Course Schedule

Author: evagle

src/CourseSchedule

@@ -0,0 +1,120 @@
+#include <iostream>
+#include <vector>
+#include <map>
+using namespace std;
+
+// 拓扑排序方法判断图是否有环
+class Solution1 {
+public:
+	// (u,v)表示从u->v的边
+    bool canFinish(int numCourses, vector<vector<int> >& prerequisites) {
+		int count[numCourses];
+		vector<int> points;
+		// edge[i]存放所有从i出发与i相连的顶点
+		std::map<int, vector<int> > edge;
+		memset(count, 0, sizeof(count));
+        for (int i = 0 ; i < prerequisites.size(); i++) {
+			vector<int> pair  = prerequisites[i];
+			int u = pair[0];
+			int v = pair[1];
+			count[v]++;
+			if (edge.find(u) == edge.end()) {
+				edge[u] = vector<int>();
+			}
+			edge[u].push_back(v);
+		}
+		
+		for (int i = 0; i < numCourses; i++) {
+			if (count[i] == 0) {
+				points.push_back(i);
+			}
+		}
+		
+		while (points.size()) {
+			int u = points.back();
+			points.pop_back();
+	        for (int v : edge[u]) {
+				count[v]--;
+				if (count[v] == 0) {
+					points.push_back(v);
+				}
+			}
+		}
+		
+		for (int i = 0; i < numCourses; i++) {
+			if (count[i] != 0) {
+				return false;
+			}
+		}
+		return true;
+    }
+};
+
+// DFS判断图是否有环
+class Solution {
+public:
+    bool canFinish(int numCourses, vector<vector<int> >& prerequisites) {
+		// edge[i]临接表形式存放所有从i出发与i相连的顶点
+		std::map<int, vector<int> > edge;
+
+        for (int i = 0 ; i < prerequisites.size(); i++) {
+			vector<int> pair  = prerequisites[i];
+			int u = pair[0];
+			int v = pair[1];
+			if (edge.find(u) == edge.end()) {
+				edge[u] = vector<int>();
+			}
+			edge[u].push_back(v);
+		}
+		bool visit[numCourses];
+		bool handled[numCourses];
+		memset(visit, 0, sizeof(visit));
+		memset(handled, 0, sizeof(handled));
+		bool hasLoop = false;
+
+		// 对每一个入度为0的点进行dfs，判断是否有环, handled表示之前dfs处理过的点不再处理
+		for (int i = 0; i < numCourses; i++) {
+			if (!handled[i]) {
+				hasLoop |= dfs(i, edge, visit, handled);
+				if (hasLoop) {
+					break;
+				}
+			}
+		}
+		
+		return !hasLoop;
+    }
+	// 对图进行深度遍历，如果一条链中有环，就会出现遍历的点已经遍历过
+	bool dfs(int start, const std::map<int, vector<int> > &edge, bool visit[], bool handled[]) {
+		if (visit[start]) {
+			return true;
+		}
+		if (edge.find(start) == edge.end()) 
+			return false;
+			
+		visit[start] = true;
+		handled[start] = true;
+		bool hasLoop = false;
+		for (int i = 0; i < edge.at(start).size(); i++) {
+			hasLoop |= dfs(edge.at(start)[i], edge, visit, handled);
+			if (hasLoop) {
+			    break;
+			}
+		}
+		visit[start] = false;
+		return hasLoop;
+	}
+};
+int main(int argc, char *argv[]) {
+	Solution s;
+	vector<vector<int> > v;
+	vector<int> v1;
+	v1.push_back(1);
+	v1.push_back(0);
+	vector<int> v2;
+	v2.push_back(0);
+	v2.push_back(1);
+	v.push_back(v1);
+	v.push_back(v2);
+	s.canFinish(2, v);
+}