图的存储之邻接表的链式前向星实现

数据结构中，我们存储图结构主要有5种方式：邻接矩阵、邻接表、十字链表、邻接多重表、边集数组。在算法竞赛中，我们用比较多是前两种，但由于邻接矩阵操作起来的时间复杂度和空间复杂度较高（如果存储稀疏图会极大浪费空间），因此我们更多采用邻接表进行存储，为了避免复杂的指针操作，在这里我们使用链式前向星进行存储。

graph.h

#pragma once
#include <iostream>
#include <vector>
using namespace std;

struct node{ //边集
	int to; //指向的结点
	int wt; //该结点与所指向的结点的权值
	int next; //下一结点
	node() { to = 0; wt = 0; next = -1; }
	node(int t, int w, int n): to(t),wt(w),next(n){}
};

class Graph{
private:
	vector<int> head; //顶点集，head[i]表示顶点i所指向的边集edge的下标
	vector<node> edge; //边集
	int nodeNum; //顶点的数目
	int edgeNum; //边的数目
	bool isDirected; //该图是有向图还是无向图
	vector<int> isvisited; 
	bool visited();
	void dfs_searching(int startIndex);
	void initVis();
public:
	Graph(int n,bool isDirected); //顶点数，是否为有向图
	void addEdge(int u, int v, int w);  //在顶点u和v之间加一条权值为w的边
	void printEdgeTable(); //打印出邻接表
	void dfs(int startIndex); //dfs搜索图的各结点
};

graph.cpp

#include "graph.h"

bool Graph::visited(){
	for (int i = 1; i <= nodeNum; i++) {
		if (isvisited[i] == 0) {
			return 0;
		}
	}
	return 1;
}

void Graph::dfs_searching(int startIndex){ //dfs搜索
	if (!isvisited[startIndex]) {
		isvisited[startIndex] = 1;
		cout << startIndex << ' ';
		int cur = head[startIndex];
		while (cur != -1) {
			dfs_searching(edge[cur].to);
			cur = edge[cur].next;
		}
	}
}

void Graph::initVis(){
	for (int i = 1; i <= nodeNum; i++) {
		isvisited[i] = 0;
	}
}

Graph::Graph(int n,bool isDirected){
	if (n <= 0) {
		return;
	}
	head.resize(n + 1, -1);
	nodeNum = n;
	edgeNum = edge.size();
	this->isDirected = isDirected;
	isvisited.resize(n + 1, 0);
}

void Graph::addEdge(int u, int v, int w){ 
	if (u > nodeNum || v > nodeNum) {
		return;
	}

	//采用类似 链表的“头插法” 插入节点
	edge.push_back(node(v,w,head[u]));
	head[u] = edge.size() - 1;

	if (!isDirected) { //如果是无向图
		edge.push_back(node(u, w, head[v]));
		head[v] = edge.size() - 1;
	}
	edgeNum++;
}

void Graph::printEdgeTable(){
	cout << "head\tedge\n";
	for (int i = 1; i <= nodeNum; i++) {
		cout << i << ":\t";
		int cur = head[i];
		while (cur != -1) {
			cout << "[" << edge[cur].to << ' ' << edge[cur].wt << "]\t";
			cur = edge[cur].next;
		}
		cout << endl;
	}
}

void Graph::dfs(int startIndex){
	dfs_searching(startIndex);
	initVis();
}

main.cpp

#include "graph.h"

void test() {
	int n, m;
	cin >> n >> m; //n为顶点数，m为边数
	Graph g(n, 0);
	for (int i = 1; i <= m; i++) {
		int u, v, w;
		cin >> u >> v >> w;
		g.addEdge(u, v, w);
	}
	g.printEdgeTable();
	cout << endl;
	g.dfs(1); //从顶点1开始dfs
}

int main() {
	test();
	return 0;
}