一、邻接表的概念
邻接表是图的一种最主要存储结构（相当于图的压缩存储）,用来描述图上的每一个点。图的邻接表存储方法跟树的孩子链表示法相类似，是一种顺序分配和链式分配相结合的存储结构。如这个表头结点所对应的顶点存在相邻顶点，则把相邻顶点依次存放于表头结点所指向的单向链表中。表结点存放的是邻接顶点在数组中的索引。对于无向图来说，使用邻接表进行存储也会出现数据冗余，表头结点A所指链表中存在一个指向C的表结点的同时，表头结点C所指链表也会存在一个指向A的表结点。
广度优先搜索遍历类似于树的按层次遍历，对于用邻接表做存储结构的图，从某个给定 顶点出发的图的遍历得到的访问结点顶点次序，随建立的邻接表的不同而可能不同
二、代码步骤
1、创建图
2、图的初始化
3、创建链队列
4、队列的初始化
5、判断队列是否为空
6、入队
7、出队
8、邻接表的结构体定义
9、定义遍历数组
10、将图转为邻接表
11、打印邻接表
12、广度遍历
13、测试代码
14、程序入口
15、运行结果
三、代码功能
1、创建图
typedef struct Graph
{
int** connections;
int numNodes;
} *GraphPtr;
2、图的初始化
GraphPtr initGraph(int paraSize, int** paraData)
{
int i, j;
GraphPtr resultPtr = (GraphPtr)malloc(sizeof(struct Graph));
resultPtr -> numNodes = paraSize;
resultPtr -> connections = (int**)malloc(paraSize * sizeof(int*));
for (i = 0; i < paraSize; i ++)
{
resultPtr -> connections[i] = (int*)malloc(paraSize * sizeof(int));
for (j = 0; j < paraSize; j ++)
{
resultPtr -> connections[i][j] = paraData[i][j];
}
}
return resultPtr;
}
3、创建链队列
typedef struct GraphNodeQueue
{
int* nodes;
int front;
int rear;
}GraphNodeQueue, *QueuePtr;
4、队列的初始化
QueuePtr initQueue()
{
QueuePtr resultQueuePtr = (QueuePtr)malloc(sizeof(struct GraphNodeQueue));
resultQueuePtr->nodes = (int*)malloc(QUEUE_SIZE * sizeof(int));
resultQueuePtr->front = 0;
resultQueuePtr->rear = 1;
return resultQueuePtr;
}
5、判断队列是否为空
bool isQueueEmpty(QueuePtr paraQueuePtr)
{
if ((paraQueuePtr->front + 1) % QUEUE_SIZE == paraQueuePtr->rear)
{
return true;
}
return false;
}
6、入队
void enqueue(QueuePtr paraQueuePtr, int paraNode)
{
if ((paraQueuePtr->rear + 1) % QUEUE_SIZE == paraQueuePtr->front % QUEUE_SIZE)
{
printf("Error, trying to enqueue %d. queue full.\r\n", paraNode);
return;
}
paraQueuePtr->nodes[paraQueuePtr->rear] = paraNode;
paraQueuePtr->rear = (paraQueuePtr->rear + 1) % QUEUE_SIZE;
}
7、出队
int dequeue(QueuePtr paraQueuePtr)
{
if (isQueueEmpty(paraQueuePtr))
{
printf("Error, empty queue\r\n");
return NULL;
}
paraQueuePtr->front = (paraQueuePtr->front + 1) % QUEUE_SIZE;
return paraQueuePtr->nodes[paraQueuePtr->front];
}
8、邻接表的结构体定义
typedef struct AdjacencyNode
{
int column;
AdjacencyNode* next;
}AdjacencyNode, *AdjacentNodePtr;
/**
* Aajacent list.
*/
typedef struct AdjacencyList
{
int numNodes;
AdjacencyNode* headers;
}AdjacencyList, *AdjacencyListPtr;
9、定义遍历数组
int* visitedPtr;
10、将图转为邻接表
AdjacencyListPtr graphToAdjacentList(GraphPtr paraPtr)
{
//Allocate space.
int i, j, tempNum;
AdjacentNodePtr p, q;
tempNum = paraPtr->numNodes;
AdjacencyListPtr resultPtr = (AdjacencyListPtr)malloc(sizeof(struct AdjacencyList));
resultPtr->numNodes = tempNum;
resultPtr->headers = (AdjacencyNode*)malloc(tempNum * sizeof(struct AdjacencyNode));
//Fill the data.
for (i = 0; i < tempNum; i ++)
{
//Initialize headers.
p = &(resultPtr->headers[i]);
p->column = -1;
p->next = NULL;
for (j = 0; j < tempNum; j ++)
{
if (paraPtr->connections[i][j] > 0)
{
//Create a new node.
q = (AdjacentNodePtr)malloc(sizeof(struct AdjacencyNode));
q->column = j;
q->next = NULL;
p->next = q;
p = q;
}
}
}
return resultPtr;
}
11、打印邻接表
void printAdjacentList(AdjacencyListPtr paraPtr)
{
int i;
AdjacentNodePtr p;
int tempNum = paraPtr->numNodes;
printf("This is the graph:\r\n");
for (i = 0; i < tempNum; i ++)
{
p = paraPtr->headers[i].next;
while (p != NULL)
{
printf("%d, ", p->column);
p = p->next;
}
printf("\r\n");
}
}
12、广度遍历
void widthFirstTranverse(AdjacencyListPtr paraListPtr, int paraStart)
{
printf("width first \r\n");
//Use a queue to manage the pointers
int i, j, tempNode;
AdjacentNodePtr p;
i = 0;
//Initialize data
visitedPtr = (int*) malloc(paraListPtr->numNodes * sizeof(int));
for (i = 0; i < paraListPtr->numNodes; i ++)
{
visitedPtr[i] = 0;
}//Of for i
QueuePtr tempQueuePtr = initQueue();
printf("%d\t", paraStart);
visitedPtr[paraStart] = 1;
enqueue(tempQueuePtr, paraStart);
while (!isQueueEmpty(tempQueuePtr))
{
tempNode = dequeue(tempQueuePtr);
for (p = &(paraListPtr->headers[tempNode]); p != NULL; p = p->next)
{
j = p->column;
if (visitedPtr[j])
continue;
printf("%d\t", j);
visitedPtr[j] = 1;
enqueue(tempQueuePtr, j);
}//Of for
}//Of while
printf("\r\n");
}
13、测试代码
void testGraphTranverse()
{
int i, j;
int myGraph[5][5] = {
{0, 1, 0, 1, 0},
{1, 0, 1, 0, 1},
{0, 1, 0, 1, 1},
{1, 0, 1, 0, 0},
{0, 1, 1, 0, 0}};
int** tempPtr;
printf("Preparing data\r\n");
tempPtr = (int**)malloc(5 * sizeof(int*));
for (i = 0; i < 5; i ++)
{
tempPtr[i] = (int*)malloc(5 * sizeof(int));
}
for (i = 0; i < 5; i ++)
{
for (j = 0; j < 5; j ++)
{
tempPtr[i][j] = myGraph[i][j];
}
}
printf("Data ready\r\n");
GraphPtr tempGraphPtr = initGraph(5, tempPtr);
AdjacencyListPtr tempListPtr = graphToAdjacentList(tempGraphPtr);
printAdjacentList(tempListPtr);
widthFirstTranverse(tempListPtr, 4);
}
14、程序入口
int main()
{
testGraphTranverse();
return 1;
}
15、运行结果
Preparing data
Data ready
This is the graph:
1, 3,
0, 2, 4,
1, 3, 4,
0, 2,
1, 2,
width first
4 1 2 0 3
四、整体代码
#include <stdio.h>
#include <malloc.h>
#define QUEUE_SIZE 10
int* visitedPtr;
/**
* The structure of a graph.
*/
typedef struct Graph
{
int** connections;
int numNodes;
} *GraphPtr;
/**
* Initialize a graph.
*/
GraphPtr initGraph(int paraSize, int** paraData)
{
int i, j;
GraphPtr resultPtr = (GraphPtr)malloc(sizeof(struct Graph));
resultPtr -> numNodes = paraSize;
resultPtr -> connections = (int**)malloc(paraSize * sizeof(int*));
for (i = 0; i < paraSize; i ++)
{
resultPtr -> connections[i] = (int*)malloc(paraSize * sizeof(int));
for (j = 0; j < paraSize; j ++)
{
resultPtr -> connections[i][j] = paraData[i][j];
}
}
return resultPtr;
}//Of initGraph
/**
* A queue with a number of indices.
*/
typedef struct GraphNodeQueue
{
int* nodes;
int front;
int rear;
}GraphNodeQueue, *QueuePtr;
/**
* Initialize the queue.
*/
QueuePtr initQueue()
{
QueuePtr resultQueuePtr = (QueuePtr)malloc(sizeof(struct GraphNodeQueue));
resultQueuePtr->nodes = (int*)malloc(QUEUE_SIZE * sizeof(int));
resultQueuePtr->front = 0;
resultQueuePtr->rear = 1;
return resultQueuePtr;
}
/**
* Is the queue empty?
*/
bool isQueueEmpty(QueuePtr paraQueuePtr)
{
if ((paraQueuePtr->front + 1) % QUEUE_SIZE == paraQueuePtr->rear)
{
return true;
}
return false;
}
/**
* Add a node to the queue.
*/
void enqueue(QueuePtr paraQueuePtr, int paraNode)
{
if ((paraQueuePtr->rear + 1) % QUEUE_SIZE == paraQueuePtr->front % QUEUE_SIZE)
{
printf("Error, trying to enqueue %d. queue full.\r\n", paraNode);
return;
}
paraQueuePtr->nodes[paraQueuePtr->rear] = paraNode;
paraQueuePtr->rear = (paraQueuePtr->rear + 1) % QUEUE_SIZE;
}
/**
* Remove an element from the queue and return.
*/
int dequeue(QueuePtr paraQueuePtr)
{
if (isQueueEmpty(paraQueuePtr))
{
printf("Error, empty queue\r\n");
return NULL;
}
paraQueuePtr->front = (paraQueuePtr->front + 1) % QUEUE_SIZE;
return paraQueuePtr->nodes[paraQueuePtr->front];
}
typedef struct AdjacencyNode
{
int column;
AdjacencyNode* next;
}AdjacencyNode, *AdjacentNodePtr;
/**
* Aajacent list.
*/
typedef struct AdjacencyList
{
int numNodes;
AdjacencyNode* headers;
}AdjacencyList, *AdjacencyListPtr;
/**
* Construct an adjacent list.
*/
AdjacencyListPtr graphToAdjacentList(GraphPtr paraPtr)
{
//Allocate space.
int i, j, tempNum;
AdjacentNodePtr p, q;
tempNum = paraPtr->numNodes;
AdjacencyListPtr resultPtr = (AdjacencyListPtr)malloc(sizeof(struct AdjacencyList));
resultPtr->numNodes = tempNum;
resultPtr->headers = (AdjacencyNode*)malloc(tempNum * sizeof(struct AdjacencyNode));
//Fill the data.
for (i = 0; i < tempNum; i ++)
{
//Initialize headers.
p = &(resultPtr->headers[i]);
p->column = -1;
p->next = NULL;
for (j = 0; j < tempNum; j ++)
{
if (paraPtr->connections[i][j] > 0)
{
//Create a new node.
q = (AdjacentNodePtr)malloc(sizeof(struct AdjacencyNode));
q->column = j;
q->next = NULL;
p->next = q;
p = q;
}
}
}
return resultPtr;
}
/**
* Print an adjacent list.
*/
void printAdjacentList(AdjacencyListPtr paraPtr)
{
int i;
AdjacentNodePtr p;
int tempNum = paraPtr->numNodes;
printf("This is the graph:\r\n");
for (i = 0; i < tempNum; i ++)
{
p = paraPtr->headers[i].next;
while (p != NULL)
{
printf("%d, ", p->column);
p = p->next;
}
printf("\r\n");
}
}
/**
* Width first tranverse.
*/
void widthFirstTranverse(AdjacencyListPtr paraListPtr, int paraStart)
{
printf("width first \r\n");
//Use a queue to manage the pointers
int i, j, tempNode;
AdjacentNodePtr p;
i = 0;
//Initialize data
visitedPtr = (int*) malloc(paraListPtr->numNodes * sizeof(int));
for (i = 0; i < paraListPtr->numNodes; i ++)
{
visitedPtr[i] = 0;
}//Of for i
QueuePtr tempQueuePtr = initQueue();
printf("%d\t", paraStart);
visitedPtr[paraStart] = 1;
enqueue(tempQueuePtr, paraStart);
while (!isQueueEmpty(tempQueuePtr))
{
tempNode = dequeue(tempQueuePtr);
for (p = &(paraListPtr->headers[tempNode]); p != NULL; p = p->next)
{
j = p->column;
if (visitedPtr[j])
continue;
printf("%d\t", j);
visitedPtr[j] = 1;
enqueue(tempQueuePtr, j);
}//Of for
}//Of while
printf("\r\n");
}//Of widthFirstTranverse
/**
* Test graph tranverse.
*/
void testGraphTranverse()
{
int i, j;
int myGraph[5][5] = {
{0, 1, 0, 1, 0},
{1, 0, 1, 0, 1},
{0, 1, 0, 1, 1},
{1, 0, 1, 0, 0},
{0, 1, 1, 0, 0}};
int** tempPtr;
printf("Preparing data\r\n");
tempPtr = (int**)malloc(5 * sizeof(int*));
for (i = 0; i < 5; i ++)
{
tempPtr[i] = (int*)malloc(5 * sizeof(int));
}
for (i = 0; i < 5; i ++)
{
for (j = 0; j < 5; j ++)
{
tempPtr[i][j] = myGraph[i][j];
}
}
printf("Data ready\r\n");
GraphPtr tempGraphPtr = initGraph(5, tempPtr);
AdjacencyListPtr tempListPtr = graphToAdjacentList(tempGraphPtr);
printAdjacentList(tempListPtr);
widthFirstTranverse(tempListPtr, 4);
}
int main()
{
testGraphTranverse();
return 1;
}
