add one exercises

data/3.算法高阶/7.leetcode图与搜索/206_课程表/config.json

+{
+    "node_id": "569d5e11c4fc5de7844053d9a733c5e8",
+    "keywords": [
+        "leetcode",
+        "课程表"
+    ],
+    "children": [],
+    "export": [
+        "solution.json"
+    ],
+    "title": "课程表"
+}
\ No newline at end of file

data/3.算法高阶/7.leetcode图与搜索/206_课程表/desc.html

+<p>你这个学期必须选修 <code>numCourses</code> 门课程，记为 <code>0</code> 到 <code>numCourses - 1</code> 。</p>
+
+<p>在选修某些课程之前需要一些先修课程。 先修课程按数组 <code>prerequisites</code> 给出，其中 <code>prerequisites[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> ，表示如果要学习课程 <code>a<sub>i</sub></code> 则 <strong>必须</strong> 先学习课程  <code>b<sub>i</sub></code><sub> </sub>。</p>
+
+<ul>
+	<li>例如，先修课程对 <code>[0, 1]</code> 表示：想要学习课程 <code>0</code> ，你需要先完成课程 <code>1</code> 。</li>
+</ul>
+
+<p>请你判断是否可能完成所有课程的学习？如果可以，返回 <code>true</code> ；否则，返回 <code>false</code> 。</p>
+
+<p> </p>
+
+<p><strong>示例 1：</strong></p>
+
+<pre>
+<strong>输入：</strong>numCourses = 2, prerequisites = [[1,0]]
+<strong>输出：</strong>true
+<strong>解释：</strong>总共有 2 门课程。学习课程 1 之前，你需要完成课程 0 。这是可能的。</pre>
+
+<p><strong>示例 2：</strong></p>
+
+<pre>
+<strong>输入：</strong>numCourses = 2, prerequisites = [[1,0],[0,1]]
+<strong>输出：</strong>false
+<strong>解释：</strong>总共有 2 门课程。学习课程 1 之前，你需要先完成​课程 0 ；并且学习课程 0 之前，你还应先完成课程 1 。这是不可能的。</pre>
+
+<p> </p>
+
+<p><strong>提示：</strong></p>
+
+<ul>
+	<li><code>1 <= numCourses <= 10<sup>5</sup></code></li>
+	<li><code>0 <= prerequisites.length <= 5000</code></li>
+	<li><code>prerequisites[i].length == 2</code></li>
+	<li><code>0 <= a<sub>i</sub>, b<sub>i</sub> < numCourses</code></li>
+	<li><code>prerequisites[i]</code> 中的所有课程对 <strong>互不相同</strong></li>
+</ul>

data/3.算法高阶/7.leetcode图与搜索/206_课程表/solution.cpp

+#include <bits/stdc++.h>
+using namespace std;
+
+class Solution
+{
+public:
+    bool canFinish(int numCourses, vector<vector<int>> &prerequisites)
+    {
+
+        vector<vector<int>> graph(numCourses, vector<int>());
+
+        for (auto num : prerequisites)
+        {
+            graph[num[1]].push_back(num[0]);
+        }
+        vector<int> visit(numCourses);
+
+        for (int i = 0; i < numCourses; i++)
+        {
+            if (!dfs(graph, visit, i))
+                return false;
+        }
+        return true;
+    }
+    bool dfs(vector<vector<int>> &g, vector<int> &visit, int i)
+    {
+        if (visit[i] == -1)
+            return false;
+        if (visit[i] == 1)
+            return true;
+        visit[i] = -1;
+        for (auto a : g[i])
+        {
+            if (!dfs(g, visit, a))
+                return false;
+        }
+        visit[i] = 1;
+        return true;
+    }
+};
\ No newline at end of file

data/3.算法高阶/7.leetcode图与搜索/206_课程表/solution.json

+{
+   "type": "code_options",
+   "author": "CSDN.net",
+   "source": "solution.md",
+   "exercise_id": "faf3b0518667467b971e642c5ed5b077"
+}
\ No newline at end of file

data/3.算法高阶/7.leetcode图与搜索/206_课程表/solution.md

+# 课程表
+<p>你这个学期必须选修 <code>numCourses</code> 门课程，记为 <code>0</code> 到 <code>numCourses - 1</code> 。</p>
+
+<p>在选修某些课程之前需要一些先修课程。 先修课程按数组 <code>prerequisites</code> 给出，其中 <code>prerequisites[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> ，表示如果要学习课程 <code>a<sub>i</sub></code> 则 <strong>必须</strong> 先学习课程  <code>b<sub>i</sub></code><sub> </sub>。</p>
+
+<ul>
+	<li>例如，先修课程对 <code>[0, 1]</code> 表示：想要学习课程 <code>0</code> ，你需要先完成课程 <code>1</code> 。</li>
+</ul>
+
+<p>请你判断是否可能完成所有课程的学习？如果可以，返回 <code>true</code> ；否则，返回 <code>false</code> 。</p>
+
+<p> </p>
+
+<p><strong>示例 1：</strong></p>
+
+<pre>
+<strong>输入：</strong>numCourses = 2, prerequisites = [[1,0]]
+<strong>输出：</strong>true
+<strong>解释：</strong>总共有 2 门课程。学习课程 1 之前，你需要完成课程 0 。这是可能的。</pre>
+
+<p><strong>示例 2：</strong></p>
+
+<pre>
+<strong>输入：</strong>numCourses = 2, prerequisites = [[1,0],[0,1]]
+<strong>输出：</strong>false
+<strong>解释：</strong>总共有 2 门课程。学习课程 1 之前，你需要先完成​课程 0 ；并且学习课程 0 之前，你还应先完成课程 1 。这是不可能的。</pre>
+
+<p> </p>
+
+<p><strong>提示：</strong></p>
+
+<ul>
+	<li><code>1 <= numCourses <= 10<sup>5</sup></code></li>
+	<li><code>0 <= prerequisites.length <= 5000</code></li>
+	<li><code>prerequisites[i].length == 2</code></li>
+	<li><code>0 <= a<sub>i</sub>, b<sub>i</sub> < numCourses</code></li>
+	<li><code>prerequisites[i]</code> 中的所有课程对 <strong>互不相同</strong></li>
+</ul>
+
+<p>以下错误的选项是？</p>
+## aop
+### before
+```cpp
+#include <bits/stdc++.h>
+using namespace std;
+```
+### after
+```cpp
+
+```
+
+## 答案
+```cpp
+class Solution
+{
+public:
+    bool canFinish(int numCourses, vector<vector<int>> &prerequisites)
+    {
+
+        unordered_map<int, vector<int>> rels;
+        int *inDs = new int[numCourses];
+        for (int i = 0; i < numCourses; i++)
+        {
+            inDs[i] = 0;
+            vector<int> temp;
+            rels[i] = temp;
+        }
+
+        for (int i = 0; i < prerequisites.size(); i++)
+        {
+            rels[prerequisites[i][1]].push_back(prerequisites[i][0]);
+            inDs[prerequisites[i][0]]++;
+        }
+        queue<int> zeroInD;
+        int num = 0;
+        while (num != numCourses)
+        {
+            for (int i = 0; i < numCourses; i++)
+            {
+                if (inDs[i] == 0)
+                {
+                    zeroInD.push(i);
+                    num++;
+                    inDs[i] = -1;
+                }
+            }
+            if (zeroInD.empty() && num != numCourses)
+                return false;
+            while (!zeroInD.empty())
+            {
+                int topV = zeroInD.front();
+                zeroInD.pop();
+                vector<int> topVEdges = rels[topV];
+                for (int j = 0; j < topVEdges.size(); j++)
+                {
+                    inDs[topVEdges[j]]++;
+                }
+            }
+        }
+        if (num == numCourses)
+            return true;
+        else
+            return false;
+    }
+};
+```
+## 选项
+
+### A
+```cpp
+class Solution
+{
+public:
+    bool canFinish(int numCourses, vector<vector<int>> &prerequisites)
+    {
+        if (numCourses == 0)
+            return true;
+
+        vector<int> course(numCourses, 0);
+        vector<vector<int>> rela(numCourses);
+        for (int i = 0; i < prerequisites.size(); i++)
+        {
+            course[prerequisites[i][0]]++;
+            rela[prerequisites[i][1]].push_back(prerequisites[i][0]);
+        }
+
+        queue<int> cq;
+        for (int i = 0; i < numCourses; i++)
+            if (course[i] == 0)
+                cq.push(i);
+
+        int num = numCourses;
+        while (!cq.empty())
+        {
+            int c = cq.front();
+            cq.pop();
+            num--;
+            for (int i = 0; i < rela[c].size(); i++)
+            {
+                int this_course = rela[c][i];
+                course[this_course]--;
+                if (course[this_course] == 0)
+                    cq.push(this_course);
+            }
+        }
+        return num == 0 ? true : false;
+    }
+};
+```
+
+### B
+```cpp
+class Solution
+{
+public:
+    bool canFinish(int numCourses, vector<vector<int>> &prerequisites)
+    {
+        vector<int> res, degree(numCourses, 0);
+        unordered_map<int, vector<int>> map;
+
+        for (auto &e : prerequisites)
+        {
+            map[e[1]].push_back(e[0]);
+            degree[e[0]]++;
+        }
+
+        queue<int> q;
+        for (int i = 0; i < numCourses; i++)
+        {
+            if (degree[i] == 0)
+            {
+                q.push(i);
+            }
+        }
+        while (!q.empty())
+        {
+            int cur = q.front();
+            res.push_back(cur);
+            q.pop();
+            for (auto &next : map[cur])
+            {
+                degree[next]--;
+                if (degree[next] == 0)
+                    q.push(next);
+            }
+        }
+        return res.size() == numCourses;
+    }
+};
+```
+
+### C
+```cpp
+class Solution
+{
+public:
+    bool canFinish(int numCourses, vector<vector<int>> &prerequisites)
+    {
+
+        vector<vector<int>> graph(numCourses, vector<int>());
+
+        for (auto num : prerequisites)
+        {
+            graph[num[1]].push_back(num[0]);
+        }
+        vector<int> visit(numCourses);
+
+        for (int i = 0; i < numCourses; i++)
+        {
+            if (!dfs(graph, visit, i))
+                return false;
+        }
+        return true;
+    }
+    bool dfs(vector<vector<int>> &g, vector<int> &visit, int i)
+    {
+        if (visit[i] == -1)
+            return false;
+        if (visit[i] == 1)
+            return true;
+        visit[i] = -1;
+        for (auto a : g[i])
+        {
+            if (!dfs(g, visit, a))
+                return false;
+        }
+        visit[i] = 1;
+        return true;
+    }
+};
+```