鄰接表與鄰接矩陣的深度優先演算法和廣度優先演算法
阿新 • • 發佈：2019-02-10
鄰接矩陣的深度優先演算法：
#include<iostream> using namespace std; #define MAX 20 // 注：鄰接矩陣是圖的順序儲存方式 typedef struct node { int no; //頂點編號 // char data; //頂點其它資訊，不常用 }VertexType; typedef struct //圖的定義 { int edges[MAX][MAX]; //鄰接矩陣定義 int n, e; //頂點數和邊數 VertexType vex[MAX]; //存放節點資訊 }MGraph; MGraph graph; bool visited[MAX];//訪問過的標誌為true 未訪問的設定為false void Create() { cout << "輸入頂點數和邊數: "; cin >> graph.n >> graph.e; int N1 = graph.n, N2 = graph.e; for (int i = 0; i < N1; i++) { graph.vex[i].no = i; } for (int i = 0; i < N1; i++)//初始化edges陣列 for (int j = 0; j < N1; j++) graph.edges[i][j] = 0; //給鄰接矩陣賦值 for (int i = 0; i < N2; i++) { int v1, v2; cout << "v1,v2 = "; cin >> v1 >> v2; graph.edges[v1][v2] = 1; } } // 鄰接矩陣的深度遍歷操作 void DFS(int i) { if (visited[i] == false) { visited[i] = true; cout << graph.vex[i].no << ' '; for (int j = 0; j < graph.n; j++) { if (graph.edges[i][j] == 1 && visited[j] == false) //如果 ij兩點可達，且j未被訪問過，就遞迴遍歷j DFS(j); } } } void DFSTraverse() { for (int i = 0; i < graph.n; i++)//初始化將visited所有點設定為false visited[i] = false; for (int j = 0; j < graph.n; j++) DFS(j); } int main(void) { Create(); DFSTraverse(); system("pause"); return 0; }
鄰接矩陣廣度優先演算法：
#include<iostream> using namespace std; #define MAX 20 // 注：鄰接矩陣是圖的順序儲存方式 typedef struct node { int no; //頂點編號 // char data; //頂點其它資訊，不常用 }VertexType; typedef struct //圖的定義 { int edges[MAX][MAX]; //鄰接矩陣定義 int n, e; //頂點數和邊數 VertexType vex[MAX]; //存放節點資訊 }MGraph; MGraph graph; bool visited[MAX];//訪問過的標誌為true 未訪問的設定為false void Create() { cout << "輸入頂點數和邊數: "; cin >> graph.n >> graph.e; int N1 = graph.n, N2 = graph.e; for (int i = 0; i < N1; i++) { graph.vex[i].no = i; } for (int i = 0; i < N1; i++)//初始化edges陣列 for (int j = 0; j < N1; j++) graph.edges[i][j] = 0; //給鄰接矩陣賦值 for (int i = 0; i < N2; i++) { int v1, v2; cout << "v1,v2 = "; cin >> v1 >> v2; graph.edges[v1][v2] = 1; } } // 鄰接矩陣的廣度遍歷操作 //類似於二叉樹的按層遍歷 void BFS() { for (int i = 0; i < graph.n; i++)//初始化visited陣列為false visited[i] = false; int queue[MAX]; memset(queue, 0, sizeof(int)*MAX); int front = -1, rear = 0; queue[0] = graph.vex[0].no;//設定從0開始遍歷 visited[0] = true; while (front != rear) { front++; cout << queue[front]; for (int j = 0; j < graph.n; j++) { //如果二者相連且該點沒有被訪問過，將此點入隊 if (graph.edges[queue[front]][j] == 1 && visited[j] == false) { queue[++rear] = j; visited[j] = true; } } } } int main(void) { Create(); BFS(); system("pause"); return 0; }
鄰接表建立圖解：
#include<iostream> using namespace std; #define MAX 20 typedef struct arcnode { int adjvex; //該邊所指向的節點的位置 struct arcnode* nextarc; //指向下一條邊的指標 // int info; //該邊的其它資訊，如權值等。 }ArcNODE; //表結點型別 typedef struct vnode { char data;//頂點資訊 ArcNODE *firstarc; //指向第一條邊的指標 }VNode;//頭結點 typedef struct { VNode adjust[MAX]; //鄰接表 int n, e;// n為頂點數，e為邊數 }AGraph; AGraph graph; bool visited[MAX]; void Create() { cout << "輸入頂點數和邊數"; cin >> graph.n >> graph.e; for (int i = 0; i < graph.n; i++)//初始化鄰接表 { graph.adjust[i].firstarc = (ArcNODE*)malloc(sizeof(ArcNODE)); graph.adjust[i].firstarc->nextarc = NULL; //將第一個節點的next指標賦值為NULL } //建立鄰接表 for (int i = 0; i < graph.n; i++) { int n; cout << "輸入" << i << "的頂點值"; cin >> graph.adjust[i].data; cout << "輸入" << i << "的出度"; cin >> n; ArcNODE *q = graph.adjust[i].firstarc; while (n) { int num; cin >> num; ArcNODE *p; p = (ArcNODE*)malloc(sizeof(ArcNODE)); p->adjvex = num; q->nextarc = p; q = p; q->nextarc = NULL; n--; } } } void DFS(int i) { if (visited[i] == 0) { visited[i] = 1; ArcNODE*p = graph.adjust[i].firstarc->nextarc;//p指向表頭節點 cout << graph.adjust[i].data << ' '; while (p != NULL) { if (visited[p->adjvex] == 0) //由於表頭裡不存放值，所以判斷nextarc的值 DFS(p->adjvex); p = p->nextarc; } } } void DFSTraverse() { for (int v = 0; v<graph.n; ++v) visited[v] = 0; for (int v = 0; v<graph.n; ++v) if (visited[v] == 0) DFS(v); } int main(void) { Create(); for (int i = 0; i < graph.n; i++) DFS(i); system("pause"); return 0; }
鄰接表的廣度優先演算法：
#include<iostream>
using namespace std;
#define MAX 20
typedef struct arcnode
{
int adjvex; //該邊所指向的節點的位置
struct arcnode* nextarc; //指向下一條邊的指標
// int info; //該邊的其它資訊，如權值等。
}ArcNODE; //表結點型別
typedef struct vnode
{
char data;//頂點資訊
ArcNODE *firstarc; //指向第一條邊的指標
}VNode;//頭結點
typedef struct
{
VNode adjust[MAX]; //鄰接表
int n, e;// n為頂點數，e為邊數
}AGraph;
AGraph graph;
bool visited[MAX];
void Create()
{
cout << "輸入頂點數和邊數";
cin >> graph.n >> graph.e;
for (int i = 0; i < graph.n; i++)//初始化鄰接表
{
graph.adjust[i].firstarc = (ArcNODE*)malloc(sizeof(ArcNODE));
graph.adjust[i].firstarc->nextarc = NULL; //將第一個節點的next指標賦值為NULL
}
//建立鄰接表
for (int i = 0; i < graph.n; i++)
{
int n;
cout << "輸入" << i << "的頂點值";
cin >> graph.adjust[i].data;
cout << "輸入" << i << "的出度";
cin >> n;
ArcNODE *q = graph.adjust[i].firstarc;
while (n)
{
int num;
cin >> num;
ArcNODE *p;
p = (ArcNODE*)malloc(sizeof(ArcNODE));
p->adjvex = num;
q->nextarc = p;
q = p;
q->nextarc = NULL;
n--;
}
}
}
void BFS()
{
for (int i = 0; i < graph.n; i++)//初始化visited陣列為false
visited[i] = false;
int queue[MAX];
int front = -1, rear = 0;
queue[0] = 0;
visited[0] = true;
while (front != rear)
{
front++;
cout << graph.adjust[queue[front]].data;
ArcNODE *p = graph.adjust[queue[front]].firstarc->nextarc;//p永遠指向佇列頭所代表的那個表頭節點的next
while (p != NULL)
{
if (visited[p->adjvex] == 0)
{
visited[p->adjvex] = 1;
queue[++rear] = p->adjvex;
}
p = p->nextarc;
}
}
}
int main(void)
{
Create();
BFS();
system("pause");
return 0;
}