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feat: add solutions to lcof2 problem: No.113 (doocs#2474)
No.113.课程顺序
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‎lcof2/剑指 Offer II 113. 课程顺序/README.md

+48-40
Original file line numberDiff line numberDiff line change
@@ -56,19 +56,27 @@
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## 解法
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59-
### 方法一
59+
### 方法一：拓扑排序
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拓扑排序的思路是，先统计每个节点的入度，然后从入度为 0 的节点开始，依次删除这些节点，同时更新与这些节点相连的节点的入度，直到所有节点都被删除。
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63+
这里使用队列来存储入度为 0 的节点，每次从队列中取出一个节点，将其加入结果数组中，然后遍历与这个节点相连的节点，将这些节点的入度减 1，如果减 1 后入度为 0，则将这些节点加入队列中。
64+
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最后判断结果数组的长度是否等于节点的个数，如果等于则返回结果数组，否则返回空数组。
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时间复杂度 $O(n + m)$，空间复杂度 $O(n + m)$。其中 $n$ 和 $m$ 分别是节点的个数和边的个数。
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6169
<!-- tabs:start -->
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6371
```python
6472
class Solution:
6573
def findOrder(self, numCourses: int, prerequisites: List[List[int]]) -> List[int]:
66-
g = defaultdict(list)
74+
g = [[] for _ in range(numCourses)]
6775
indeg = [0] * numCourses
6876
for a, b in prerequisites:
6977
g[b].append(a)
7078
indeg[a] += 1
71-
q = deque([i for i, v in enumerate(indeg) if v == 0])
79+
q = deque(i for i, v in enumerate(indeg) if v == 0)
7280
ans = []
7381
while q:
7482
i = q.popleft()
@@ -117,23 +125,29 @@ class Solution {
117125
class Solution {
118126
public:
119127
vector<int> findOrder(int numCourses, vector<vector<int>>& prerequisites) {
120-
vector<vector<int>> g(numCourses);
128+
vector<int> g[numCourses];
121129
vector<int> indeg(numCourses);
122130
for (auto& p : prerequisites) {
123131
int a = p[0], b = p[1];
124132
g[b].push_back(a);
125133
++indeg[a];
126134
}
127135
queue<int> q;
128-
for (int i = 0; i < numCourses; ++i)
129-
if (indeg[i] == 0) q.push(i);
136+
for (int i = 0; i < numCourses; ++i) {
137+
if (indeg[i] == 0) {
138+
q.push(i);
139+
}
140+
}
130141
vector<int> ans;
131-
while (!q.empty()) {
142+
while (q.size()) {
132143
int i = q.front();
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q.pop();
134145
ans.push_back(i);
135-
for (int j : g[i])
136-
if (--indeg[j] == 0) q.push(j);
146+
for (int j : g[i]) {
147+
if (--indeg[j] == 0) {
148+
q.push(j);
149+
}
150+
}
137151
}
138152
return ans.size() == numCourses ? ans : vector<int>();
139153
}
@@ -176,61 +190,55 @@ func findOrder(numCourses int, prerequisites [][]int) []int {
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177191
```ts
178192
function findOrder(numCourses: number, prerequisites: number[][]): number[] {
179-
let g = Array.from({ length: numCourses }, () => []);
180-
let indeg = new Array(numCourses).fill(0);
181-
for (let [a, b] of prerequisites) {
193+
const g: number[][] = Array.from({ length: numCourses }, () => []);
194+
const indeg: number[] = Array(numCourses).fill(0);
195+
for (const [a, b] of prerequisites) {
182196
g[b].push(a);
183197
++indeg[a];
184198
}
185-
let q = [];
186-
for (let i = 0; i < numCourses; ++i) {
187-
if (!indeg[i]) {
188-
q.push(i);
189-
}
190-
}
191-
let ans = [];
199+
const q: number[] = indeg.map((v, i) => (v === 0 ? i : -1)).filter(v => v !== -1);
200+
const ans: number[] = [];
192201
while (q.length) {
193-
const i = q.shift();
202+
const i = q.pop()!;
194203
ans.push(i);
195-
for (let j of g[i]) {
196-
if (--indeg[j] == 0) {
204+
for (const j of g[i]) {
205+
if (--indeg[j] === 0) {
197206
q.push(j);
198207
}
199208
}
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}
201-
return ans.length == numCourses ? ans : [];
210+
return ans.length === numCourses ? ans : [];
202211
}
203212
```
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```cs
206215
public class Solution {
207216
public int[] FindOrder(int numCourses, int[][] prerequisites) {
208-
var g = new List<int>[numCourses];
209-
for (int i = 0; i < numCourses; ++i)
210-
{
217+
List<int>[] g = new List<int>[numCourses];
218+
for (int i = 0; i < numCourses; i++) {
211219
g[i] = new List<int>();
212220
}
213-
var indeg = new int[numCourses];
214-
foreach (var p in prerequisites)
215-
{
221+
int[] indeg = new int[numCourses];
222+
foreach (var p in prerequisites) {
216223
int a = p[0], b = p[1];
217224
g[b].Add(a);
218225
++indeg[a];
219226
}
220-
var q = new Queue<int>();
221-
for (int i = 0; i < numCourses; ++i)
222-
{
223-
if (indeg[i] == 0) q.Enqueue(i);
227+
Queue<int> q = new Queue<int>();
228+
for (int i = 0; i < numCourses; ++i) {
229+
if (indeg[i] == 0) {
230+
q.Enqueue(i);
231+
}
224232
}
225-
var ans = new int[numCourses];
226-
var cnt = 0;
227-
while (q.Count > 0)
228-
{
233+
int[] ans = new int[numCourses];
234+
int cnt = 0;
235+
while (q.Count > 0) {
229236
int i = q.Dequeue();
230237
ans[cnt++] = i;
231-
foreach (int j in g[i])
232-
{
233-
if (--indeg[j] == 0) q.Enqueue(j);
238+
foreach (int j in g[i]) {
239+
if (--indeg[j] == 0) {
240+
q.Enqueue(j);
241+
}
234242
}
235243
}
236244
return cnt == numCourses ? ans : new int[0];

‎lcof2/剑指 Offer II 113. 课程顺序/Solution.cpp

+12-6
Original file line numberDiff line numberDiff line change
@@ -1,23 +1,29 @@
11
class Solution {
22
public:
33
vector<int> findOrder(int numCourses, vector<vector<int>>& prerequisites) {
4-
vector<vector<int>> g(numCourses);
4+
vector<int> g[numCourses];
55
vector<int> indeg(numCourses);
66
for (auto& p : prerequisites) {
77
int a = p[0], b = p[1];
88
g[b].push_back(a);
99
++indeg[a];
1010
}
1111
queue<int> q;
12-
for (int i = 0; i < numCourses; ++i)
13-
if (indeg[i] == 0) q.push(i);
12+
for (int i = 0; i < numCourses; ++i) {
13+
if (indeg[i] == 0) {
14+
q.push(i);
15+
}
16+
}
1417
vector<int> ans;
15-
while (!q.empty()) {
18+
while (q.size()) {
1619
int i = q.front();
1720
q.pop();
1821
ans.push_back(i);
19-
for (int j : g[i])
20-
if (--indeg[j] == 0) q.push(j);
22+
for (int j : g[i]) {
23+
if (--indeg[j] == 0) {
24+
q.push(j);
25+
}
26+
}
2127
}
2228
return ans.size() == numCourses ? ans : vector<int>();
2329
}

‎lcof2/剑指 Offer II 113. 课程顺序/Solution.cs

+17-18
Original file line numberDiff line numberDiff line change
@@ -1,33 +1,32 @@
11
public class Solution {
22
public int[] FindOrder(int numCourses, int[][] prerequisites) {
3-
var g = new List<int>[numCourses];
4-
for (int i = 0; i < numCourses; ++i)
5-
{
3+
List<int>[] g = new List<int>[numCourses];
4+
for (int i = 0; i < numCourses; i++) {
65
g[i] = new List<int>();
76
}
8-
var indeg = new int[numCourses];
9-
foreach (var p in prerequisites)
10-
{
7+
int[] indeg = new int[numCourses];
8+
foreach (var p in prerequisites) {
119
int a = p[0], b = p[1];
1210
g[b].Add(a);
1311
++indeg[a];
1412
}
15-
var q = new Queue<int>();
16-
for (int i = 0; i < numCourses; ++i)
17-
{
18-
if (indeg[i] == 0) q.Enqueue(i);
13+
Queue<int> q = new Queue<int>();
14+
for (int i = 0; i < numCourses; ++i) {
15+
if (indeg[i] == 0) {
16+
q.Enqueue(i);
17+
}
1918
}
20-
var ans = new int[numCourses];
21-
var cnt = 0;
22-
while (q.Count > 0)
23-
{
19+
int[] ans = new int[numCourses];
20+
int cnt = 0;
21+
while (q.Count > 0) {
2422
int i = q.Dequeue();
2523
ans[cnt++] = i;
26-
foreach (int j in g[i])
27-
{
28-
if (--indeg[j] == 0) q.Enqueue(j);
24+
foreach (int j in g[i]) {
25+
if (--indeg[j] == 0) {
26+
q.Enqueue(j);
27+
}
2928
}
3029
}
3130
return cnt == numCourses ? ans : new int[0];
3231
}
33-
}
32+
}

‎lcof2/剑指 Offer II 113. 课程顺序/Solution.py

+2-2
Original file line numberDiff line numberDiff line change
@@ -1,11 +1,11 @@
11
class Solution:
22
def findOrder(self, numCourses: int, prerequisites: List[List[int]]) -> List[int]:
3-
g = defaultdict(list)
3+
g = [[] for _ in range(numCourses)]
44
indeg = [0] * numCourses
55
for a, b in prerequisites:
66
g[b].append(a)
77
indeg[a] += 1
8-
q = deque([i for i, v in enumerate(indeg) if v == 0])
8+
q = deque(i for i, v in enumerate(indeg) if v == 0)
99
ans = []
1010
while q:
1111
i = q.popleft()

‎lcof2/剑指 Offer II 113. 课程顺序/Solution.ts

+9-14
Original file line numberDiff line numberDiff line change
@@ -1,25 +1,20 @@
11
function findOrder(numCourses: number, prerequisites: number[][]): number[] {
2-
let g = Array.from({ length: numCourses }, () => []);
3-
let indeg = new Array(numCourses).fill(0);
4-
for (let [a, b] of prerequisites) {
2+
const g: number[][] = Array.from({ length: numCourses }, () => []);
3+
const indeg: number[] = Array(numCourses).fill(0);
4+
for (const [a, b] of prerequisites) {
55
g[b].push(a);
66
++indeg[a];
77
}
8-
let q = [];
9-
for (let i = 0; i < numCourses; ++i) {
10-
if (!indeg[i]) {
11-
q.push(i);
12-
}
13-
}
14-
let ans = [];
8+
const q: number[] = indeg.map((v, i) => (v === 0 ? i : -1)).filter(v => v !== -1);
9+
const ans: number[] = [];
1510
while (q.length) {
16-
const i = q.shift();
11+
const i = q.pop()!;
1712
ans.push(i);
18-
for (let j of g[i]) {
19-
if (--indeg[j] == 0) {
13+
for (const j of g[i]) {
14+
if (--indeg[j] === 0) {
2015
q.push(j);
2116
}
2217
}
2318
}
24-
return ans.length == numCourses ? ans : [];
19+
return ans.length === numCourses ? ans : [];
2520
}

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