C++如何实现图算法 C++图算法的实现与优化

// 邻接表示例
#include <iostream>
#include <vector>

using namespace std;

int main() {
    int n = 5; // 顶点数量
    vector<vector<int>> adjList(n);

    // 添加边 (0, 1), (0, 2), (1, 3), (2, 4)
    adjList[0].push_back(1);
    adjList[0].push_back(2);
    adjList[1].push_back(3);
    adjList[2].push_back(4);

    // 打印邻接表
    for (int i = 0; i < n; ++i) {
        cout << "Vertex " << i << ": ";
        for (int neighbor : adjList[i]) {
            cout << neighbor << " ";
        }
        cout << endl;
    }

    return 0;
}

// BFS示例
#include <iostream>
#include <vector>
#include <queue>

using namespace std;

void bfs(const vector<vector<int>>& adjList, int startNode) {
    int n = adjList.size();
    vector<bool> visited(n, false);
    queue<int> q;

    visited[startNode] = true;
    q.push(startNode);

    while (!q.empty()) {
        int u = q.front();
        q.pop();
        cout << u << " ";

        for (int v : adjList[u]) {
            if (!visited[v]) {
                visited[v] = true;
                q.push(v);
            }
        }
    }
    cout << endl;
}

int main() {
    int n = 5;
    vector<vector<int>> adjList(n);
    adjList[0].push_back(1);
    adjList[0].push_back(2);
    adjList[1].push_back(3);
    adjList[2].push_back(4);

    cout << "BFS traversal starting from node 0: ";
    bfs(adjList, 0);

    return 0;
}

// Dijkstra算法示例
#include <iostream>
#include <vector>
#include <queue>
#include <limits>

using namespace std;

const int INF = numeric_limits<int>::max();

void dijkstra(const vector<vector<pair<int, int>>>& adjList, int startNode) {
    int n = adjList.size();
    vector<int> dist(n, INF);
    dist[startNode] = 0;

    priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
    pq.push({0, startNode});

    while (!pq.empty()) {
        int d = pq.top().first;
        int u = pq.top().second;
        pq.pop();

        if (d > dist[u]) continue; // 已经找到更短的路径

        for (const auto& edge : adjList[u]) {
            int v = edge.first;
            int weight = edge.second;

            if (dist[v] > dist[u] + weight) {
                dist[v] = dist[u] + weight;
                pq.push({dist[v], v});
            }
        }
    }

    cout << "Shortest distances from node " << startNode << ":" << endl;
    for (int i = 0; i < n; ++i) {
        cout << "To node " << i << ": ";
        if (dist[i] == INF) {
            cout << "INF" << endl;
        } else {
            cout << dist[i] << endl;
        }
    }
}

int main() {
    int n = 5;
    vector<vector<pair<int, int>>> adjList(n); // (邻接点, 权重)

    adjList[0].push_back({1, 2});
    adjList[0].push_back({2, 4});
    adjList[1].push_back({2, 1});
    adjList[1].push_back({3, 7});
    adjList[2].push_back({3, 3});
    adjList[3].push_back({4, 1});

    dijkstra(adjList, 0);

    return 0;
}