求图最短路径

2017-1/hh-bo/第七次作业/main.c

@@ -0,0 +1,318 @@
+//
+//  main.c
+//  homework7
+//
+//  Created by Huhongbo on 2017/5/17.
+//  Copyright © 2017年 Huhongbo. All rights reserved.
+//
+
+#include <stdio.h>
+#include <stdlib.h>
+
+typedef enum
+{
+    OK,
+    ERROR,
+    OVERFLOW
+}Status;
+
+typedef enum
+{
+    true,
+    false
+}bool;
+
+
+//图的数组存储结构
+#define MAX_VERTEX_NUM 10
+#define VRType int
+#define InfoType int
+#define VertexType int
+#define INFINITY -1
+
+typedef struct ArcCell
+{
+    VRType adj;
+    InfoType *info;
+}ArcCell, AdjMatrix[MAX_VERTEX_NUM][MAX_VERTEX_NUM];
+
+typedef struct
+{
+    VertexType vexs[MAX_VERTEX_NUM];
+    AdjMatrix arcs;
+    int vexnum, arcnum; //图的顶点数和弧数;
+}MGraph;
+
+
+//队列的双链存储结构
+#define QElemType int
+
+typedef struct QNode
+{
+    QElemType data;
+    struct QNode *next;
+    struct QNode *pre;
+}QNode, *QueuePtr;
+
+typedef struct LinkQueue
+{
+    QueuePtr front;
+    QueuePtr rear;
+}LinkQueue;
+
+//队列的基本操作
+Status InitQueue(LinkQueue *Q);
+Status EnQueue(LinkQueue*Q, QElemType e);
+Status DeQueue(LinkQueue*Q, QElemType*e);
+bool QueueEmpty(LinkQueue*Q);
+Status DestroyQueue(LinkQueue*Q);
+
+//图的基本操作
+Status LocateVex(MGraph *G, int v1, int v2);
+Status CreateUDN(MGraph *G);
+int FirstAdjVex(MGraph *G, int u);
+int NextAdjvex(MGraph *G, int u, int w);
+Status BFSTraverse(MGraph*G, LinkQueue *Q, int a, int b);
+Status print(LinkQueue *Q, int a);
+
+//队列的基本操作
+Status InitQueue(LinkQueue *Q)
+{
+    Q->front = Q->rear = (QueuePtr)malloc(sizeof(QNode));
+    if (!Q->front)
+    {
+        return ERROR;
+    }
+    Q->front->next = Q->rear->next = NULL;
+    return OK;
+}
+
+Status EnQueue(LinkQueue*Q, QElemType e)
+{
+    QueuePtr p = (QueuePtr)malloc(sizeof(QNode));
+    if (!p)
+    {
+        return ERROR;
+    }
+    else
+    {
+        p->data = e;
+        p->next = NULL;
+        p->pre = Q->front;
+        Q->rear->next = p;
+        Q->rear = p;
+        return OK;
+    }
+}
+
+Status DeQueue(LinkQueue*Q, QElemType*e)
+{
+    if (Q->front == Q->rear)
+    {
+        return ERROR;
+    }
+    Q->front = Q->front->next;
+    *e = Q->front->data;
+    return OK;
+}
+
+bool QueueEmpty(LinkQueue*Q)
+{
+    if (Q->front == Q->rear)
+    {
+        return true;
+    }
+    else
+    {
+        return false;
+    }
+}
+
+Status DestroyQueue(LinkQueue*Q)
+{
+    while (Q->front)
+    {
+        Q->rear = Q->front->next;
+        free(Q->front);
+        Q->front = Q->rear;
+    }
+    return OK;
+}
+//图的基本操作
+
+Status LocateVex(MGraph *G,int v1,int v2)
+{
+    int i;
+    int j;
+    int m = 0;
+    int n = 0;
+    for (i = 0; i <= G->vexnum; i++)
+    {
+        if (G->vexs[i]==v1)
+        {
+            m = i;
+            break;
+        }
+    }
+    for (j = 0; j <= G->vexnum; j++)
+    {
+        if (G->vexs[j] == v2)
+        {
+            n = j;
+            break;
+        }
+    }
+    G->arcs[i][j].adj = 1;//两点之间有连线，弧值为1;
+    G->arcs[j][i] = G->arcs[i][j];
+    return OK;
+}
+
+//构建图
+Status CreateUDN(MGraph *G)
+{
+    int i;
+    int j;
+    //根据用例直接赋值。
+    G->vexnum = 9;
+    G->arcnum = 12;
+    for (i = 1; i <= G->vexnum; i++)
+    {
+        G->vexs[i] = i;//构建顶点向量;
+    }
+    for (i = 0; i <= G->vexnum; i++)//初始化邻接矩阵;
+    {
+        for (j = 0; j <= G->vexnum; j++)
+        {
+            G->arcs[i][j].adj = INFINITY;
+            G->arcs[i][j].info = NULL;
+        }
+    }
+    //构建邻接矩阵;
+    LocateVex(G, 1, 2);
+    LocateVex(G, 1, 3);
+    LocateVex(G, 1, 4);
+    LocateVex(G, 1, 7);
+    LocateVex(G, 2, 3);
+    LocateVex(G, 4, 5);
+    LocateVex(G, 4, 6);
+    LocateVex(G, 5, 6);
+    LocateVex(G, 6, 8);
+    LocateVex(G, 7, 8);
+    LocateVex(G, 7, 9);
+    LocateVex(G, 8, 9);
+
+    return OK;
+}
+
+//找出第一个邻接点
+int FirstAdjVex(MGraph *G, int u)
+{
+    int i;
+    for (i = 1; i <= G->vexnum; i++)
+    {
+        if (G->arcs[u][i].adj == 1)
+        {
+            return i;
+        }
+    }
+    return -1;
+}
+
+//找出下一个邻接点
+int NextAdjvex(MGraph *G, int u, int w)
+{
+    int i;
+    for (i = w + 1; i <= G->vexnum; i++)
+    {
+        if (G->arcs[u][i].adj == 1)
+        {
+            return i;
+        }
+    }
+    return -1;
+}
+//广度优先遍历图,求两点a,b间的最短路径;
+Status BFSTraverse(MGraph*G, LinkQueue *Q,int a,int b)
+{
+
+    int v;
+    int u = 0;
+    int w = 0;
+    bool visited[MAX_VERTEX_NUM];
+    for (v = 1; v <= G->vexnum; v++)
+    {
+        visited[v] = false;  //标记数组，标记图中已访问的点
+    }
+
+    EnQueue(Q, a); //a先入队列;
+    while (QueueEmpty(Q)!= true)
+    {
+        DeQueue(Q, &u);
+        for (w = FirstAdjVex(G, u); w >=0; w = NextAdjvex(G, u, w))
+        {
+            if (visited[w] == false)//判断w是否已经访问过
+            {
+                visited[w] = true;
+                EnQueue(Q, w); 
+            }
+            if (w == b)
+            {
+                break;
+            }
+        }
+        if (w == b)
+        {
+            break;
+        }
+    }
+    return OK;
+}
+
+Status print(LinkQueue *Q,int a)
+{
+    if (Q->rear->data == a)
+    {
+        printf("%d->%d\n", a, a);
+        return OK;
+    }
+
+    int i = 0;
+    int j;
+    int num[MAX_VERTEX_NUM] = { 0 };
+    while (Q->rear->data!=a)//倒序进入数组
+    {
+        num[i] = Q->rear->data;
+        Q->rear = Q->rear->pre;
+        i++;
+    }
+    printf("%d", a);
+    for (j = i - 1; j >= 0; j--)
+    {
+        printf("->%d", num[j]);
+    }
+
+
+    printf("\n");
+    return OK;
+}
+int main()
+{
+    int i;
+    int j;
+
+    MGraph Graph;
+    CreateUDN(&Graph);
+    for (i = 1; i <= Graph.vexnum; i++)
+    {
+        for (j = 1; j <= Graph.vexnum; j++)
+        {
+            LinkQueue Q;
+            InitQueue(&Q);
+            printf("%d<->%d:", i, j);
+            BFSTraverse(&Graph, &Q, i, j);
+            print(&Q, i);
+            DestroyQueue(&Q);
+        }
+    }
+
+}