图的创建（邻接矩阵，邻接表）——C语言描述
图的创建（邻接矩阵，邻接表）——C语言描述
0 测试用例框架
1 定义
图是由顶点的有穷非空集合和顶点之间边的集合组成的，表示为G(V, E).先把key值存到表里面去，存的过程哈希表Hashkey与表里面的值（Key）一一对应，存表冲突时使用开放地址法解决。时间复杂度为O(1)，空间复杂度为O(n).
2 邻接矩阵法
用一维数组表示图的顶点，用二维数组表示边的关系
2.1 数据结构
#define MAX_VEXS_SIZE (100)
#define MAX_VALUE (65535)
#pragma pack(1)
typedef struct _M_GRAPH {
int VectorNum;
int EadgeNum;
int Vector[MAX_VEXS_SIZE];
int Eadge[MAX_VEXS_SIZE][MAX_VEXS_SIZE];
}M_GRAPH;
#pragma pack()
void PrintMGraph(M_GRAPH *MGraph);
void BuildMGraph(M_GRAPH *MGraph, int *Vector, int *Eadge, int VectorNum, int EadgeNum);
2.2 构建图代码
/*BuildMGraph*/
void PrintMGraph(M_GRAPH *MGraph) {
int i, j;
printf("MGraph->VectorNum = %d\n", MGraph->VectorNum);
printf("MGraph->EadgeNum = %d\n", MGraph->EadgeNum);
for (i = 0; i < MGraph->VectorNum; i++) {
printf("MGraph->Vector[%d] = %d\n", i, MGraph->Vector[i]);
}
for (i = 0; i < MGraph->VectorNum; i++) {
for (j = 0; j < MGraph->VectorNum; j++) {
printf("MGraph->Vector[%d][%d] = %d, ", i, j, MGraph->Eadge[i][j]);
}
printf("\n");
}
}
void BuildMGraph(M_GRAPH *MGraph, int *Vector, int *Eadge, int VectorNum, int EadgeNum) {
int i = 0, j = 0;
int *EadgeArr = Eadge;
if ((MGraph == NULL) || (Vector == NULL) || (Eadge == NULL)) {
return;
}
MGraph->VectorNum = VectorNum;
MGraph->EadgeNum = EadgeNum;
for (i = 0; i < VectorNum; i++) {
MGraph->Vector[i] = Vector[i];
}
//printf("Eadge = 0x%lx, EadgeArr = 0x%lx\n", Eadge, EadgeArr);
for (i = 0; i < VectorNum; i++) {
Eadge = (EadgeArr + i * VectorNum);
//Eadge = (int *)((unsigned long long)EadgeArr + i * VectorNum * sizeof(int));
for (j = 0; j < VectorNum; j++) {
//printf("Eadge[%d][%d] = %d, Eadge[%d] = 0x%lx\n", i, j, Eadge[j], j, &Eadge[j]);
MGraph->Eadge[i][j] = Eadge[j];
}
}
}
（2）测试用例
/*TestBuildMGraph*/
void TestMGraph(M_GRAPH *MGraph01, M_GRAPH *MGraph02) {
int i, j;
TestNum++;
if ((MGraph01->VectorNum != MGraph02->VectorNum) || (MGraph01->EadgeNum != MGraph02->EadgeNum)) {
FaildNum++;
return;
}
for (i = 0; i < MGraph01->VectorNum; i++) {
if (MGraph01->Vector[i] != MGraph02->Vector[i]) {
FaildNum++;
return;
}
}
for (i = 0; i < MGraph01->VectorNum; i++) {
for (j = 0; j < MGraph01->VectorNum; j++) {
if (MGraph01->Eadge[i][j] != MGraph02->Eadge[i][j]) {
FaildNum++;
return;
}
}
}
PassNum++;
}
void TestBuildMGraph(void) {
/*Test01*/
M_GRAPH MGraph01;
int Vector01[] = { 0, 1, 2, 3 };
int Eadge01[][4] = {{0, 1, 1, 1},
{1, 0, 1, 0},
{1, 1, 0, 1},
{1, 0, 1, 0}
};
int VectorNum01 = 4;
int EadgeNum01 = 5;
M_GRAPH CmpGraph01 = { 4, 5, {0, 1, 2, 3},
{{0, 1, 1, 1},
{1, 0, 1, 0},
{1, 1, 0, 1},
{1, 0, 1, 0}
}
};
/*Test02*/
M_GRAPH MGraph02;
int Vector02[] = { 0, 1, 2, 3, 4, 5, 6, 7, 8 };
// A B C D E F G H I
int Eadge02[][9] = { {0, 1, 0, 0, 0, 1, 0, 0, 0}, //A
{1, 0, 1, 0, 0, 0, 1, 0, 1}, //B
{0, 1, 0, 1, 0, 0, 0, 0, 1}, //C
{0, 0, 1, 0, 1, 0, 1, 1, 1}, //D
{0, 0, 0, 1, 0, 1, 0, 1, 0}, //E
{1, 0, 0, 0, 1, 0, 1, 0, 0}, //F
{0, 1, 0, 1, 0, 1, 0, 1, 0}, //G
{0, 0, 0, 1, 1, 0, 1, 0, 0}, //H
{0, 1, 1, 1, 0, 0, 0, 0, 0}, //I
};
int VectorNum02 = 9;
int EadgeNum02 = 15;
M_GRAPH CmpGraph02 = { 9, 15, { 0, 1, 2, 3, 4, 5, 6, 7, 8},
{{0, 1, 0, 0, 0, 1, 0, 0, 0}, //A
{1, 0, 1, 0, 0, 0, 1, 0, 1}, //B
{0, 1, 0, 1, 0, 0, 0, 0, 1}, //C
{0, 0, 1, 0, 1, 0, 1, 1, 1}, //D
{0, 0, 0, 1, 0, 1, 0, 1, 0}, //E
{1, 0, 0, 0, 1, 0, 1, 0, 0}, //F
{0, 1, 0, 1, 0, 1, 0, 1, 0}, //G
{0, 0, 0, 1, 1, 0, 1, 0, 0}, //H
{0, 1, 1, 1, 0, 0, 0, 0, 0}, //I
}
};
printf("-------Test start----------\n");
InitNum();
/*Test01*/
printf("\n-------Test 01----------\n");
BuildMGraph(&MGraph01, Vector01, (int *)Eadge01, VectorNum01, EadgeNum01);
PrintMGraph(&MGraph01);
TestMGraph(&CmpGraph01, &MGraph01);
/*Test02*/
printf("\n-------Test 02----------\n");
BuildMGraph(&MGraph02, Vector02, Eadge02, VectorNum02, EadgeNum02);
PrintMGraph(&MGraph02);
TestMGraph(&CmpGraph02, &MGraph02);
/*Test Result*/
printf("\n-------Test result----------\n");
TestResult();
}
（3）打印结果
-------Test start----------
-------Test 01----------
MGraph->VectorNum = 4
MGraph->EadgeNum = 5
MGraph->Vector[0] = 0
MGraph->Vector[1] = 1
MGraph->Vector[2] = 2
MGraph->Vector[3] = 3
MGraph->Vector[0][0] = 0, MGraph->Vector[0][1] = 1, MGraph->Vector[0][2] = 1, MGraph->Vector[0][3] = 1,
MGraph->Vector[1][0] = 1, MGraph->Vector[1][1] = 0, MGraph->Vector[1][2] = 1, MGraph->Vector[1][3] = 0,
MGraph->Vector[2][0] = 1, MGraph->Vector[2][1] = 1, MGraph->Vector[2][2] = 0, MGraph->Vector[2][3] = 1,
MGraph->Vector[3][0] = 1, MGraph->Vector[3][1] = 0, MGraph->Vector[3][2] = 1, MGraph->Vector[3][3] = 0,
-------Test 02----------
MGraph->VectorNum = 9
MGraph->EadgeNum = 15
MGraph->Vector[0] = 0
MGraph->Vector[1] = 1
MGraph->Vector[2] = 2
MGraph->Vector[3] = 3
MGraph->Vector[4] = 4
MGraph->Vector[5] = 5
MGraph->Vector[6] = 6
MGraph->Vector[7] = 7
MGraph->Vector[8] = 8
MGraph->Vector[0][0] = 0, MGraph->Vector[0][1] = 1, MGraph->Vector[0][2] = 0, MGraph->Vector[0][3] = 0, MGraph->Vector[0][4] = 0, MGraph->Vector[0][5] = 1, MGraph->Vector[0][6] = 0, MGraph->Vector[0][7] = 0, MGraph->Vector[0][8] = 0,
MGraph->Vector[1][0] = 1, MGraph->Vector[1][1] = 0, MGraph->Vector[1][2] = 1, MGraph->Vector[1][3] = 0, MGraph->Vector[1][4] = 0, MGraph->Vector[1][5] = 0, MGraph->Vector[1][6] = 1, MGraph->Vector[1][7] = 0, MGraph->Vector[1][8] = 1,
MGraph->Vector[2][0] = 0, MGraph->Vector[2][1] = 1, MGraph->Vector[2][2] = 0, MGraph->Vector[2][3] = 1, MGraph->Vector[2][4] = 0, MGraph->Vector[2][5] = 0, MGraph->Vector[2][6] = 0, MGraph->Vector[2][7] = 0, MGraph->Vector[2][8] = 1,
MGraph->Vector[3][0] = 0, MGraph->Vector[3][1] = 0, MGraph->Vector[3][2] = 1, MGraph->Vector[3][3] = 0, MGraph->Vector[3][4] = 1, MGraph->Vector[3][5] = 0, MGraph->Vector[3][6] = 1, MGraph->Vector[3][7] = 1, MGraph->Vector[3][8] = 1,
MGraph->Vector[4][0] = 0, MGraph->Vector[4][1] = 0, MGraph->Vector[4][2] = 0, MGraph->Vector[4][3] = 1, MGraph->Vector[4][4] = 0, MGraph->Vector[4][5] = 1, MGraph->Vector[4][6] = 0, MGraph->Vector[4][7] = 1, MGraph->Vector[4][8] = 0,
MGraph->Vector[5][0] = 1, MGraph->Vector[5][1] = 0, MGraph->Vector[5][2] = 0, MGraph->Vector[5][3] = 0, MGraph->Vector[5][4] = 1, MGraph->Vector[5][5] = 0, MGraph->Vector[5][6] = 1, MGraph->Vector[5][7] = 0, MGraph->Vector[5][8] = 0,
MGraph->Vector[6][0] = 0, MGraph->Vector[6][1] = 1, MGraph->Vector[6][2] = 0, MGraph->Vector[6][3] = 1, MGraph->Vector[6][4] = 0, MGraph->Vector[6][5] = 1, MGraph->Vector[6][6] = 0, MGraph->Vector[6][7] = 1, MGraph->Vector[6][8] = 0,
MGraph->Vector[7][0] = 0, MGraph->Vector[7][1] = 0, MGraph->Vector[7][2] = 0, MGraph->Vector[7][3] = 1, MGraph->Vector[7][4] = 1, MGraph->Vector[7][5] = 0, MGraph->Vector[7][6] = 1, MGraph->Vector[7][7] = 0, MGraph->Vector[7][8] = 0,
MGraph->Vector[8][0] = 0, MGraph->Vector[8][1] = 1, MGraph->Vector[8][2] = 1, MGraph->Vector[8][3] = 1, MGraph->Vector[8][4] = 0, MGraph->Vector[8][5] = 0, MGraph->Vector[8][6] = 0, MGraph->Vector[8][7] = 0, MGraph->Vector[8][8] = 0,
-------Test result----------
Print test result;
TestNum = 2, PassNum = 2, FaildNum = 0
3 邻接表
顶点用一维数组存，边的信息用链表存，数据结构如下图所示：
/*ADJUST_LIST_GRAPH*/
typedef struct _LIST_NODE_DATA {
int Num;
int Vector[MAX_VEXS_SIZE];
}LIST_NODE_DATA;
typedef struct _LIST_NODE {
int VectorIndex;
struct _LIST_NODE *Next;
}LIST_NODE;
typedef struct _ADJUST_LIST {
int Data;
LIST_NODE *FirstEadge;
}ADJUST_LIST;
typedef struct _ADJUST_LIST_GRAPH {
int VectorNum;
int EadgeNum;
ADJUST_LIST AdjustGraph[MAX_VEXS_SIZE];
}ADJUST_LIST_GRAPH;
void BuildAdjustListGraph(ADJUST_LIST_GRAPH *AdjListGraph, ADJUST_LIST_GRAPH *AdjListGraphData, LIST_NODE_DATA *LstNodeData);
void PrintAdjLstGraph(const ADJUST_LIST_GRAPH *AdjListGraph01);
3.1 代码
/*BuildAdjustListGraph*/
void PrintLstNode(const LIST_NODE *LstNode) {
if (LstNode == NULL) {
return;
}
while (LstNode != NULL) {
//printf("LstNode = 0x%lx, LstNode->VectorIndex = %d, LstNode->Next = 0x%lx\n", LstNode, LstNode->VectorIndex, LstNode->Next);
printf("LstNode->VectorIndex = %d\n", LstNode->VectorIndex);
LstNode = LstNode->Next;
}
}
void PrintAdjLstGraph(const ADJUST_LIST_GRAPH *AdjLstGraph) {
int i = 0;
if (AdjLstGraph == NULL) {
return;
}
printf("AdjLstGraph->VectorNum = %d\n", AdjLstGraph->VectorNum);
printf("AdjLstGraph->EadgeNum = %d\n", AdjLstGraph->EadgeNum);
for (i = 0; i < AdjLstGraph->VectorNum; i++) {
printf("AdjLstGraph->AdjustGraph[%d].Data = %d\n", i, AdjLstGraph->AdjustGraph[i].Data);
//printf("AdjLstGraph->AdjustGraph[%d].FirstEadge = 0x%lx\n", i, AdjLstGraph->AdjustGraph[i].FirstEadge);
PrintLstNode(AdjLstGraph->AdjustGraph[i].FirstEadge);
}
}
void AddAdjLstNode(LIST_NODE **FirstEadge, LIST_NODE_DATA *LstNodeData) {
int i = 0;
LIST_NODE *AddNode = NULL;
LIST_NODE *PreNode = NULL;
if ((FirstEadge == NULL) || (LstNodeData == NULL)) {
return;
}
for (i = 0; i < LstNodeData->Num; i++) {
AddNode = (LIST_NODE *)malloc(sizeof(LIST_NODE));
if (AddNode == NULL) {
return;
}
AddNode->VectorIndex = LstNodeData->Vector[i];
AddNode->Next = NULL;
if (*FirstEadge == NULL) {
*FirstEadge = AddNode;
PreNode = AddNode;
}
else {
AddNode->Next = PreNode->Next;
PreNode->Next = AddNode;
PreNode = PreNode->Next;
}
}
}
void BuildAdjustListGraph(ADJUST_LIST_GRAPH *AdjListGraph, ADJUST_LIST_GRAPH *AdjListGraphData, LIST_NODE_DATA *LstNodeData) {
int i = 0;
if ((AdjListGraph == NULL) || (AdjListGraphData == NULL) || (LstNodeData == NULL)) {
return;
}
AdjListGraph->VectorNum = AdjListGraphData->VectorNum;
AdjListGraph->EadgeNum = AdjListGraphData->EadgeNum;
for (i = 0; i < AdjListGraphData->VectorNum; i++) {
AdjListGraph->AdjustGraph[i].Data = AdjListGraphData->AdjustGraph[i].Data;
AdjListGraph->AdjustGraph[i].FirstEadge = NULL;
AddAdjLstNode(&(AdjListGraph->AdjustGraph[i].FirstEadge), &LstNodeData[i]);
}
}
3.2 测试用例
/*TestBuildAdjustListGraph*/
bool TestAdjLst(const LIST_NODE *CmpAdjLst, const LIST_NODE *AdjLst) {
LIST_NODE *PCmpNode = CmpAdjLst;
LIST_NODE *PNode = AdjLst;
if ((CmpAdjLst == NULL) || (AdjLst == NULL)) {
return false;
}
while ((PCmpNode != NULL) && (PNode != NULL)) {
if (CmpAdjLst->VectorIndex != AdjLst->VectorIndex) {
return false;
}
else {
PCmpNode = PCmpNode->Next;
PNode = PNode->Next;
}
}
if (PCmpNode != PNode) {
return false;
}
return true;
}
void TestAdjLstGraph(const ADJUST_LIST_GRAPH *CmpAdjLstGraph, const ADJUST_LIST_GRAPH *AdjLstGraph) {
int i = 0;
TestNum++;
if ((CmpAdjLstGraph == NULL) || (AdjLstGraph == NULL)) {
FaildNum++;
return;
}
if ((CmpAdjLstGraph->VectorNum != AdjLstGraph->VectorNum) || (CmpAdjLstGraph->EadgeNum != AdjLstGraph->EadgeNum)) {
FaildNum++;
return;
}
for (i = 0; i < CmpAdjLstGraph->VectorNum; i++) {
if (CmpAdjLstGraph->AdjustGraph[i].Data != AdjLstGraph->AdjustGraph[i].Data) {
FaildNum++;
return;
}
}
for (i = 0; i < CmpAdjLstGraph->VectorNum; i++) {
if (TestAdjLst(CmpAdjLstGraph->AdjustGraph[i].FirstEadge, AdjLstGraph->AdjustGraph[i].FirstEadge) == false) {
FaildNum++;
return;
}
}
PassNum++;
}
void BuildCmpAdjListGraph(ADJUST_LIST_GRAPH *AdjLstGraph, LIST_NODE_DATA *LstNodeData) {
int i = 0;
if ((AdjLstGraph == NULL) || (LstNodeData == NULL)) {
return;
}
for (i = 0; i < AdjLstGraph->VectorNum; i++) {
AddAdjLstNode(&(AdjLstGraph->AdjustGraph[i].FirstEadge), &LstNodeData[i]);
}
}
void TestBuildAdjustListGraph(void) {
/*Test01*/
ADJUST_LIST_GRAPH AdjLstGraph01;
ADJUST_LIST_GRAPH AdjLstGraphData01 = { 4, 5, {{0, NULL}, {10, NULL}, {20, NULL}, {30, NULL}} };
LIST_NODE_DATA AdjLstNodeData01[] = { {3, {1, 2, 3}}, {2, {0, 2}}, {3, {0, 1, 3}}, {2, {0, 2}} };
ADJUST_LIST_GRAPH CmpAdjLstGraph01 = { 4, 5, {{0, NULL}, {10, NULL}, {20, NULL}, {30, NULL}} };
/*Test02*/
ADJUST_LIST_GRAPH AdjLstGraph02; //A B C D E F G H I
ADJUST_LIST_GRAPH AdjLstGraphData02 = { 9, 15, {{0, NULL}, {10, NULL}, {20, NULL}, {30, NULL}, {40, NULL}, {50, NULL}, {60, NULL}, {70, NULL}, {80, NULL},
}
};
//A B C D E F G H I
LIST_NODE_DATA AdjLstNodeData02[] = { {2, {1, 5}}, {4, {0, 2, 6, 8}}, {3, {1, 3, 8}}, {5, {2, 4, 6, 7, 8}}, {3, {3, 5, 7}}, {3, {0, 4, 6}}, {4, {1, 3, 5, 7}}, {3, {3, 4, 6}}, {3, {1, 2, 3}}
};
ADJUST_LIST_GRAPH CmpAdjLstGraph02 = { 9, 15, {{0, NULL}, {10, NULL}, {20, NULL}, {30, NULL}, {40, NULL}, {50, NULL}, {60, NULL}, {70, NULL}, {80, NULL},
}
};
printf("-------Test start----------\n");
InitNum();
printf("-------Test01----------\n");
BuildAdjustListGraph(&AdjLstGraph01, &AdjLstGraphData01, AdjLstNodeData01);
PrintAdjLstGraph(&AdjLstGraph01);
BuildCmpAdjListGraph(&CmpAdjLstGraph01, AdjLstNodeData01);
TestAdjLstGraph(&CmpAdjLstGraph01, &AdjLstGraph01);
printf("-------Test02----------\n");
BuildAdjustListGraph(&AdjLstGraph02, &AdjLstGraphData02, AdjLstNodeData02);
PrintAdjLstGraph(&AdjLstGraph02);
BuildCmpAdjListGraph(&CmpAdjLstGraph02, AdjLstNodeData02);
TestAdjLstGraph(&CmpAdjLstGraph02, &AdjLstGraph02);
/*Test Result*/
printf("\n-------Test result----------\n");
TestResult();
}
结果：
-------Test start----------
-------Test01----------
AdjLstGraph->VectorNum = 4
AdjLstGraph->EadgeNum = 5
AdjLstGraph->AdjustGraph[0].Data = 0
LstNode->VectorIndex = 1
LstNode->VectorIndex = 2
LstNode->VectorIndex = 3
AdjLstGraph->AdjustGraph[1].Data = 10
LstNode->VectorIndex = 0
LstNode->VectorIndex = 2
AdjLstGraph->AdjustGraph[2].Data = 20
LstNode->VectorIndex = 0
LstNode->VectorIndex = 1
LstNode->VectorIndex = 3
AdjLstGraph->AdjustGraph[3].Data = 30
LstNode->VectorIndex = 0
LstNode->VectorIndex = 2
-------Test02----------
AdjLstGraph->VectorNum = 9
AdjLstGraph->EadgeNum = 15
AdjLstGraph->AdjustGraph[0].Data = 0
LstNode->VectorIndex = 1
LstNode->VectorIndex = 5
AdjLstGraph->AdjustGraph[1].Data = 10
LstNode->VectorIndex = 0
LstNode->VectorIndex = 2
LstNode->VectorIndex = 6
LstNode->VectorIndex = 8
AdjLstGraph->AdjustGraph[2].Data = 20
LstNode->VectorIndex = 1
LstNode->VectorIndex = 3
LstNode->VectorIndex = 8
AdjLstGraph->AdjustGraph[3].Data = 30
LstNode->VectorIndex = 2
LstNode->VectorIndex = 4
LstNode->VectorIndex = 6
LstNode->VectorIndex = 7
LstNode->VectorIndex = 8
AdjLstGraph->AdjustGraph[4].Data = 40
LstNode->VectorIndex = 3
LstNode->VectorIndex = 5
LstNode->VectorIndex = 7
AdjLstGraph->AdjustGraph[5].Data = 50
LstNode->VectorIndex = 0
LstNode->VectorIndex = 4
LstNode->VectorIndex = 6
AdjLstGraph->AdjustGraph[6].Data = 60
LstNode->VectorIndex = 1
LstNode->VectorIndex = 3
LstNode->VectorIndex = 5
LstNode->VectorIndex = 7
AdjLstGraph->AdjustGraph[7].Data = 70
LstNode->VectorIndex = 3
LstNode->VectorIndex = 4
LstNode->VectorIndex = 6
AdjLstGraph->AdjustGraph[8].Data = 80
LstNode->VectorIndex = 1
LstNode->VectorIndex = 2
LstNode->VectorIndex = 3
-------Test result----------
Print test result;
TestNum = 2, PassNum = 2, FaildNum = 0
