算法导论 ch23 最小生成树 Kruskal

最新推荐文章于 2023-07-02 22:17:03 发布

最新推荐文章于 2023-07-02 22:17:03 发布 · 2.2k 阅读

本文介绍了一种使用Kruskal算法寻找最小生成树的方法。通过定义边类MSTEdge，并实现比较运算符来确保能够正确地按权重排序边。此外，还提供了用于查找集合和合并集合的函数，以避免形成环路。

1. Kruskal 实现

1) MSTEdge.h

#ifndef MSTEDGE_H_ #define MSTEDGE_H_ #include <iostream> using namespace std; /* * Edge class for MST */ class MSTEdge { public: int from; int to; int weight; public: bool operator < (MSTEdge &that){ return weight < that.weight; } }; ostream& operator <<(ostream& os, MSTEdge &e); #endif /*MSTEDGE_H_*/

2) MSTEdge.cpp

#include "MSTEdge.h" ostream& operator <<(ostream& os, MSTEdge &q) { os << "("<< q.from<< ", "<< q.to<< ", "<< q.weight<< ")"; return os; }

3) Kruskal.cpp

#include "MSTEdge.h" #include <iostream> #include <vector> #include <algorithm> using namespace std; bool MSTEdgeCompare(MSTEdge i, MSTEdge j) { return (i<j); } int findSet(int p[], int numberOfVertexes, int v) { while(p[v] != v) { v = p[v]; } return v; } void unionSet(int **p, int x, int y) { do{ int py = (*p)[y]; (*p)[y] = x; y = py; }while((*p)[y] != x); // for (int i = 0; i < 10; i++) { // cout << (*p)[i] << " "; // } // cout << endl; } void mst_kruskal(MSTEdge e[], unsigned int numberOfEdges, int numberOfVertexes) { int* p = new int[numberOfVertexes + 1]; for (int i = 0; i < numberOfVertexes + 1; i++) { p[i] = i; } vector<MSTEdge> vecEdges(e, e + numberOfEdges); vector<MSTEdge> mst; sort(vecEdges.begin(), vecEdges.end(), MSTEdgeCompare); vector<MSTEdge>::iterator it; for (it = vecEdges.begin(); it != vecEdges.end(); ++it) { cout <<"now checking edge "<< *it << endl; int from = (*it).from; int to = (*it).to; int fromSet = findSet(p, numberOfVertexes, from ); int toSet = findSet(p, numberOfVertexes, to); // cout << "p of " << from << " is " << fromSet << endl; // cout << "p of " << to << " is " << toSet << endl; if(fromSet != toSet){ // find an tree edge mst.push_back(*it); unionSet(&p, from, to); } } int weight = 0; cout << "The MST constructed using Kruskal algorithm is " << endl; for (it = mst.begin(); it != mst.end(); ++it) { cout << *it << endl; weight += (*it).weight; } cout << "Weight is " << weight << endl; // for (int i = 0; i < numberOfVertexes + 1; i++) { // cout << p[i] << " "; // } // cout << endl; } int main() { MSTEdge e[] = { { 1, 2, 4 }, { 1, 8, 8 }, { 2, 8, 11 }, { 2, 3, 8 }, { 3, 4, 7 }, { 3, 6, 4 }, { 3, 9, 2 }, { 4, 5, 9 }, { 4, 6, 14 }, { 5, 6, 10 }, { 6, 7, 2 }, { 7, 8, 1 }, { 7, 9, 6 }, { 8, 9, 7 } }; unsigned int numberOfEdges = sizeof(e)/sizeof(MSTEdge); mst_kruskal(e, numberOfEdges, 9); }

4) run result

now checking edge (7, 8, 1) now checking edge (3, 9, 2) now checking edge (6, 7, 2) now checking edge (1, 2, 4) now checking edge (3, 6, 4) now checking edge (7, 9, 6) now checking edge (3, 4, 7) now checking edge (8, 9, 7) now checking edge (1, 8, 8) now checking edge (2, 3, 8) now checking edge (4, 5, 9) now checking edge (5, 6, 10) now checking edge (2, 8, 11) now checking edge (4, 6, 14) The MST constructed using Kruskal algorithm is (7, 8, 1) (3, 9, 2) (6, 7, 2) (1, 2, 4) (3, 6, 4) (3, 4, 7) (1, 8, 8) (4, 5, 9) Weight is 37