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Author: koralkulacoglu

LeetCode/1558-course-schedule-iv/README.md

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+<p>There are a total of <code>numCourses</code> courses you have to take, labeled from <code>0</code> to <code>numCourses - 1</code>. You are given an array <code>prerequisites</code> where <code>prerequisites[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that you <strong>must</strong> take course <code>a<sub>i</sub></code> first if you want to take course <code>b<sub>i</sub></code>.</p>
+
+<ul>
+	<li>For example, the pair <code>[0, 1]</code> indicates that you have to take course <code>0</code> before you can take course <code>1</code>.</li>
+</ul>
+
+<p>Prerequisites can also be <strong>indirect</strong>. If course <code>a</code> is a prerequisite of course <code>b</code>, and course <code>b</code> is a prerequisite of course <code>c</code>, then course <code>a</code> is a prerequisite of course <code>c</code>.</p>
+
+<p>You are also given an array <code>queries</code> where <code>queries[j] = [u<sub>j</sub>, v<sub>j</sub>]</code>. For the <code>j<sup>th</sup></code> query, you should answer whether course <code>u<sub>j</sub></code> is a prerequisite of course <code>v<sub>j</sub></code> or not.</p>
+
+<p>Return <i>a boolean array </i><code>answer</code><i>, where </i><code>answer[j]</code><i> is the answer to the </i><code>j<sup>th</sup></code><i> query.</i></p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+<img alt="" src="https://assets.leetcode.com/uploads/2021/05/01/courses4-1-graph.jpg" style="width: 222px; height: 62px;" />
+<pre>
+<strong>Input:</strong> numCourses = 2, prerequisites = [[1,0]], queries = [[0,1],[1,0]]
+<strong>Output:</strong> [false,true]
+<strong>Explanation:</strong> The pair [1, 0] indicates that you have to take course 1 before you can take course 0.
+Course 0 is not a prerequisite of course 1, but the opposite is true.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<pre>
+<strong>Input:</strong> numCourses = 2, prerequisites = [], queries = [[1,0],[0,1]]
+<strong>Output:</strong> [false,false]
+<strong>Explanation:</strong> There are no prerequisites, and each course is independent.
+</pre>
+
+<p><strong class="example">Example 3:</strong></p>
+<img alt="" src="https://assets.leetcode.com/uploads/2021/05/01/courses4-3-graph.jpg" style="width: 222px; height: 222px;" />
+<pre>
+<strong>Input:</strong> numCourses = 3, prerequisites = [[1,2],[1,0],[2,0]], queries = [[1,0],[1,2]]
+<strong>Output:</strong> [true,true]
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>2 &lt;= numCourses &lt;= 100</code></li>
+	<li><code>0 &lt;= prerequisites.length &lt;= (numCourses * (numCourses - 1) / 2)</code></li>
+	<li><code>prerequisites[i].length == 2</code></li>
+	<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt;= numCourses - 1</code></li>
+	<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
+	<li>All the pairs <code>[a<sub>i</sub>, b<sub>i</sub>]</code> are <strong>unique</strong>.</li>
+	<li>The prerequisites graph has no cycles.</li>
+	<li><code>1 &lt;= queries.length &lt;= 10<sup>4</sup></code></li>
+	<li><code>0 &lt;= u<sub>i</sub>, v<sub>i</sub> &lt;= numCourses - 1</code></li>
+	<li><code>u<sub>i</sub> != v<sub>i</sub></code></li>
+</ul>

LeetCode/1558-course-schedule-iv/solution.cpp

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+class Solution {
+public:
+    vector<bool> checkIfPrerequisite(int numCourses, vector<vector<int>>& prerequisites, vector<vector<int>>& queries) {
+        vector<vector<int>> graph(numCourses);
+        for (vector<int>& i : prerequisites) graph[i[0]].push_back(i[1]);
+
+        int t = 0;
+        vector<bitset<100>> isPrereq(numCourses);
+        vector<bool> seen(numCourses, false);
+
+        auto dfs = [&](auto&& self, int node) -> void {
+            seen[node] = true;
+            for (int neigh : graph[node]) {
+                if (!seen[neigh]) self(self, neigh);
+                isPrereq[node] |= isPrereq[neigh];
+                isPrereq[node].set(neigh);
+            }
+        };
+
+        for (int i=0; i<numCourses; i++) if (!seen[i]) dfs(dfs, i);
+
+        vector<bool> res;
+        for (vector<int>& q : queries) res.push_back(isPrereq[q[0]].test(q[1]));
+
+        return res;
+    }
+};