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邻接矩阵实现

news 来源：原创 2024/9/29 7:18:28

图

图的描述方式:

邻接矩阵
邻接链表

邻接矩阵实现

#pragma once
#include "graph.h"
#include <vector>
#include <iostream>
#include <iomanip>
#include <queue>
#include <exception>
//#include <string>
#define  NPOS  -1template <typename V, typename E>
class AdjenctMatrix : public GraphBase<V, E>
{
private:std::vector<V>  m_vctVertexes;std::vector<std::vector<E>> m_matrix;public:AdjenctMatrix(int nSize, bool isWeight = true, bool isDirected = true);virtual ~AdjenctMatrix() {};bool InsertVertex(const V& vertex);bool InsertEdge(const V& vertex1, const V& vertex2, const E& weight);void ShowMatrix();//bool RemoveEdge(const V& vertex1, const V& vertex2);//bool RemoveVertex(const V& vertex);int GetVertexPosition(const V& vertex);V GetVertexValueByPos(int nPos) //根据顶点在顶点表中的位置(下标) 来获取顶点的值{if (!(0 <= nPos && nPos < this->m_vctVertexes.size())){throw std::runtime_error("invalid pos");}return this->m_vctVertexes[nPos];}void DFSTraverse(); //深度优先遍历void BFSTraverse(); //广度优先遍历int FristAdjenctVertex(int i); //获取顶点i 的第一个邻接顶点int NextAdjenctVertex(int i, int n); //返回 i 的邻接顶点 n 的下一个邻接顶点std::vector<std::vector<E>>& GetMatrix() { return this->m_matrix; };E GetWeight(int v1, int v2); //根据顶点在顶点表中的位置, 获取边的权重protected:void DFS(int n, std::vector<bool> &vctVisited);
};template <typename V, typename E>AdjenctMatrix<V, E>::AdjenctMatrix(int nSize, bool isWeight  , bool isDirected )
{this->m_nMaxVertexesCount = nSize;this->m_nVertexesCount = 0;this->m_nEdgesCount = 0;this->m_fDirected = isDirected;this->m_fWeight = isWeight;this->m_vctVertexes.resize(this->m_nMaxVertexesCount);this->m_matrix.resize(this->m_nMaxVertexesCount);for (auto &it : this->m_matrix){it.resize(this->m_nMaxVertexesCount);}for (auto &v : this->m_matrix){for (auto &vv : v){vv = MAGIC_MAX_WEIGHT;}}}template <typename V, typename E>
int AdjenctMatrix<V, E>::GetVertexPosition(const V& vertex)
{for (size_t i = 0; i < this->m_nMaxVertexesCount; i++){if (vertex == this->m_vctVertexes[i]){return i;}}return NPOS;
}template <typename V, typename E>
bool AdjenctMatrix<V, E>::InsertVertex(const V& vertex)
{if (this->m_nVertexesCount == this->m_nMaxVertexesCount){std::cerr<< "size overflow" << std::endl;return false;}if (NPOS != GetVertexPosition(vertex)){std::cerr<< "vertex " << vertex << "already existed" << std::endl;return false;}this->m_vctVertexes[this->m_nVertexesCount++] = vertex; //插入return true;
}template< typename V, typename E>
bool AdjenctMatrix<V, E>::InsertEdge(const V& vertex1, const V& vertex2, const E& weight)
{int nV1Pos = GetVertexPosition(vertex1);int nV2Pos = GetVertexPosition(vertex2);if (NPOS == nV1Pos){std::cerr << "vertex1  not exist" << std::endl;return false;}if (NPOS == nV2Pos){std::cerr << "vertex2  not exist" << std::endl;return false;}if (!(this->MAX_WEIGHT == m_matrix[nV1Pos][nV2Pos] || 0 == m_matrix[nV1Pos][nV2Pos])){std::cerr << "edge: " << vertex1 << " , " << vertex2 << "already existed" << std::endl;return false;}if (this->m_fDirected){ //有向图m_matrix[nV1Pos][nV2Pos] = weight;}else { //无向图m_matrix[nV1Pos][nV2Pos] = weight;m_matrix[nV2Pos][nV1Pos] = weight;}this->m_nEdgesCount ++;return true;
}template <typename V, typename E>
void AdjenctMatrix<V, E>::ShowMatrix()
{//输出顶点for (auto const &it : m_vctVertexes){std::cout << it << ", ";}std::cout << std::endl << "===================" << std::endl;//输出邻接矩阵for (int i = 0; i < this->m_nVertexesCount; i++){for (int j = 0; j < this->m_nVertexesCount; j++){if (this->MAX_WEIGHT == m_matrix[i][j]) {std::cout << std::setw(7) << "∞";}else {std::cout << std::setw(7) << m_matrix[i][j];}}std::cout << std::endl;}}template <typename V, typename E> 
void AdjenctMatrix<V, E>::DFSTraverse() //深度优先遍历
{std::vector<bool> vctVisited(this->m_nVertexesCount, false);for (int i = 0; i < this->m_nVertexesCount; i++){if (!vctVisited[i]){DFS(i, vctVisited);}}}template <typename V, typename E>
void AdjenctMatrix<V, E>::DFS(int i, std::vector<bool> &vctVisited)
{vctVisited[i] = true;std::cout << this->m_vctVertexes[i] << " , ";for (int j = 0; j < this->m_nVertexesCount; j++){if (!vctVisited[j] &&this->m_matrix[i][j] != 0&& this->m_matrix[j][i] != this->MAX_WEIGHT){DFS(j, vctVisited);}}}template <typename V, typename E>
void AdjenctMatrix<V, E>::BFSTraverse() //广度优先遍历
{std::vector<bool> vctVisited(this->m_nVertexesCount, false);std::queue<int> que;for (int i = 0; i < this->m_nVertexesCount; i++){if(vctVisited[i]) continue;que.push(i);vctVisited[i] = true;std::cout << this->m_vctVertexes[i] << " , ";while (!que.empty()){int parent = que.front();que.pop();int child = FristAdjenctVertex(parent);for (int child = FristAdjenctVertex(parent); child >= 0; child = NextAdjenctVertex(parent, child)){if (vctVisited[child])continue;que.push(child);std::cout << this->m_vctVertexes[child] << " , ";vctVisited[child] = true;}}}}template <typename V, typename E>
int AdjenctMatrix<V, E>::NextAdjenctVertex(int i, int n)
{if (!(0 <= i && i < this->m_matrix.size())){std::cerr << "i is invalid" << std::endl;return NPOS;}if (!(0 <= n && n < this->m_matrix.size())){std::cerr << "n is invalid" << std::endl;return NPOS;}for (int col = n + 1; col < this->m_matrix.size() && col < this->m_nVertexesCount; col++){if (this->MAX_WEIGHT != this->m_matrix[i][col] && 0 != this->m_matrix[i][col]){return col;}}return NPOS;
}template <typename V, typename E>
int AdjenctMatrix<V, E>::FristAdjenctVertex(int i)
{if (!(0 <= i && i < this->m_matrix.size())){std::cerr << "i is invalid" << std::endl;return NPOS;}for (int col = 0; col < this->m_nVertexesCount; col++){if (this->MAX_WEIGHT != this->m_matrix[i][col] && 0 != this->m_matrix[i][col]){return col;}}return NPOS;
}template <typename V, typename E>
E AdjenctMatrix<V, E>::GetWeight(int v1, int v2)
{if (0 <= v1 && v1 <= this->m_nVertexesCount && 0 <= v2 && v2 <= this->m_nVertexesCount){return this->m_matrix[v1][v2];}std::cerr << "GetWeight error" << std::endl;throw std::runtime_error("invalid v1 and v2");
}

单源最短路径-- Dijskra

#pragma once
#include <iostream>
#include <vector>
#include <string>//************************************
// Method:    Dijkstra
// FullName:  Dijkstra
// Access:    public 
// Returns:   void
// Qualifier:
// Parameter: int nVertexCount  顶点个数
// Parameter: int nBeginVertexIndex   起始顶点(在顶点表中的下标,例如: 第1个下表为0)
// Parameter: std::vector<int> & vctPrevious   记录最短路径的前驱节点 , 获取一条具体路径, 则反向生成即可
//                                   例如: p为 [0, 1, 1, 3, 4]  
//                                     从第1个顶点到第5个顶点的最短路径为  1, 3, 4, 5  , 
//                                      即  5  <== p[5 - 1] 即 4 <<== p[ 4 - 1 ] 即 3  <<== p[3 - 1] 即 1 
// Parameter: std::vector<int> & vctMinPath  记录起始顶点到各个顶点的权重
// Parameter: const std::vector<std::vector<int>> & matrix   邻接矩阵
//************************************
void Dijkstra(int nVertexCount, int nBeginVertexIndex, std::vector<int>&vctPrevious,std::vector<int>&vctMinPath, const std::vector<std::vector<int>>& matrix)
{int min = MAGIC_MAX_WEIGHT , k = 0;std::vector<bool> vctVisitedRows(nVertexCount, false);for (int i = 0; i < nVertexCount; i++){vctMinPath[i] = matrix[nBeginVertexIndex][i];}vctMinPath[nBeginVertexIndex] = 0;   //表示v到v路径长度为0vctVisitedRows[nBeginVertexIndex] = true;   //表示v到v路径不需要求for (int i = 0; i < nVertexCount; ++i){// 从  vctMinPath 中获取最小的 , 未访问过的 的 索引// 当然也可以使用小根堆来实现min = MAGIC_MAX_WEIGHT;for (int j = 0; j < nVertexCount; ++j){if (!vctVisitedRows[j] && 0 != vctMinPath[j]  && vctMinPath[j] < min){k = j;min = vctMinPath[j];}}vctVisitedRows[k] = true;   for (int w = 0; w < nVertexCount; w++){//如果复合路径(就是有多条边)的权重   小于   单路径(直达)的权重    则调整最小权重路径vctMinPath// 不可直达的权重初始化为 MAGIC_MAX_WEIGHT  即无穷大if (!vctVisitedRows[w] && 0 != matrix[k][w] &&(min + matrix[k][w]) < vctMinPath[w]){vctMinPath[w] = min + matrix[k][w];vctPrevious[w] = k;    //将此顶点加入到最短路径前驱}}}
}void Floyd(int num, std::vector<std::vector<int>> &p, std::vector<std::vector<int>>& d)
{for (int i = 0; i < num; ++i)   //初始化p{for (int j = 0; j < num; ++j){//d[i][j] = g[i][j];p[i][j] = j;}}for (int i = 0; i < num; ++i)   //初始化d和p{for (int j = 0; j < num; ++j){for (int k = 0; k < num; k++){if (d[j][k] > d[j][i] + d[i][k]){d[j][k] = d[j][i] + d[i][k];p[j][k] = p[j][i];}}}}
}

测试

// datastructure.cpp : 此文件包含 "main" 函数。程序执行将在此处开始并结束。
//#include <iostream>
#include "adjenct_matrix.h"
#include "algo.h"
#include <stack>int main()
{AdjenctMatrix<int, int>  adjmatrx(10);adjmatrx.InsertVertex(1);adjmatrx.InsertVertex(2);adjmatrx.InsertVertex(3);adjmatrx.InsertVertex(4);adjmatrx.InsertEdge(1, 2, 1);adjmatrx.InsertEdge(1, 3, 2);adjmatrx.InsertEdge(2, 4, 5);adjmatrx.InsertEdge(3, 4, 1);adjmatrx.ShowMatrix();std::cout << "========" << std::endl;adjmatrx.DFSTraverse();std::cout << "========" << std::endl;adjmatrx.BFSTraverse();std::cout << "========" << std::endl;int nVertexCount = adjmatrx.GetVertexCount();int nBeginVertex = 1;int nBeginVertexIndex = adjmatrx.GetVertexPosition(nBeginVertex);std::vector<int> vctPrevious(nVertexCount,  nBeginVertexIndex );std::vector<int> vctMinPath(nVertexCount, MAGIC_MAX_WEIGHT);Dijkstra(nVertexCount, nBeginVertexIndex, vctPrevious, vctMinPath, adjmatrx.GetMatrix());for (auto const &item : vctMinPath){std::cout << item << " , ";}std::cout << std::endl;int nEndVertex = 4;int nEndVertexIndex = adjmatrx.GetVertexPosition(nEndVertex);std::stack<int>  minPath;minPath.push(nEndVertexIndex);for (int i = nEndVertexIndex; ; ){minPath.push( vctPrevious[i] );i = vctPrevious[i];if (nBeginVertexIndex == i){break;}}for ( ; !minPath.empty() ; ){int pos = minPath.top();std::cout << adjmatrx.GetVertexValueByPos(pos);minPath.pop();if (minPath.size() > 0){std::cout << "->";}}std::cout << std::endl;std::cout << "Hello World!\n"; 
}