破圈法实现最小生成树c++编写程序
时间: 2024-07-25 18:00:49 浏览: 47
破圈法(Kruskal's Algorithm),也称为普利姆算法(Prim's Algorithm),是一种用于求解无向连通加权图中最小生成树的算法。它的基本思想是从图中任选一个顶点开始,每次选择一条当前未加入到已构成的树中的最短边,直到所有顶点都被包含在内,形成一棵树。
以下是使用 C++ 实现破圈法的一个简短版本:
```cpp
#include <iostream>
#include <vector>
#include <set>
using namespace std;
struct Edge {
int src, dest, weight;
};
bool compare(Edge e1, Edge e2) {
return e1.weight < e2.weight;
}
int kruskal(int vertices, vector<Edge> edges) {
set<pair<int, int>> minEdges;
for (Edge edge : edges)
minEdges.insert({edge.weight, edge.src + edge.dest});
int result = 0;
for (int i = 0; i < vertices - 1 && !minEdges.empty(); ++i) {
int weight = minEdges.begin()->first;
int u = minEdges.begin()->second / 2;
int v = minEdges.begin()->second % 2 + u;
minEdges.erase(minEdges.begin());
// Check if adding the edge doesn't form a cycle in the current tree
bool doesCycle = false;
for (auto it = minEdges.begin(); it != minEdges.end(); ++it) {
if (u == it->second / 2 || v == it->second % 2 + u)
doesCycle = true;
}
if (!doesCycle)
result += weight;
}
return result;
}
// 示例使用
int main() {
int vertices = 5;
vector<Edge> edges = {{0, 1, 10}, {0, 4, 20}, {1, 2, 5}, {1, 3, 15}, {2, 4, 30}, {3, 4, 25}};
cout << "Minimum spanning tree using Kruskal's algorithm: " << kruskal(vertices, edges);
return 0;
}
```
在这个程序中,`kruskal` 函数首先将边按照权重排序,然后逐次添加边,同时检查新添加的边是否会形成环。如果不会,就将其权重累加到结果上。这个过程会持续到添加完所有的边并构建出最小生成树为止。