, t)
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return ans
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```
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### **Java**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```java
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class Solution {
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public int maxBuilding(int n, int[][] restrictions) {
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List<int[]> r = new ArrayList<>();
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r.addAll(Arrays.asList(restrictions));
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r.add(new int[] {1, 0});
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Collections.sort(r, (a, b) -> a[0] - b[0]);
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if (r.get(r.size() - 1)[0] != n) {
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r.add(new int[] {n, n - 1});
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}
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int m = r.size();
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for (int i = 1; i < m; ++i) {
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int[] a = r.get(i - 1), b = r.get(i);
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b[1] = Math.min(b[1], a[1] + b[0] - a[0]);
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}
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for (int i = m - 2; i > 0; --i) {
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int[] a = r.get(i), b = r.get(i + 1);
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a[1] = Math.min(a[1], b[1] + b[0] - a[0]);
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}
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int ans = 0;
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for (int i = 0; i < m - 1; ++i) {
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int[] a = r.get(i), b = r.get(i + 1);
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int t = (a[1] + b[1] + b[0] - a[0]) / 2;
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ans = Math.max(ans, t);
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}
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return ans;
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}
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}
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```
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### **C++**
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```cpp
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class Solution {
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public:
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int maxBuilding(int n, vector<vector<int>>& restrictions) {
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auto&& r = restrictions;
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r.push_back({1, 0});
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sort(r.begin(), r.end());
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if (r[r.size() - 1][0] != n) r.push_back({n, n - 1});
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int m = r.size();
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for (int i = 1; i < m; ++i) {
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r[i][1] = min(r[i][1], r[i - 1][1] + r[i][0] - r[i - 1][0]);
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}
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for (int i = m - 2; i > 0; --i) {
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r[i][1] = min(r[i][1], r[i + 1][1] + r[i + 1][0] - r[i][0]);
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}
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int ans = 0;
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for (int i = 0; i < m - 1; ++i) {
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int t = (r[i][1] + r[i + 1][1] + r[i + 1][0] - r[i][0]) / 2;
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ans = max(ans, t);
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}
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return ans;
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}
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};
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```
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### **Go**
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```go
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func maxBuilding(n int, restrictions [][]int) (ans int) {
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r := restrictions
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r = append(r, []int{1, 0})
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sort.Slice(r, func(i, j int) bool { return r[i][0] < r[j][0] })
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if r[len(r)-1][0] != n {
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r = append(r, []int{n, n - 1})
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}
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m := len(r)
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for i := 1; i < m; i++ {
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r[i][1] = min(r[i][1], r[i-1][1]+r[i][0]-r[i-1][0])
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}
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for i := m - 2; i > 0; i-- {
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r[i][1] = min(r[i][1], r[i+1][1]+r[i+1][0]-r[i][0])
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}
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for i := 0; i < m-1; i++ {
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t := (r[i][1] + r[i+1][1] + r[i+1][0] - r[i][0]) / 2
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ans = max(ans, t)
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}
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return ans
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}
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func max(a, b int) int {
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if a > b {
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return a
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}
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return b
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}
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func min(a, b int) int {
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if a < b {
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return a
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}
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return b
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}
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```
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### **...**

‎solution/1800-1899/1840.Maximum Building Height/README_EN.md

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@@ -65,13 +65,121 @@ We can build the buildings with heights [0,1,2,3,3,4,4,5,4,3], and the tallest b
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### **Python3**
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```python
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class Solution:
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def maxBuilding(self, n: int, restrictions: List[List[int]]) -> int:
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r = restrictions
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r.append([1, 0])
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r.sort()
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if r[-1][0] != n:
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r.append([n, n - 1])
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m = len(r)
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for i in range(1, m):
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r[i][1] = min(r[i][1], r[i - 1][1] + r[i][0] - r[i - 1][0])
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for i in range(m - 2, 0, -1):
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r[i][1] = min(r[i][1], r[i + 1][1] + r[i + 1][0] - r[i][0])
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ans = 0
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for i in range(m - 1):
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t = (r[i][1] + r[i + 1][1] + r[i + 1][0] - r[i][0]) // 2
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ans = max(ans, t)
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return ans
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```
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### **Java**
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```java
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class Solution {
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public int maxBuilding(int n, int[][] restrictions) {
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List<int[]> r = new ArrayList<>();
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r.addAll(Arrays.asList(restrictions));
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r.add(new int[] {1, 0});
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Collections.sort(r, (a, b) -> a[0] - b[0]);
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if (r.get(r.size() - 1)[0] != n) {
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r.add(new int[] {n, n - 1});
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}
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int m = r.size();
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for (int i = 1; i < m; ++i) {
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int[] a = r.get(i - 1), b = r.get(i);
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b[1] = Math.min(b[1], a[1] + b[0] - a[0]);
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}
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for (int i = m - 2; i > 0; --i) {
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int[] a = r.get(i), b = r.get(i + 1);
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a[1] = Math.min(a[1], b[1] + b[0] - a[0]);
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}
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int ans = 0;
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for (int i = 0; i < m - 1; ++i) {
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int[] a = r.get(i), b = r.get(i + 1);
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int t = (a[1] + b[1] + b[0] - a[0]) / 2;
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ans = Math.max(ans, t);
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}
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return ans;
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}
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}
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```
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### **C++**
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```cpp
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class Solution {
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public:
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int maxBuilding(int n, vector<vector<int>>& restrictions) {
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auto&& r = restrictions;
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r.push_back({1, 0});
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sort(r.begin(), r.end());
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if (r[r.size() - 1][0] != n) r.push_back({n, n - 1});
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int m = r.size();
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for (int i = 1; i < m; ++i) {
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r[i][1] = min(r[i][1], r[i - 1][1] + r[i][0] - r[i - 1][0]);
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}
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for (int i = m - 2; i > 0; --i) {
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r[i][1] = min(r[i][1], r[i + 1][1] + r[i + 1][0] - r[i][0]);
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}
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int ans = 0;
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for (int i = 0; i < m - 1; ++i) {
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int t = (r[i][1] + r[i + 1][1] + r[i + 1][0] - r[i][0]) / 2;
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ans = max(ans, t);
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}
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return ans;
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}
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};
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```
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### **Go**
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```go
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func maxBuilding(n int, restrictions [][]int) (ans int) {
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r := restrictions
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r = append(r, []int{1, 0})
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sort.Slice(r, func(i, j int) bool { return r[i][0] < r[j][0] })
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if r[len(r)-1][0] != n {
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r = append(r, []int{n, n - 1})
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}
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m := len(r)
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for i := 1; i < m; i++ {
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r[i][1] = min(r[i][1], r[i-1][1]+r[i][0]-r[i-1][0])
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}
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for i := m - 2; i > 0; i-- {
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r[i][1] = min(r[i][1], r[i+1][1]+r[i+1][0]-r[i][0])
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}
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for i := 0; i < m-1; i++ {
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t := (r[i][1] + r[i+1][1] + r[i+1][0] - r[i][0]) / 2
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ans = max(ans, t)
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}
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return ans
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}
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func max(a, b int) int {
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if a > b {
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return a
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}
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return b
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}
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func min(a, b int) int {
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if a < b {
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return a
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}
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return b
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}
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```
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### **...**

‎solution/1800-1899/1840.Maximum Building Height/Solution.cpp

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class Solution {
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public:
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int maxBuilding(int n, vector<vector<int>>& restrictions) {
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auto&& r = restrictions;
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r.push_back({1, 0});
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sort(r.begin(), r.end());
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if (r[r.size() - 1][0] != n) r.push_back({n, n - 1});
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int m = r.size();
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for (int i = 1; i < m; ++i) {
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r[i][1] = min(r[i][1], r[i - 1][1] + r[i][0] - r[i - 1][0]);
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}
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for (int i = m - 2; i > 0; --i) {
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r[i][1] = min(r[i][1], r[i + 1][1] + r[i + 1][0] - r[i][0]);
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}
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int ans = 0;
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for (int i = 0; i < m - 1; ++i) {
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int t = (r[i][1] + r[i + 1][1] + r[i + 1][0] - r[i][0]) / 2;
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ans = max(ans, t);
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}
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return ans;
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}
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};

‎solution/1800-1899/1840.Maximum Building Height/Solution.go

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func maxBuilding(n int, restrictions [][]int) (ans int) {
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r := restrictions
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r = append(r, []int{1, 0})
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sort.Slice(r, func(i, j int) bool { return r[i][0] < r[j][0] })
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if r[len(r)-1][0] != n {
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r = append(r, []int{n, n - 1})
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}
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m := len(r)
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for i := 1; i < m; i++ {
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r[i][1] = min(r[i][1], r[i-1][1]+r[i][0]-r[i-1][0])
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}
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for i := m - 2; i > 0; i-- {
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r[i][1] = min(r[i][1], r[i+1][1]+r[i+1][0]-r[i][0])
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}
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for i := 0; i < m-1; i++ {
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t := (r[i][1] + r[i+1][1] + r[i+1][0] - r[i][0]) / 2
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ans = max(ans, t)
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}
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return ans
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}
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func max(a, b int) int {
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if a > b {
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return a
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}
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return b
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}
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func min(a, b int) int {
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if a < b {
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return a
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}
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return b
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}

‎solution/1800-1899/1840.Maximum Building Height/Solution.java

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,27 @@
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class Solution {
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public int maxBuilding(int n, int[][] restrictions) {
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List<int[]> r = new ArrayList<>();
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r.addAll(Arrays.asList(restrictions));
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r.add(new int[] {1, 0});
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Collections.sort(r, (a, b) -> a[0] - b[0]);
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if (r.get(r.size() - 1)[0] != n) {
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r.add(new int[] {n, n - 1});
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}
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int m = r.size();
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for (int i = 1; i < m; ++i) {
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int[] a = r.get(i - 1), b = r.get(i);
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b[1] = Math.min(b[1], a[1] + b[0] - a[0]);
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}
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for (int i = m - 2; i > 0; --i) {
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int[] a = r.get(i), b = r.get(i + 1);
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a[1] = Math.min(a[1], b[1] + b[0] - a[0]);
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}
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int ans = 0;
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for (int i = 0; i < m - 1; ++i) {
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int[] a = r.get(i), b = r.get(i + 1);
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int t = (a[1] + b[1] + b[0] - a[0]) / 2;
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ans = Math.max(ans, t);
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}
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return ans;
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}
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}

‎solution/1800-1899/1840.Maximum Building Height/Solution.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,17 @@
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class Solution:
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def maxBuilding(self, n: int, restrictions: List[List[int]]) -> int:
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r = restrictions
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r.append([1, 0])
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r.sort()
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if r[-1][0] != n:
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r.append([n, n - 1])
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m = len(r)
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for i in range(1, m):
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r[i][1] = min(r[i][1], r[i - 1][1] + r[i][0] - r[i - 1][0])
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for i in range(m - 2, 0, -1):
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r[i][1] = min(r[i][1], r[i + 1][1] + r[i + 1][0] - r[i][0])
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ans = 0
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for i in range(m - 1):
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t = (r[i][1] + r[i + 1][1] + r[i + 1][0] - r[i][0]) // 2
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ans = max(ans, t)
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return ans

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