圖之圖的廣度優先遍曆

廣度優先遍曆是連通圖的一種遍曆策略。其基本思想如下：

1、某個頂點V0出發，並訪問此頂點；

2、從V0出發，訪問V0的各個未曾訪問的鄰接點W1，W2，…,Wk;然後,依次從W1,W2,…,Wk出發訪問各自未被訪問的鄰接點；

3、重複步驟2，直到全部頂點都被訪問為止。

例如中：1.從0開始，首先找到0的關聯頂點3,42.由3出發，找到1，2；由4出發，找到1，但是1已經遍曆過，所以忽略。3.由1出發，沒有關聯頂點；由2出發，沒有關聯頂點。所以最後順序是0,3,4,1,2c語言實現如下：（使用鄰接矩陣儲存）

#include <stdio.h>#include <malloc.h>#define VERTEXNUM 5//隊列的元素typedef struct qElement{        int value;        struct qElement* pre;        struct qElement* next;}st_qElement;//隊列的前端和後端，最後一個入隊列的元素為rear，第一個出隊列的元素為frontst_qElement* front = NULL;st_qElement* rear = NULL;void createGraph(int (*edge)[VERTEXNUM], int start, int end);void displayGraph(int (*edge)[VERTEXNUM]);void BFT(int (*edge)[VERTEXNUM],int* vertexStatusArr);void BFTcore(int (*edge)[VERTEXNUM],int i,int* vertexStatusArr);void putQueue(int vertex);int* getQueue();void putRelatedInQueue(int (*edge)[VERTEXNUM], int vertex);int main(void){//動態建立存放邊的二維數組         int (*edge)[VERTEXNUM] = (int (*)[VERTEXNUM])malloc(sizeof(int)*VERTEXNUM*VERTEXNUM);        int i,j;        for(i=0;i<VERTEXNUM;i++){                for(j=0;j<VERTEXNUM;j++){                        edge[i][j] = 0;                }        }//存放頂點的遍曆狀態，0：未遍曆，1：已遍曆        int* vertexStatusArr = (int*)malloc(sizeof(int)*VERTEXNUM);        for(i=0;i<VERTEXNUM;i++){                vertexStatusArr[i] = 0;        }        printf("after init:\n");        displayGraph(edge);//建立圖        createGraph(edge,0,3);        createGraph(edge,0,4);        createGraph(edge,3,1);        createGraph(edge,3,2);        createGraph(edge,4,1);        printf("after create:\n");        displayGraph(edge);//廣度優先遍曆        BFT(edge,vertexStatusArr);        free(edge);        return 0;}//建立圖void createGraph(int (*edge)[VERTEXNUM], int start, int end){        edge[start][end] = 1;}//列印儲存的圖void displayGraph(int (*edge)[VERTEXNUM]){        int i,j;        for(i=0;i<VERTEXNUM;i++){                for(j=0;j<VERTEXNUM;j++){                        printf("%d ",edge[i][j]);                }                printf("\n");        }}//廣度優先遍曆void BFT(int (*edge)[VERTEXNUM], int* vertexStatusArr){        printf("start BFT graph:\n");        int i;        for(i=0;i<VERTEXNUM;i++){                BFTcore(edge,i,vertexStatusArr);        }        printf("\n");}void BFTcore(int (*edge)[VERTEXNUM],int i,int* vertexStatusArr){        putQueue(i);        int* qeValue = NULL;        while((qeValue = getQueue()) != NULL){                if(vertexStatusArr[*qeValue] == 0){                        printf("%d ",*qeValue);                        vertexStatusArr[*qeValue] = 1;                        putRelatedInQueue(edge, *qeValue);                }                free(qeValue);                qeValue = NULL;        }}//將元素放到隊列中void putQueue(int vertex){        st_qElement* qe = (st_qElement*)malloc(sizeof(st_qElement));        qe->value = vertex;        qe->next = NULL;        qe->pre = NULL;        if(front == NULL || rear == NULL){                front = rear = qe;        }else{                rear->next = qe;                qe->pre = rear;                rear = qe;        }}//從隊列中擷取一個元素int* getQueue(){        if(front == NULL || rear == NULL){                return NULL;        }else{                int* res = (int*)malloc(sizeof(int));                *res = front->value;                st_qElement* p = front;                front = front->next;                if(front == NULL){                        rear = front;                }else{                        front->pre = NULL;                }                free(p);                p = NULL;                return res;        }}//將頂點關聯的元素放到隊列中void putRelatedInQueue(int (*edge)[VERTEXNUM], int vertex){        int i;        for(i=0;i<VERTEXNUM;i++){                if(edge[vertex][i] == 1){                        putQueue(i);                }        }}

c語言實現如下：（使用鄰接表格儲存體）

#include <stdio.h>#include <malloc.h>#define VERTEXNUM 5//存放頂點的鄰接表元素typedef struct edge{        int vertex;        struct edge* next;}st_edge;//隊列的元素typedef struct qElement{        int value;        struct qElement* pre;        struct qElement* next;}st_qElement;//隊列的前端和後端，最後一個入隊列的元素為rear，第一個出隊列的元素為frontst_qElement* front = NULL;st_qElement* rear = NULL;void createGraph(st_edge** edge, int start, int end);void displayGraph(st_edge** edge);void delGraph(st_edge** edge);void BFT(st_edge** edge,int* vertexStatusArr);void BFTcore(st_edge** edge,int i,int* vertexStatusArr);void putQueue(int vertex);int* getQueue();void putRelatedInQueue(st_edge** edge, int vertex);int main(void){//動態建立存放邊的指標數組         st_edge** edge = (st_edge**)malloc(sizeof(st_edge*)*VERTEXNUM);        int i;        for(i=0;i<VERTEXNUM;i++){                edge[i] = NULL;        }//存放頂點的遍曆狀態，0：未遍曆，1：已遍曆        int* vertexStatusArr = (int*)malloc(sizeof(int)*VERTEXNUM);        for(i=0;i<VERTEXNUM;i++){                vertexStatusArr[i] = 0;        }        printf("after init:\n");        displayGraph(edge);//建立圖        createGraph(edge,0,3);        createGraph(edge,0,4);        createGraph(edge,3,1);        createGraph(edge,3,2);        createGraph(edge,4,1);        printf("after create:\n");        displayGraph(edge);//廣度優先遍曆        BFT(edge,vertexStatusArr);//釋放鄰接表佔用的記憶體        delGraph(edge);        edge = NULL;        free(vertexStatusArr);        vertexStatusArr = NULL;        return 0;}//建立圖void createGraph(st_edge** edge, int start, int end){        st_edge* newedge = (st_edge*)malloc(sizeof(st_edge));        newedge->vertex = end;        newedge->next = NULL;        edge = edge + start;        while(*edge != NULL){                edge = &((*edge)->next);        }        *edge = newedge;}//列印儲存的圖void displayGraph(st_edge** edge){        int i;        st_edge* p;        for(i=0;i<VERTEXNUM;i++){                printf("%d:",i);                p = *(edge+i);                while(p != NULL){                        printf("%d ",p->vertex);                        p = p->next;                }                printf("\n");        }}//釋放鄰接表佔用的記憶體void delGraph(st_edge** edge){        int i;        st_edge* p;        st_edge* del;        for(i=0;i<VERTEXNUM;i++){                p = *(edge+i);                while(p != NULL){                        del = p;                        p = p->next;                        free(del);                }                edge[i] = NULL;        }        free(edge);}//廣度優先遍曆void BFT(st_edge** edge,int* vertexStatusArr){        printf("start BFT graph:\n");        int i;        for(i=0;i<VERTEXNUM;i++){                BFTcore(edge,i,vertexStatusArr);        }        printf("\n");}void BFTcore(st_edge** edge,int i,int* vertexStatusArr){        putQueue(i);        int* qeValue = NULL;        while((qeValue = getQueue()) != NULL){                if(vertexStatusArr[*qeValue] == 0){                        printf("%d ",*qeValue);                        vertexStatusArr[*qeValue] = 1;                        putRelatedInQueue(edge, *qeValue);                }                free(qeValue);                qeValue = NULL;        }}//將元素放到隊列中void putQueue(int vertex){        st_qElement* qe = (st_qElement*)malloc(sizeof(st_qElement));        qe->value = vertex;        qe->next = NULL;        qe->pre = NULL;        if(front == NULL || rear == NULL){                front = rear = qe;        }else{                rear->next = qe;                qe->pre = rear;                rear = qe;        }}//從隊列中擷取一個元素int* getQueue(){        if(front == NULL || rear == NULL){                return NULL;        }else{                int* res = (int*)malloc(sizeof(int));                *res = front->value;                st_qElement* p = front;                front = front->next;                if(front == NULL){                        rear = front;                }else{                        front->pre = NULL;                }                free(p);                p = NULL;                return res;        }}//將頂點關聯的元素放到隊列中void putRelatedInQueue(st_edge** edge, int vertex){        st_edge* p = *(edge+vertex);        while(p != NULL){                putQueue(p->vertex);                p = p->next;        }}