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Commit 61ec285

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feat: add solutions to lc problem: No.1840 (doocs#3814)
No.1840.Maximum Building Height
1 parent 7e4cfbf commit 61ec285

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4 files changed

+144
-8
lines changed

4 files changed

+144
-8
lines changed

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

Lines changed: 45 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -160,8 +160,10 @@ public:
160160
int maxBuilding(int n, vector<vector<int>>& restrictions) {
161161
auto&& r = restrictions;
162162
r.push_back({1, 0});
163-
sort(r.begin(), r.end());
164-
if (r[r.size() - 1][0] != n) r.push_back({n, n - 1});
163+
ranges::sort(r);
164+
if (r[r.size() - 1][0] != n) {
165+
r.push_back({n, n - 1});
166+
}
165167
int m = r.size();
166168
for (int i = 1; i < m; ++i) {
167169
r[i][1] = min(r[i][1], r[i - 1][1] + r[i][0] - r[i - 1][0]);
@@ -204,6 +206,47 @@ func maxBuilding(n int, restrictions [][]int) (ans int) {
204206
}
205207
```
206208

209+
#### TypeScript
210+
211+
```ts
212+
function maxBuilding(n: number, restrictions: number[][]): number {
213+
restrictions.push([1, 0]);
214+
restrictions.sort((a, b) => a[0] - b[0]);
215+
if (restrictions[restrictions.length - 1][0] !== n) {
216+
restrictions.push([n, n - 1]);
217+
}
218+
219+
const m = restrictions.length;
220+
for (let i = 1; i < m; ++i) {
221+
restrictions[i][1] = Math.min(
222+
restrictions[i][1],
223+
restrictions[i - 1][1] + restrictions[i][0] - restrictions[i - 1][0],
224+
);
225+
}
226+
227+
for (let i = m - 2; i >= 0; --i) {
228+
restrictions[i][1] = Math.min(
229+
restrictions[i][1],
230+
restrictions[i + 1][1] + restrictions[i + 1][0] - restrictions[i][0],
231+
);
232+
}
233+
234+
let ans = 0;
235+
for (let i = 0; i < m - 1; ++i) {
236+
const t = Math.floor(
237+
(restrictions[i][1] +
238+
restrictions[i + 1][1] +
239+
restrictions[i + 1][0] -
240+
restrictions[i][0]) /
241+
2,
242+
);
243+
ans = Math.max(ans, t);
244+
}
245+
246+
return ans;
247+
}
248+
```
249+
207250
<!-- tabs:end -->
208251

209252
<!-- solution:end -->

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

Lines changed: 58 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -80,7 +80,19 @@ We can build the buildings with heights [0,1,2,3,3,4,4,5,4,3], and the tallest b
8080

8181
<!-- solution:start -->
8282

83-
### Solution 1
83+
### Solution 1: Sorting + Mathematics
84+
85+
First, we sort all the constraints by the building number in ascending order.
86+
87+
Then we traverse all the constraints from left to right. For each constraint, we can get an upper bound on the maximum height, i.e., $r_i[1] = \min(r_i[1], r_{i-1}[1] + r_i[0] - r_{i-1}[0]),ドル where $r_i$ represents the $i$-th constraint, and $r_i[0]$ and $r_i[1]$ represent the building number and the upper bound on the maximum height of the building, respectively.
88+
89+
Next, we traverse all the constraints from right to left. For each constraint, we can get an upper bound on the maximum height, i.e., $r_i[1] = \min(r_i[1], r_{i+1}[1] + r_{i+1}[0] - r_i[0])$.
90+
91+
In this way, we obtain the upper bound on the maximum height for each constrained building.
92+
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The problem asks for the height of the tallest building. We can enumerate the buildings between two adjacent constraints $i$ and $i+1$. To maximize the height, the height should first increase and then decrease. Suppose the maximum height is $t,ドル then $t - r_i[1] + t - r_{i+1}[1] \leq r_{i+1}[0] - r_i[0],ドル i.e., $t \leq \frac{r_i[1] + r_{i+1}[1] + r_{i+1}[0] - r_{i}[0]}{2}$. We take the maximum value of all such $t$.
94+
95+
The time complexity is $O(m \times \log m),ドル and the space complexity is $O(m)$. Here, $m$ is the number of constraints.
8496

8597
<!-- tabs:start -->
8698

@@ -146,8 +158,10 @@ public:
146158
int maxBuilding(int n, vector<vector<int>>& restrictions) {
147159
auto&& r = restrictions;
148160
r.push_back({1, 0});
149-
sort(r.begin(), r.end());
150-
if (r[r.size() - 1][0] != n) r.push_back({n, n - 1});
161+
ranges::sort(r);
162+
if (r[r.size() - 1][0] != n) {
163+
r.push_back({n, n - 1});
164+
}
151165
int m = r.size();
152166
for (int i = 1; i < m; ++i) {
153167
r[i][1] = min(r[i][1], r[i - 1][1] + r[i][0] - r[i - 1][0]);
@@ -190,6 +204,47 @@ func maxBuilding(n int, restrictions [][]int) (ans int) {
190204
}
191205
```
192206

207+
#### TypeScript
208+
209+
```ts
210+
function maxBuilding(n: number, restrictions: number[][]): number {
211+
restrictions.push([1, 0]);
212+
restrictions.sort((a, b) => a[0] - b[0]);
213+
if (restrictions[restrictions.length - 1][0] !== n) {
214+
restrictions.push([n, n - 1]);
215+
}
216+
217+
const m = restrictions.length;
218+
for (let i = 1; i < m; ++i) {
219+
restrictions[i][1] = Math.min(
220+
restrictions[i][1],
221+
restrictions[i - 1][1] + restrictions[i][0] - restrictions[i - 1][0],
222+
);
223+
}
224+
225+
for (let i = m - 2; i >= 0; --i) {
226+
restrictions[i][1] = Math.min(
227+
restrictions[i][1],
228+
restrictions[i + 1][1] + restrictions[i + 1][0] - restrictions[i][0],
229+
);
230+
}
231+
232+
let ans = 0;
233+
for (let i = 0; i < m - 1; ++i) {
234+
const t = Math.floor(
235+
(restrictions[i][1] +
236+
restrictions[i + 1][1] +
237+
restrictions[i + 1][0] -
238+
restrictions[i][0]) /
239+
2,
240+
);
241+
ans = Math.max(ans, t);
242+
}
243+
244+
return ans;
245+
}
246+
```
247+
193248
<!-- tabs:end -->
194249

195250
<!-- solution:end -->

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

Lines changed: 5 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -3,8 +3,10 @@ class Solution {
33
int maxBuilding(int n, vector<vector<int>>& restrictions) {
44
auto&& r = restrictions;
55
r.push_back({1, 0});
6-
sort(r.begin(), r.end());
7-
if (r[r.size() - 1][0] != n) r.push_back({n, n - 1});
6+
ranges::sort(r);
7+
if (r[r.size() - 1][0] != n) {
8+
r.push_back({n, n - 1});
9+
}
810
int m = r.size();
911
for (int i = 1; i < m; ++i) {
1012
r[i][1] = min(r[i][1], r[i - 1][1] + r[i][0] - r[i - 1][0]);
@@ -19,4 +21,4 @@ class Solution {
1921
}
2022
return ans;
2123
}
22-
};
24+
};
Lines changed: 36 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,36 @@
1+
function maxBuilding(n: number, restrictions: number[][]): number {
2+
restrictions.push([1, 0]);
3+
restrictions.sort((a, b) => a[0] - b[0]);
4+
if (restrictions[restrictions.length - 1][0] !== n) {
5+
restrictions.push([n, n - 1]);
6+
}
7+
8+
const m = restrictions.length;
9+
for (let i = 1; i < m; ++i) {
10+
restrictions[i][1] = Math.min(
11+
restrictions[i][1],
12+
restrictions[i - 1][1] + restrictions[i][0] - restrictions[i - 1][0],
13+
);
14+
}
15+
16+
for (let i = m - 2; i >= 0; --i) {
17+
restrictions[i][1] = Math.min(
18+
restrictions[i][1],
19+
restrictions[i + 1][1] + restrictions[i + 1][0] - restrictions[i][0],
20+
);
21+
}
22+
23+
let ans = 0;
24+
for (let i = 0; i < m - 1; ++i) {
25+
const t = Math.floor(
26+
(restrictions[i][1] +
27+
restrictions[i + 1][1] +
28+
restrictions[i + 1][0] -
29+
restrictions[i][0]) /
30+
2,
31+
);
32+
ans = Math.max(ans, t);
33+
}
34+
35+
return ans;
36+
}

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