从图中某一顶点出发，并系统地访问完图中的所有顶点，且都恰好访问一次的运算操作就被称作 图的遍历
图的遍历理解起来并不是很难，可以分开理解：“遍”意为全部，“历”意为经历、经过，合起来就是：全部顶点都经过一遍
图的遍历方式分为两种：深度优先遍历与广度优先遍历，二者的时间复杂度都是O(n2)
深度优先遍历：（可以用来判断图中是否存在环）
思路:从图的某一顶点V0出发，访问此顶点；然后依次从V0的未被访问的邻接点出发，深度优先遍历图，直至图中所有和V0相通的顶点都被访问到；若此时图中尚有顶点未被访问，则另选图中一个未被访问的顶点作起点，重复上述过程，直至图中所有顶点都被访问为止。
在深度优先遍历中，由于没为有规定访问邻接点的顺序，所以深度优先序列不是唯一的。
广度优先遍历：
思路
从图中的某个顶点V0出发，并在访问此顶点之后依次访问V0的所有未被访问过的邻接点，之后按这些顶点被访问的先后次序依次访问它们的邻接点，直至图中所有和V0有路径相通的顶点都被访问到。
若此时图中尚有顶点未被访问，则另选图中一个未曾被访问的顶点作起始点，重复上述过程，直至图中所有顶点都被访问到为止。
从图中某顶点v出发：
- 访问顶点v ；（容易实现）
- 访问v的所有未被访问的邻接点
w1 ,w2 , …wk ； （容易实现） - 依次从这些邻接点（在步骤 2）访问的顶点出发，访问 它们的所有未被访问的邻接点; 依此类推，直到图中所有访问过的顶点的邻接点都被访问；
为实现 3，需要保存在步骤(2）中访问的顶点，而且访问这些顶点邻接点的顺序为：先保存的顶点，其邻接点先被访问。
1.定义
typedef struct Graph{
int** connections;
int numNodes;
} *GraphPtr;
2.循环队列
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;
}//Of initQueue
bool isQueueEmpty(QueuePtr paraQueuePtr){
if ((paraQueuePtr->front + 1) % QUEUE_SIZE == paraQueuePtr->rear) {
return true;
}//Of if
return false;
}//Of isQueueEmpty
void enqueue(QueuePtr paraQueuePtr, int paraNode){
//printf("front = %d, rear = %d.rn", paraQueuePtr->front, paraQueuePtr->rear);
if ((paraQueuePtr->rear + 1) % QUEUE_SIZE == paraQueuePtr->front % QUEUE_SIZE) {
printf("Error, trying to enqueue %d. queue full.rn", paraNode);
return;
}//Of if
paraQueuePtr->nodes[paraQueuePtr->rear] = paraNode;
paraQueuePtr->rear = (paraQueuePtr->rear + 1) % QUEUE_SIZE;
//printf("enqueue %d ends.rn", paraNode);
}//Of enqueue
int dequeue(QueuePtr paraQueuePtr){
if (isQueueEmpty(paraQueuePtr)) {
printf("Error, empty queuern");
return NULL;
}//Of if
paraQueuePtr->front = (paraQueuePtr->front + 1) % QUEUE_SIZE;
//printf("dequeue %d ends.rn", paraQueuePtr->nodes[paraQueuePtr->front]);
return paraQueuePtr->nodes[paraQueuePtr->front];
}//Of dequeue
3.对图初始化
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];
}//Of for j
}//Of for i
return resultPtr;
}//Of initGraph
4.对相应数组进行初始化
void initTranverse(GraphPtr paraGraphPtr) {
int i;
//Initialize data
visitedPtr = (int*) malloc(paraGraphPtr -> numNodes * sizeof(int));
for (i = 0; i < paraGraphPtr -> numNodes; i ++) {
visitedPtr[i] = 0;
}//Of for i
}//Of initTranverse
5.深度遍历和广度遍历
//深度遍历
void depthFirstTranverse(GraphPtr paraGraphPtr, int paraNode) {
int i;
visitedPtr[paraNode] = 1;
printf("%dt", paraNode);
for (i = 0; i < paraGraphPtr -> numNodes; i ++) {
if (!visitedPtr[i]){
if (paraGraphPtr -> connections[paraNode][i]) {
depthFirstTranverse(paraGraphPtr, i);
}//Of if
}//Of if
}//Of for i
}//Of depthFirstTranverse
//广度遍历
void widthFirstTranverse(GraphPtr paraGraphPtr, int paraStart){
//Use a queue to manage the pointers
int i, j, tempNode;
i = 0;
QueuePtr tempQueuePtr = initQueue();
printf("%dt", 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("%dt", j);
visitedPtr[j] = 1;
enqueue(tempQueuePtr, j);
}//Of for j
}//Of while
}//Of widthFirstTranverse
6.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 datarn");
tempPtr = (int**)malloc(5 * sizeof(int*));
for (i = 0; i < 5; i ++) {
tempPtr[i] = (int*)malloc(5 * sizeof(int));
}//Of for i
for (i = 0; i < 5; i ++) {
for (j = 0; j < 5; j ++) {
//printf("i = %d, j = %d, ", i, j);
//printf("%drn", tempPtr[i][j]);
tempPtr[i][j] = myGraph[i][j];
//printf("i = %d, j = %d, %drn", i, j, tempPtr[i][j]);
}//Of for j
}//Of for i
printf("Data readyrn");
GraphPtr tempGraphPtr = initGraph(5, tempPtr);
printf("num nodes = %d rn", tempGraphPtr -> numNodes);
printf("Graph initializedrn");
printf("Depth first visit:rn");
initTranverse(tempGraphPtr);
depthFirstTranverse(tempGraphPtr, 4);
printf("rnWidth first visit:rn");
initTranverse(tempGraphPtr);
widthFirstTranverse(tempGraphPtr, 4);
}//Of testGraphTranverse
7.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 3三.完整代码
#include#include #define QUEUE_SIZE 10 int* 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; }//Of initQueue bool isQueueEmpty(QueuePtr paraQueuePtr){ if ((paraQueuePtr->front + 1) % QUEUE_SIZE == paraQueuePtr->rear) { return true; }//Of if return false; }//Of isQueueEmpty void enqueue(QueuePtr paraQueuePtr, int paraNode){ //printf("front = %d, rear = %d.rn", paraQueuePtr->front, paraQueuePtr->rear); if ((paraQueuePtr->rear + 1) % QUEUE_SIZE == paraQueuePtr->front % QUEUE_SIZE) { printf("Error, trying to enqueue %d. queue full.rn", paraNode); return; }//Of if paraQueuePtr->nodes[paraQueuePtr->rear] = paraNode; paraQueuePtr->rear = (paraQueuePtr->rear + 1) % QUEUE_SIZE; //printf("enqueue %d ends.rn", paraNode); }//Of enqueue int dequeue(QueuePtr paraQueuePtr){ if (isQueueEmpty(paraQueuePtr)) { printf("Error, empty queuern"); return NULL; }//Of if paraQueuePtr->front = (paraQueuePtr->front + 1) % QUEUE_SIZE; //printf("dequeue %d ends.rn", paraQueuePtr->nodes[paraQueuePtr->front]); return paraQueuePtr->nodes[paraQueuePtr->front]; }//Of dequeue typedef struct Graph{ int** connections; int numNodes; } *GraphPtr; //void deepFirst(GraphPtr paraGraphPtr, int paraNode); 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]; }//Of for j }//Of for i return resultPtr; }//Of initGraph void initTranverse(GraphPtr paraGraphPtr) { int i; //Initialize data visitedPtr = (int*) malloc(paraGraphPtr -> numNodes * sizeof(int)); for (i = 0; i < paraGraphPtr -> numNodes; i ++) { visitedPtr[i] = 0; }//Of for i }//Of initTranverse void depthFirstTranverse(GraphPtr paraGraphPtr, int paraNode) { int i; visitedPtr[paraNode] = 1; printf("%dt", paraNode); for (i = 0; i < paraGraphPtr -> numNodes; i ++) { if (!visitedPtr[i]){ if (paraGraphPtr -> connections[paraNode][i]) { depthFirstTranverse(paraGraphPtr, i); }//Of if }//Of if }//Of for i }//Of depthFirstTranverse void widthFirstTranverse(GraphPtr paraGraphPtr, int paraStart){ //Use a queue to manage the pointers int i, j, tempNode; i = 0; QueuePtr tempQueuePtr = initQueue(); printf("%dt", 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("%dt", j); visitedPtr[j] = 1; enqueue(tempQueuePtr, j); }//Of for j }//Of while }//Of widthFirstTranverse 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 datarn"); tempPtr = (int**)malloc(5 * sizeof(int*)); for (i = 0; i < 5; i ++) { tempPtr[i] = (int*)malloc(5 * sizeof(int)); }//Of for i for (i = 0; i < 5; i ++) { for (j = 0; j < 5; j ++) { //printf("i = %d, j = %d, ", i, j); //printf("%drn", tempPtr[i][j]); tempPtr[i][j] = myGraph[i][j]; //printf("i = %d, j = %d, %drn", i, j, tempPtr[i][j]); }//Of for j }//Of for i printf("Data readyrn"); GraphPtr tempGraphPtr = initGraph(5, tempPtr); printf("num nodes = %d rn", tempGraphPtr -> numNodes); printf("Graph initializedrn"); printf("Depth first visit:rn"); initTranverse(tempGraphPtr); depthFirstTranverse(tempGraphPtr, 4); printf("rnWidth first visit:rn"); initTranverse(tempGraphPtr); widthFirstTranverse(tempGraphPtr, 4); }//Of testGraphTranverse int main(){ testGraphTranverse(); return 1; }//Of main
