数据结构——拓扑排序算法_数据结构拓扑排序算法

拓扑排序的深度优先算法（Topological Sort with Depth-First Search）是一种在有向无环图（DAG）中进行排序的方法。
。该算法使用递归来进行深度优先搜索，并在搜索完成后将节点添加到排序结果中。

#include <iostream>
#include <vector>
#include <stack>
using namespace std;

class Graph {
private:
    int numVertices; // 图中节点的数量
    vector<vector<int>> adjacencyList; // 邻接表

public:
    Graph(int vertices) : numVertices(vertices) {
        adjacencyList.resize(vertices);
    }

    // 添加有向边
    void addEdge(int start, int end) {
        adjacencyList[start].push_back(end);
    }

    // 深度优先搜索拓扑排序算法
    void topologicalSortDFS(int vertex, vector<bool>& visited, stack<int>& result) {
        visited[vertex] = true;

        // 递归访问相邻节点
        for (int neighbor : adjacencyList[vertex]) {
            if (!visited[neighbor]) {
                topologicalSortDFS(neighbor, visited, result);
            }
        }

        // 将当前节点压入栈中
        result.push(vertex);
    }

    // 执行拓扑排序
    vector<int> topologicalSort() {
        vector<bool> visited(numVertices, false);
        stack<int> result;

        // 对每个未访问的节点执行深度优先搜索
        for (int i = 0; i < numVertices; ++i) {
            if (!visited[i]) {
                topologicalSortDFS(i, visited, result);
            }
        }

        // 从栈中提取排序结果
        vector<int> sortedResult;
        while (!result.empty()) {
            sortedResult.push_back(result.top());
            result.pop();
        }

        return sortedResult;
    }
};

int main() {
    Graph graph(6);

    graph.addEdge(5, 2);
    graph.addEdge(5, 0);
    graph.addEdge(4, 0);
    graph.addEdge(4, 1);
    graph.addEdge(2, 3);
    graph.addEdge(3, 1);

    vector<int> result = graph.topologicalSort();

    cout << "Topological Sort: ";
    for (int vertex : result) {
        cout << vertex << " ";
    }
    cout << endl;

    return 0;
}

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拓扑排序的广度优先算法（Topological Sort with Breadth-First Search）是一种在有向无环图（DAG）中进行排序的方法。与深度优先算法不同，广度优先算法使用队列来实现拓扑排序。

#include <iostream>
#include <vector>
#include <queue>
using namespace std;

class Graph {
private:
    int numVertices; // 图中节点的数量
    vector<vector<int>> adjacencyList; // 邻接表

public:
    Graph(int vertices) : numVertices(vertices) {
        adjacencyList.resize(vertices);
    }

    // 添加有向边
    void addEdge(int start, int end) {
        adjacencyList[start].push_back(end);
    }

    // 拓扑排序算法
    vector<int> topologicalSort() {
        vector<int> inDegree(numVertices, 0); // 记录每个节点的入度
        queue<int> q; // 用于BFS的队列

        // 计算每个节点的入度
        for (int i = 0; i < numVertices; ++i) {
            for (int neighbor : adjacencyList[i]) {
                inDegree[neighbor]++;
            }
        }

        // 将入度为0的节点加入队列
        for (int i = 0; i < numVertices; ++i) {
            if (inDegree[i] == 0) {
                q.push(i);
            }
        }

        vector<int> result; // 用于存储排序结果

        // 执行广度优先搜索
        while (!q.empty()) {
            int current = q.front();
            q.pop();
            result.push_back(current);

            // 更新相邻节点的入度，并将入度为0的节点加入队列
            for (int neighbor : adjacencyList[current]) {
                inDegree[neighbor]--;
                if (inDegree[neighbor] == 0) {
                    q.push(neighbor);
                }
            }
        }

        return result;
    }
};

int main() {
    Graph graph(6);

    graph.addEdge(5, 2);
    graph.addEdge(5, 0);
    graph.addEdge(4, 0);
    graph.addEdge(4, 1);
    graph.addEdge(2, 3);
    graph.addEdge(3, 1);

    vector<int> result = graph.topologicalSort();

    cout << "Topological Sort: ";
    for (int vertex : result) {
        cout << vertex << " ";
    }
    cout << endl;

    return 0;
}

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