圖的代碼實現(鄰接矩陣)

不知上期各位讀者思考得怎么樣了，這期的文章是接上一期的。

 

本文的主要內容為：圖的C++代碼實現 (鄰接矩陣法)，主要為各個類的具體實現

 

圖的抽象基類

// FilenName: Graph.cpp

#include "Graph.h"

const int CGraph::UNVISITED = 0;
const int CGraph::VISITED = 1;

CGraph::CGraph(int numVertex) {
    this->numVertex = numVertex;
    this->numEdge = 0;
    this->mark = new int[this->numVertex];
    this->inDegree = new int[this->numVertex];

    for(int i = 0; i < this->numVertex; i++){
        this->mark[i] = CGraph::UNVISITED;
        this->inDegree[i] = 0;
    }
}

CGraph::~CGraph() {
    delete[] this->mark;
    delete[] this->inDegree;
}

int CGraph::GetVerticesNum() {
    return this->numVertex;
}

int CGraph::GetEdgesNum() {
    return this->numEdge;
}

int CGraph::GetFromVertex(CEdge oneEdge) {
    return oneEdge.from;
}

int CGraph::GetToVertex(CEdge oneEdge) {
    return oneEdge.to;
}

int CGraph::GetWeight(CEdge oneEdge) {
    return oneEdge.weight;
}

bool CGraph::IsEdge(CEdge oneEdge) {
    return (oneEdge.from >= 0 && oneEdge.to >=0 && oneEdge.weight >= 0);
}

void CGraph::ResetMark() {
    for(int i = 0; i < this->numVertex; i++){
        this->mark[i] = CGraph::UNVISITED;
    }
}

 

圖的鄰接矩陣實現類

// FileName: GraphAdjacentMatrix.cpp

#include "GraphAdjacentMatrix.h"
#include <queue>
using namespace std;

/**********************************************
 * 函數功能：構造函數，動態分配鄰接矩陣二維數組，
 *          調用者無需釋放，析構函數會自動釋放
 * @param:
 *     numVertex: 圖的頂點數目
 * @return:
 *     無
 *********************************************/
CGraphM::CGraphM(int numVertex) : CGraph(numVertex) {
    this->matrix = (int**) new int*[this->numVertex];
    for(int i = 0; i < numVertex; i++){
        this->matrix[i] = new int[this->numVertex];
    }

    for(int i = 0; i < numVertex; i++){
        for(int j = 0; j < numVertex; j++){
            this->matrix[i][j] = 0;
        }
    }
}


/************************************************
 * 函數功能：析構函數，釋放動態分配的鄰接矩陣二維數組
 * @param:
 *     Null
 * @return:
 *     無
 ***********************************************/
CGraphM::~CGraphM() {
    for(int i = 0; i < this->numVertex; i++){
        delete [] this->matrix[i];
    }
    delete [] this->matrix;
}


/**********************************************
 * 函數功能：刪除邊
 * @param:
 *     from: 邊的起點
 *     to: 邊的終點
 * @return:
 *     void
 *********************************************/
void CGraphM::delEdge(int from, int to) {
    if(from == to){
        this->matrix[from][to] = 0;
    }
    else{
        this->matrix[from][to] = -1;
    }
    this->inDegree[to]--;
    this->numEdge--;
}

/**********************************************
 * 函數功能：設置邊
 * @param:
 *     from: 邊的起點
 *     to: 邊的終點
 *     weight：邊的權值
 * @return:
 *     void
 *********************************************/
void CGraphM::SetEdge(int from, int to, int weight) {
    if(from == to){
        this->matrix[from][to] = 0;
    }
    else{
        this->matrix[from][to] = weight;
    }
    this->inDegree[to]++;
    this->numEdge++;
}

/**********************************************
 * 函數功能：獲取以參數 oneVertex 為起點的第一條邊
 * @param:
 *     oneVertex: 邊的起點
 * @return:
 *     邊類對象
 *********************************************/
CEdge CGraphM::FirstEdge(int oneVertex) {
    CEdge resultEdge;   // 函數返回值
    resultEdge.from = oneVertex;    // 起點

    for(int i = 0; i < this->numVertex; i++){
        if(this->matrix[resultEdge.from][i] > 0){
            resultEdge.to = i;
            resultEdge.weight = this->matrix[resultEdge.from][i];
            break;
        }
    }
    return resultEdge;
}

/**********************************************
 * 函數功能：獲取和參數 perEdge 同起點的下一條邊
 * @param:
 *     preEdge： 上一條邊
 * @return:
 *     邊類對象
 *********************************************/
CEdge CGraphM::NextEdge(CEdge preEdge) {
    CEdge resultEdge;   // 函數返回值
    resultEdge.from = preEdge.from; // 起點
    if(preEdge.to < this->numVertex - 1){ // 如果上一條邊的終點 小於 頂點的個數減1 則存在下一條邊
        for(int i = preEdge.to + 1; i < this->numVertex; i++){
            if(this->matrix[preEdge.from][i] > 0){
                resultEdge.to = i;
                resultEdge.weight = this->matrix[preEdge.from][i];
                break;
            }
        }
    }
    return resultEdge;
}

/**********************************************
 * 函數功能：初始化圖
 * @param:
 *     pWArray2D: 二維鄰接矩陣的一維指針
 * @return:
 *     void
 *********************************************/
void CGraphM::InitGraphM(int *pWArray2D) {
    int N = this->numVertex;
    int array_i_j = 0;

    for(int i = 0; i < N; i++){
        for(int j = 0; j < N; j++){
            array_i_j = *(pWArray2D + i * N + j); // 用一維數組的方式訪問二維數組 *(起點地址 + 行數 * 總行數 + 列數)
            if(array_i_j > 0){
                this->SetEdge(i, j, array_i_j);
            }
        }
    }
}

/**********************************************
 * 函數功能：深度優先搜索
 * @param:
 *     oneVertex: 開始搜索的起點
 * @return:
 *     void
 *********************************************/
void CGraphM::DFS(int oneVertex) {
    this->mark[oneVertex] = CGraph::VISITED;
    this->Visit(oneVertex);

    for(CEdge edge = this->FirstEdge(oneVertex); this->IsEdge(edge); edge = this->NextEdge(edge)){
        if(this->mark[edge.to] == CGraph::UNVISITED){
            this->DFS(edge.to);
        }
    }
}

/**********************************************
 * 函數功能：廣度優先搜索
 * @param:
 *     oneVertex: 開始搜索的起點
 * @return:
 *     void
 *********************************************/
void CGraphM::BFS(int oneVertex) {
    queue<int> queueEdge;
    this->Visit(oneVertex);
    this->mark[oneVertex] = CGraph::VISITED;
    queueEdge.push(oneVertex);

    while(!queueEdge.empty()){
        int u = queueEdge.front();
        queueEdge.pop();
        for(CEdge edge = this->FirstEdge(oneVertex); this->IsEdge(edge); edge = this->NextEdge(edge)){
            if(this->mark[edge.to] == CGraph::UNVISITED){
                this->Visit(edge.to);
                this->mark[edge.to] = CGraph::VISITED;
                queueEdge.push(edge.to);
            }
        }
    }
}


/**********************************************
 * 函數功能：訪問頂點
 * @param:
 *     oneVertex: 要訪問的頂點
 * @return:
 *     void
 *********************************************/
void CGraphM::Visit(int oneVertex) {
    cout << "C" << oneVertex << " ";
}


/**********************************************
 * 函數功能：圖的周游接口合並
 * @param:
 *     startVertex: 開始周游的起點
 *     travelType: 周游類型
 *         travelType = 0: DFS
 *         travelType = 1: BFS
 * @return:
 *     void
 *********************************************/
void CGraphM::Travel(int startVertex, int travelType) {
    for(int i = startVertex, n = 0; n < this->numVertex; i++, n++){
        i %= this->numVertex;
        if(this->mark[i] == CGraph::UNVISITED){
            switch(travelType){
                case 0:
                    this->DFS(i);
                    break;
                case 1:
                    this->BFS(i);
                    break;
                default:
                    cout << "Error: travelType must be in [0, 1]" << endl;
                    break;
            }
        }
    }
}

 

以上就是圖的鄰接矩陣的具體的實現方法。

有不懂之處，歡迎各位讀者留言評論交流。

有不足之處，希望各位讀者多多包涵，也希望讀者們能留言評論指出我的不足，十分感謝！

 

下期預告：利用圖實現：拓撲排序算法，最小路徑算法，最小生成樹算法，敬請期待。