Chazelle最小生成树算法的c++代码实现

Chazelle最小生成树算法是一种高效的算法，用于求解最小生成树问题。下面是Chazelle最小生成树算法的C++代码实现：

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

struct Edge {
    int src, dest, weight;
};

struct Subset {
    int parent, rank;
};

class Graph {
private:
    int V, E;
    vector<Edge> edges;

public:
    Graph(int V, int E) {
        this->V = V;
        this->E = E;
    }

    void addEdge(int src, int dest, int weight) {
        Edge edge;
        edge.src = src;
        edge.dest = dest;
        edge.weight = weight;
        edges.push_back(edge);
    }

    int find(Subset subsets[], int i) {
        if (subsets[i].parent != i)
            subsets[i].parent = find(subsets, subsets[i].parent);
        return subsets[i].parent;
    }

    void Union(Subset subsets[], int x, int y) {
        int xroot = find(subsets, x);
        int yroot = find(subsets, y);

        if (subsets[xroot].rank < subsets[yroot].rank)
            subsets[xroot].parent = yroot;
        else if (subsets[xroot].rank > subsets[yroot].rank)
            subsets[yroot].parent = xroot;
        else {
            subsets[yroot].parent = xroot;
            subsets[xroot].rank++;
        }
    }

    void ChazelleMST() {
        vector<Edge> result(V);
        int e = 0;
        int i = 0;

        sort(edges.begin(), edges.end(), [](const Edge& a, const Edge& b) {
            return a.weight < b.weight;
        });

        Subset* subsets = new Subset[V];
        for (int v = 0; v < V; v++) {
            subsets[v].parent = v;
            subsets[v].rank = 0;
        }

        while (e < V - 1 && i < E) {
            Edge next_edge = edges[i++];

            int x = find(subsets, next_edge.src);
            int y = find(subsets, next_edge.dest);

            if (x != y) {
                result[e++] = next_edge;
                Union(subsets, x, y);
            }
        }

        cout << "Chazelle最小生成树的边：" << endl;
        for (i = 0; i < e; i++) {
            cout << result[i].src << " - " << result[i].dest << " : " << result[i].weight << endl;
        }
    }
};

int main() {
    int V = 4; // 图的顶点数
    int E = 5; // 图的边数

    Graph graph(V, E);

    // 添加边
    graph.addEdge(0, 1, 10);
    graph.addEdge(0, 2, 6);
    graph.addEdge(0, 3, 5);
    graph.addEdge(1, 3, 15);
    graph.addEdge(2, 3, 4);

    // 执行Chazelle最小生成树算法
    graph.ChazelleMST();

    return 0;
}

以上是Chazelle最小生成树算法的C++代码实现。该算法通过对边进行排序，并使用并查集数据结构来判断是否形成环路，从而得到最小生成树的边集合。在上述代码中，我们创建了一个Graph类来表示图，并实现了ChazelleMST函数来执行算法。在main函数中，我们创建了一个包含4个顶点和5条边的图，并调用ChazelleMST函数来求解最小生成树，并输出结果。