C语言数据结构_图、图的深度优先遍历、广度优先遍历

图

图是一种多对多的关系，可以有零个或多个直接前驱，也可以有零个或多个直接后驱。相较于线性表和树，图的结点可以是任意的，而线性表有头结点，只要知道了头结点，那么整个线性表就可以直接访问，树有根结点，可以根据树的根结点直接访问整棵树的所有结点，也就是说线性表和树如果要访问的话只有从头部进入访问。而图就不一样了，可以选择任意的结点进行访问。所以在遍历图的时候就一定会有多个遍历方式。

图的创建

在创建图的时候我们一般采用二维数组的形式。根据bool矩阵来进行存储图的关系。行和列都代表结点

typedef struct Graph
{int **connections;//创建一个二维数组int numNodes;//记录结点个数，从0开始编号如果有五个结点编号 0 1 2 3 4
} * GraphPtr;//初始化图
GraphPtr initGraph(int paraSize, int **paraData)
{int i, j;GraphPtr resultPtr = (GraphPtr)malloc(sizeof(Graph));//申请图的空间resultPtr->numNodes = paraSize;// resultPtr -> connections = (int**)malloc(paraSize * paraSize * sizeof(int));//申请二维数组空间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];//将图结点以0 1矩阵的方式存储} }      return resultPtr;
}

在这里声明一下visitedPtr数组用来记录每一个结点是否被访问，下标代表结点，如果没有被访问数组值为0被访问数组值为1。

深度优先遍历

函数传入的参数是图和首先访问的结点，首先访问传入的结点，一旦访问就标记为1，然后从0 1 矩阵的该结点的行从左到右依次遍历，如果找到矩阵数为1，并且该列数没有被标记为1，那么就直接访问该结点。这里用到了递归的调用，在递归里面有for循环所以在递归到最后for循环截止的时候，就会返回上一个for循环继续向后递归，这里非常向N皇后问题，就不多做阐述。

void depthFirstTranverse(GraphPtr paraGraphPtr, int paraNode)
{int i;visitedPtr[paraNode] = 1;//如果结点被访问就标记为1，之后不再访问该结点printf("%d\t", paraNode);//打印出遍历的结点for (i = 0; i < paraGraphPtr->numNodes; i++){if (!visitedPtr[i]){if (paraGraphPtr->connections[paraNode][i]){//如果该结点connection[paraNode][i]（结点编号为i）与paraNode结点相连，那么就打印，再次递归调用该函数、depthFirstTranverse(paraGraphPtr, i);} }    }
}

广度优先遍历

广度优先遍历用到了队列，该函数传入的参数是图，首先遍历的结点。还是像深度优先遍历一样如果结点被访问标记为1，没有被访问标记为0。首先进行打印遍历，然后再将该结点入队，同深度优先遍历一样，如果结点的行有矩阵数为1并且该列列数没有被标记为1那么就直接打印遍历。

void widthFirstTranverse(GraphPtr paraGraphPtr, int paraStart)
{int i, j, tempNode;i = 0;QueuePtr tempQueuePtr = initQueue();//队列创建并初始化printf("%d\t", paraStart);//打印结点visitedPtr[paraStart] = 1;//标记结点enqueue(tempQueuePtr, paraStart);//入队while (!isQueueEmpty(tempQueuePtr)){tempNode = dequeue(tempQueuePtr);visitedPtr[tempNode] = 1;// For output.i++;for (j = 0; j < paraGraphPtr->numNodes; j++){if (visitedPtr[j])continue;if (paraGraphPtr->connections[tempNode][j] == 0)continue;printf("%d\t", j);visitedPtr[j] = 1;enqueue(tempQueuePtr, j);} }
}

所有代码

#include <stdio.h>
#include <malloc.h>#define QUEUE_SIZE 10int *visitedPtr;typedef struct GraphNodeQueue
{int *nodes;int front;int rear;
} GraphNodeQueue, *QueuePtr;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;
}bool isQueueEmpty(QueuePtr paraQueuePtr)
{if ((paraQueuePtr->front + 1) % QUEUE_SIZE == paraQueuePtr->rear){return true;}return false;
} void enqueue(QueuePtr paraQueuePtr, int paraNode)
{// printf("front = %d, rear = %d.\r\n", paraQueuePtr->front, paraQueuePtr->rear);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;// printf("enqueue %d ends.\r\n", paraNode);
} int dequeue(QueuePtr paraQueuePtr)
{if (isQueueEmpty(paraQueuePtr)){printf("Error, empty queue\r\n");return NULL;} paraQueuePtr->front = (paraQueuePtr->front + 1) % QUEUE_SIZE;// printf("dequeue %d ends.\r\n", paraQueuePtr->nodes[paraQueuePtr->front]);return paraQueuePtr->nodes[paraQueuePtr->front];
} typedef struct Graph
{int **connections;int numNodes;
} * GraphPtr;GraphPtr initGraph(int paraSize, int **paraData)
{int i, j;GraphPtr resultPtr = (GraphPtr)malloc(sizeof(Graph));resultPtr->numNodes = paraSize;// resultPtr -> connections = (int**)malloc(paraSize * paraSize * sizeof(int));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;
} void initTranverse(GraphPtr paraGraphPtr)
{int i;visitedPtr = (int *)malloc(paraGraphPtr->numNodes * sizeof(int));for (i = 0; i < paraGraphPtr->numNodes; i++){visitedPtr[i] = 0;}
}void depthFirstTranverse(GraphPtr paraGraphPtr, int paraNode)
{int i;visitedPtr[paraNode] = 1;printf("%d\t", paraNode);for (i = 0; i < paraGraphPtr->numNodes; i++){if (!visitedPtr[i]){if (paraGraphPtr->connections[paraNode][i]){depthFirstTranverse(paraGraphPtr, i);} }     }
} void widthFirstTranverse(GraphPtr paraGraphPtr, int paraStart)
{int i, j, tempNode;i = 0;QueuePtr tempQueuePtr = initQueue();printf("%d\t", paraStart);visitedPtr[paraStart] = 1;enqueue(tempQueuePtr, paraStart);while (!isQueueEmpty(tempQueuePtr)){tempNode = dequeue(tempQueuePtr);visitedPtr[tempNode] = 1;// For output.i++;for (j = 0; j < paraGraphPtr->numNodes; j++){if (visitedPtr[j])continue;if (paraGraphPtr->connections[tempNode][j] == 0)continue;printf("%d\t", j);visitedPtr[j] = 1;enqueue(tempQueuePtr, j);} }
} 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++){// printf("i = %d, j = %d, ", i, j);// printf("%d\r\n", tempPtr[i][j]);tempPtr[i][j] = myGraph[i][j];// printf("i = %d, j = %d, %d\r\n", i, j, tempPtr[i][j]);} }      printf("Data ready\r\n");GraphPtr tempGraphPtr = initGraph(5, tempPtr);printf("num nodes = %d \r\n", tempGraphPtr->numNodes);printf("Graph initialized\r\n");printf("Depth first visit:\r\n");initTranverse(tempGraphPtr);depthFirstTranverse(tempGraphPtr, 4);printf("\r\nWidth first visit:\r\n");initTranverse(tempGraphPtr);widthFirstTranverse(tempGraphPtr, 4);
} int main()
{testGraphTranverse();return 1;
}

运行结果

Preparing data
Data ready
num nodes = 5
Graph initialized
Depth first visit:
4       1       0       3       2
Width first visit:
4       1       2       0       3
PS D:\Data Struction\weekSix\student>