数据结构笔记-----图
图的定义
都是图，可以用来描述生活里的各种情况
社交网络应用
小结
图的存储结构
邻接矩阵法
代码:
<strong><span style="font-size:18px;">#ifndef _MGRAPH_H_ #define _MGRAPH_H_ typedef void MGraph; typedef void MVertex; typedef void (MGraph_Printf)(MVertex*); MGraph* MGraph_Create(MVertex** v, int n); void MGraph_Destroy(MGraph* graph); void MGraph_Clear(MGraph* graph); int MGraph_AddEdge(MGraph* graph, int v1, int v2, int w); int MGraph_RemoveEdge(MGraph* graph, int v1, int v2); int MGraph_GetEdge(MGraph* graph, int v1, int v2); int MGraph_TD(MGraph* graph, int v); int MGraph_VertexCount(MGraph* graph); int MGraph_EdgeCount(MGraph* graph); void MGraph_DFS(MGraph* graph, int v, MGraph_Printf* pFunc); void MGraph_BFS(MGraph* graph, int v, MGraph_Printf* pFunc); void MGraph_Display(MGraph* graph, MGraph_Printf* pFunc); #endif</span></strong>
<strong><span style="font-size:18px;">#include <malloc.h>
#include <stdio.h>
#include "MGraph.h"
#include "LinkQueue.h"
typedef struct _tag_MGraph
{
int count;
MVertex** v;
int** matrix;
} TMGraph;
static void recursive_dfs(TMGraph* graph, int v, int visited[], MGraph_Printf* pFunc)
{
int i = 0;
pFunc(graph->v[v]);
visited[v] = 1;
printf(", ");
for(i=0; i<graph->count; i++)
{
if( (graph->matrix[v][i] != 0) && !visited[i] )
{
recursive_dfs(graph, i, visited, pFunc);
}
}
}
static void bfs(TMGraph* graph, int v, int visited[], MGraph_Printf* pFunc)
{
LinkQueue* queue = LinkQueue_Create();
if( queue != NULL )
{
LinkQueue_Append(queue, graph->v + v);
//不可以在队列中加入值为0的元素
visited[v] = 1;
while( LinkQueue_Length(queue) > 0 )
{
int i = 0;
v = (MVertex**)LinkQueue_Retrieve(queue) - graph->v;
pFunc(graph->v[v]);
printf(", ");
for(i=0; i<graph->count; i++)
{
if( (graph->matrix[v][i] != 0) && !visited[i] )
{
LinkQueue_Append(queue, graph->v + i);
visited[i] = 1;
}
}
}
}
LinkQueue_Destroy(queue);
}
MGraph* MGraph_Create(MVertex** v, int n) // O(n)
{
TMGraph* ret = NULL;
if( (v != NULL ) && (n > 0) )
{
ret = (TMGraph*)malloc(sizeof(TMGraph));
if( ret != NULL )
{
int* p = NULL;
ret->count = n;
ret->v = (MVertex**)malloc(sizeof(MVertex*) * n);
//结点
ret->matrix = (int**)malloc(sizeof(int*) * n);
//通过二级指针动态申请一维指针数组
p = (int*)calloc(n * n, sizeof(int));
//通过一级指针申请数据空间
if( (ret->v != NULL) && (ret->matrix != NULL) && (p != NULL) )
{
int i = 0;
for(i=0; i<n; i++)
{
ret->v[i] = v[i];
ret->matrix[i] = p + i * n;
//将一维指针数组中的指针连接到数据空间
}
}
else
{//异常处理
free(p);
free(ret->matrix);
free(ret->v);
free(ret);
ret = NULL;
}
}
}
return ret;
}
void MGraph_Destroy(MGraph* graph) // O(1)
{
TMGraph* tGraph = (TMGraph*)graph;
if( tGraph != NULL )
{
free(tGraph->v);
free(tGraph->matrix[0]);
//释放首地址
free(tGraph->matrix);
//释放一维数组
free(tGraph);
//这几步不能乱
}
}
void MGraph_Clear(MGraph* graph) // O(n*n)
{
TMGraph* tGraph = (TMGraph*)graph;
if( tGraph != NULL )
{
int i = 0;
int j = 0;
for(i=0; i<tGraph->count; i++)
{
for(j=0; j<tGraph->count; j++)
{
tGraph->matrix[i][j] = 0;
}
}
}
}
int MGraph_AddEdge(MGraph* graph, int v1, int v2, int w) // O(1)
{
TMGraph* tGraph = (TMGraph*)graph;
int ret = (tGraph != NULL);
ret = ret && (0 <= v1) && (v1 < tGraph->count);
ret = ret && (0 <= v2) && (v2 < tGraph->count);
ret = ret && (0 <= w);
if( ret )
{
tGraph->matrix[v1][v2] = w;
}
return ret;
}
int MGraph_RemoveEdge(MGraph* graph, int v1, int v2) // O(1)
{
int ret = MGraph_GetEdge(graph, v1, v2);
if( ret != 0 )
{
((TMGraph*)graph)->matrix[v1][v2] = 0;
}
return ret;
}
int MGraph_GetEdge(MGraph* graph, int v1, int v2) // O(1)
{
TMGraph* tGraph = (TMGraph*)graph;
int condition = (tGraph != NULL);
int ret = 0;
condition = condition && (0 <= v1) && (v1 < tGraph->count);
condition = condition && (0 <= v2) && (v2 < tGraph->count);
if( condition )
{
ret = tGraph->matrix[v1][v2];
}
return ret;
}
int MGraph_TD(MGraph* graph, int v) // O(n) 度
{
TMGraph* tGraph = (TMGraph*)graph;
int condition = (tGraph != NULL);
int ret = 0;
condition = condition && (0 <= v) && (v < tGraph->count);
if( condition )
{
int i = 0;
for(i=0; i<tGraph->count; i++)
{
if( tGraph->matrix[v][i] != 0 )
{
ret++;
}
if( tGraph->matrix[i][v] != 0 )
{
ret++;
}
}
}
return ret;
}
int MGraph_VertexCount(MGraph* graph) // O(1)
{
TMGraph* tGraph = (TMGraph*)graph;
int ret = 0;
if( tGraph != NULL )
{
ret = tGraph->count;
}
return ret;
}
int MGraph_EdgeCount(MGraph* graph) // O(n*n)
{
TMGraph* tGraph = (TMGraph*)graph;
int ret = 0;
if( tGraph != NULL )
{
int i = 0;
int j = 0;
for(i=0; i<tGraph->count; i++)
{
for(j=0; j<tGraph->count; j++)
{
if( tGraph->matrix[i][j] != 0 )
{
ret++;
}
}
}
}
return ret;
}
void MGraph_DFS(MGraph* graph, int v, MGraph_Printf* pFunc)
{//深度优先遍历
TMGraph* tGraph = (TMGraph*)graph;
int* visited = NULL;
int condition = (tGraph != NULL);
condition = condition && (0 <= v) && (v < tGraph->count);
condition = condition && (pFunc != NULL);
condition = condition && ((visited = (int*)calloc(tGraph->count, sizeof(int))) != NULL);
if( condition )
{
int i = 0;
recursive_dfs(tGraph, v, visited, pFunc);
for(i=0; i<tGraph->count; i++)
{
if( !visited[i] )
{
recursive_dfs(tGraph, i, visited, pFunc);
}
}
printf("\n");
}
free(visited);
}</span></strong><strong><span style="font-size:18px;">void MGraph_BFS(MGraph* graph, int v, MGraph_Printf* pFunc)
{//广度优先遍历
TMGraph* tGraph = (TMGraph*)graph;
int* visited = NULL;
int condition = (tGraph != NULL);
condition = condition && (0 <= v) && (v < tGraph->count);
condition = condition && (pFunc != NULL);
condition = condition && ((visited = (int*)calloc(tGraph->count, sizeof(int))) != NULL);
if( condition )
{
int i = 0;
bfs(tGraph, v, visited, pFunc);
for(i=0; i<tGraph->count; i++)
{
if( !visited[i] )
{
bfs(tGraph, i, visited, pFunc);
}
}
printf("\n");
}
free(visited);
}
void MGraph_Display(MGraph* graph, MGraph_Printf* pFunc) // O(n*n)
{ //MGraph_Display(graph, print_data);
TMGraph* tGraph = (TMGraph*)graph;
if( (tGraph != NULL) && (pFunc != NULL) )
{
int i = 0;
int j = 0;
for(i=0; i<tGraph->count; i++)
{
printf("%d:", i);
pFunc(tGraph->v[i]);
printf(" ");
}
printf("\n");
for(i=0; i<tGraph->count; i++)
{
for(j=0; j<tGraph->count; j++)
{
if( tGraph->matrix[i][j] != 0 )
{
printf("<");
pFunc(tGraph->v[i]);
//print_data
printf(", ");
pFunc(tGraph->v[j]);
printf(", %d", tGraph->matrix[i][j]);
printf(">");
printf(" ");
}
}
}
printf("\n");
}
}
</span></strong><strong><span style="font-size:18px;">#include <stdio.h>
#include <stdlib.h>
#include "MGraph.h"
/* run this program using the console pauser or add your own getch, system("pause") or input loop */
void print_data(MVertex* v)
{
printf("%s", (char*)v);
}
int main(int argc, char *argv[])
{
MVertex* v[] = {"A", "B", "C", "D", "E", "F"};
MGraph* graph = MGraph_Create(v, 6);
MGraph_AddEdge(graph, 0, 1, 1);
MGraph_AddEdge(graph, 0, 2, 1);
MGraph_AddEdge(graph, 0, 3, 1);
MGraph_AddEdge(graph, 1, 5, 1);
MGraph_AddEdge(graph, 1, 4, 1);
MGraph_AddEdge(graph, 2, 1, 1);
MGraph_AddEdge(graph, 3, 4, 1);
MGraph_AddEdge(graph, 4, 2, 1);
MGraph_Display(graph, print_data);
MGraph_DFS(graph, 0, print_data);
MGraph_BFS(graph, 0, print_data);
MGraph_Destroy(graph);
return 0;
}</span></strong>图的遍历
深度优先遍历
广度优先遍历
代码
<strong><span style="font-size:18px;">#include <malloc.h>
#include <stdio.h>
#include "LGraph.h"
#include "LinkList.h"
#include "LinkQueue.h"
typedef struct _tag_LGraph
{
int count;
LVertex** v;
LinkList** la;
} TLGraph;
typedef struct _tag_ListNode
{
LinkListNode header;
int v;
int w;
} TListNode;
static void recursive_dfs(TLGraph* graph, int v, int visited[], LGraph_Printf* pFunc)
{
int i = 0;
pFunc(graph->v[v]);
visited[v] = 1;
printf(", ");
for(i=0; i<LinkList_Length(graph->la[v]); i++)
{
TListNode* node = (TListNode*)LinkList_Get(graph->la[v], i);
if( !visited[node->v] )
{
recursive_dfs(graph, node->v, visited, pFunc);
}
}
}
static void bfs(TLGraph* graph, int v, int visited[], LGraph_Printf* pFunc)
{
LinkQueue* queue = LinkQueue_Create();
if( queue != NULL )
{
LinkQueue_Append(queue, graph->v + v);
visited[v] = 1;
while( LinkQueue_Length(queue) > 0 )
{
int i = 0;
v = (LVertex**)LinkQueue_Retrieve(queue) - graph->v;
pFunc(graph->v[v]);
printf(", ");
for(i=0; i<LinkList_Length(graph->la[v]); i++)
{
TListNode* node = (TListNode*)LinkList_Get(graph->la[v], i);
if( !visited[node->v] )
{
LinkQueue_Append(queue, graph->v + node->v);
visited[node->v] = 1;
}
}
}
}
LinkQueue_Destroy(queue);
}
LGraph* LGraph_Create(LVertex** v, int n) // O(n)
{
TLGraph* ret = NULL;
int ok = 1;
if( (v != NULL ) && (n > 0) )
{
ret = (TLGraph*)malloc(sizeof(TLGraph));
if( ret != NULL )
{
ret->count = n;
ret->v = (LVertex**)calloc(n, sizeof(LVertex*));
ret->la = (LinkList**)calloc(n, sizeof(LinkList*));
ok = (ret->v != NULL) && (ret->la != NULL);
if( ok )
{
int i = 0;
for(i=0; i<n; i++)
{
ret->v[i] = v[i];
}
for(i=0; (i<n) && ok; i++)
{
ok = ok && ((ret->la[i] = LinkList_Create()) != NULL);
}
}
if( !ok )
{
if( ret->la != NULL )
{
int i = 0;
for(i=0; i<n; i++)
{
LinkList_Destroy(ret->la[i]);
}
}
free(ret->la);
free(ret->v);
free(ret);
ret = NULL;
}
}
}
return ret;
}
void LGraph_Destroy(LGraph* graph) // O(n*n)
{
TLGraph* tGraph = (TLGraph*)graph;
LGraph_Clear(tGraph);
if( tGraph != NULL )
{
int i = 0;
for(i=0; i<tGraph->count; i++)
{
LinkList_Destroy(tGraph->la[i]);
}
free(tGraph->la);
free(tGraph->v);
free(tGraph);
}
}
void LGraph_Clear(LGraph* graph) // O(n*n)
{
TLGraph* tGraph = (TLGraph*)graph;
if( tGraph != NULL )
{
int i = 0;
for(i=0; i<tGraph->count; i++)
{
while( LinkList_Length(tGraph->la[i]) > 0 )
{
free(LinkList_Delete(tGraph->la[i], 0));
}
}
}
}
int LGraph_AddEdge(LGraph* graph, int v1, int v2, int w) // O(1)
{
TLGraph* tGraph = (TLGraph*)graph;
TListNode* node = NULL;
int ret = (tGraph != NULL);
ret = ret && (0 <= v1) && (v1 < tGraph->count);
ret = ret && (0 <= v2) && (v2 < tGraph->count);
ret = ret && (0 < w) && ((node = (TListNode*)malloc(sizeof(TListNode))) != NULL);
if( ret )
{
node->v = v2;
node->w = w;
LinkList_Insert(tGraph->la[v1], (LinkListNode*)node, 0);
}
return ret;
}
int LGraph_RemoveEdge(LGraph* graph, int v1, int v2) // O(n*n)
{
TLGraph* tGraph = (TLGraph*)graph;
int condition = (tGraph != NULL);
int ret = 0;
condition = condition && (0 <= v1) && (v1 < tGraph->count);
condition = condition && (0 <= v2) && (v2 < tGraph->count);
if( condition )
{
TListNode* node = NULL;
int i = 0;
for(i=0; i<LinkList_Length(tGraph->la[v1]); i++)
{
node = (TListNode*)LinkList_Get(tGraph->la[v1], i);
if( node->v == v2)
{
ret = node->w;
LinkList_Delete(tGraph->la[v1], i);
free(node);
break;
}
}
}
return ret;
}
int LGraph_GetEdge(LGraph* graph, int v1, int v2) // O(n*n)
{
TLGraph* tGraph = (TLGraph*)graph;
int condition = (tGraph != NULL);
int ret = 0;
condition = condition && (0 <= v1) && (v1 < tGraph->count);
condition = condition && (0 <= v2) && (v2 < tGraph->count);
if( condition )
{
TListNode* node = NULL;
int i = 0;
for(i=0; i<LinkList_Length(tGraph->la[v1]); i++)
{
node = (TListNode*)LinkList_Get(tGraph->la[v1], i);
if( node->v == v2)
{
ret = node->w;
break;
}
}
}
return ret;
}
int LGraph_TD(LGraph* graph, int v) // O(n*n*n)
{
TLGraph* tGraph = (TLGraph*)graph;
int condition = (tGraph != NULL);
int ret = 0;
condition = condition && (0 <= v) && (v < tGraph->count);
if( condition )
{
int i = 0;
int j = 0;
for(i=0; i<tGraph->count; i++)
{
for(j=0; j<LinkList_Length(tGraph->la[i]); j++)
{
TListNode* node = (TListNode*)LinkList_Get(tGraph->la[i], j);
if( node->v == v )
{
ret++;
}
}
}
ret += LinkList_Length(tGraph->la[v]);
}
return ret;
}
int LGraph_VertexCount(LGraph* graph) // O(1)
{
TLGraph* tGraph = (TLGraph*)graph;
int ret = 0;
if( tGraph != NULL )
{
ret = tGraph->count;
}
return ret;
}
int LGraph_EdgeCount(LGraph* graph) // O(n)
{
TLGraph* tGraph = (TLGraph*)graph;
int ret = 0;
if( tGraph != NULL )
{
int i = 0;
for(i=0; i<tGraph->count; i++)
{
ret += LinkList_Length(tGraph->la[i]);
}
}
return ret;
}
void LGraph_DFS(LGraph* graph, int v, LGraph_Printf* pFunc)
{
TLGraph* tGraph = (TLGraph*)graph;
int* visited = NULL;
int condition = (tGraph != NULL);
condition = condition && (0 <= v) && (v < tGraph->count);
condition = condition && (pFunc != NULL);
condition = condition && ((visited = (int*)calloc(tGraph->count, sizeof(int))) != NULL);
if( condition )
{
int i = 0;
recursive_dfs(tGraph, v, visited, pFunc);
for(i=0; i<tGraph->count; i++)
{
if( !visited[i] )
{
recursive_dfs(tGraph, i, visited, pFunc);
}
}
printf("\n");
}
free(visited);
}
void LGraph_BFS(LGraph* graph, int v, LGraph_Printf* pFunc)
{//借助队列实现
TLGraph* tGraph = (TLGraph*)graph;
int* visited = NULL;
int condition = (tGraph != NULL);
condition = condition && (0 <= v) && (v < tGraph->count);
condition = condition && (pFunc != NULL);
condition = condition && ((visited = (int*)calloc(tGraph->count, sizeof(int))) != NULL);
if( condition )
{
int i = 0;
bfs(tGraph, v, visited, pFunc);
for(i=0; i<tGraph->count; i++)
{
if( !visited[i] )
{
bfs(tGraph, i, visited, pFunc);
}
}
printf("\n");
}
free(visited);
}
void LGraph_Display(LGraph* graph, LGraph_Printf* pFunc) // O(n*n*n)
{
TLGraph* tGraph = (TLGraph*)graph;
if( (tGraph != NULL) && (pFunc != NULL) )
{
int i = 0;
int j = 0;
for(i=0; i<tGraph->count; i++)
{
printf("%d:", i);
pFunc(tGraph->v[i]);
printf(" ");
}
printf("\n");
for(i=0; i<tGraph->count; i++)
{
for(j=0; j<LinkList_Length(tGraph->la[i]); j++)
{
TListNode* node = (TListNode*)LinkList_Get(tGraph->la[i], j);
printf("<");
pFunc(tGraph->v[i]);
printf(", ");
pFunc(tGraph->v[node->v]);
printf(", %d", node->w);
printf(">");
printf(" ");
}
}
printf("\n");
}
}
</span></strong><strong><span style="font-size:18px;">#ifndef _LGRAPH_H_ #define _LGRAPH_H_ typedef void LGraph; typedef void LVertex; typedef void (LGraph_Printf)(LVertex*); LGraph* LGraph_Create(LVertex** v, int n); void LGraph_Destroy(LGraph* graph); void LGraph_Clear(LGraph* graph); int LGraph_AddEdge(LGraph* graph, int v1, int v2, int w); int LGraph_RemoveEdge(LGraph* graph, int v1, int v2); int LGraph_GetEdge(LGraph* graph, int v1, int v2); int LGraph_TD(LGraph* graph, int v); int LGraph_VertexCount(LGraph* graph); int LGraph_EdgeCount(LGraph* graph); void LGraph_DFS(LGraph* graph, int v, LGraph_Printf* pFunc); void LGraph_BFS(LGraph* graph, int v, LGraph_Printf* pFunc); void LGraph_Display(LGraph* graph, LGraph_Printf* pFunc); #endif</span></strong>
<strong><span style="font-size:18px;">#include <stdio.h>
#include <stdlib.h>
#include "LGraph.h"
/* run this program using the console pauser or add your own getch, system("pause") or input loop */
void print_data(LVertex* v)
{
printf("%s", (char*)v);
}
int main(int argc, char *argv[])
{
LVertex* v[] = {"A", "B", "C", "D", "E", "F"};
LGraph* graph = LGraph_Create(v, 6);
LGraph_AddEdge(graph, 0, 1, 1);
LGraph_AddEdge(graph, 0, 2, 1);
LGraph_AddEdge(graph, 0, 3, 1);
LGraph_AddEdge(graph, 1, 5, 1);
LGraph_AddEdge(graph, 1, 4, 1);
LGraph_AddEdge(graph, 2, 1, 1);
LGraph_AddEdge(graph, 3, 4, 1);
LGraph_AddEdge(graph, 4, 2, 1);
LGraph_Display(graph, print_data);
LGraph_DFS(graph, 0, print_data);
LGraph_BFS(graph, 0, print_data);
LGraph_Destroy(graph);
return 0;
}</span></strong>邻接矩阵法实现在上面图的存储结构代码
小结
广度优先遍历与深度优先遍历是图结构的基础算法，也是其他图算法的基础。
思考：
借助栈数据结构
最小连通网
运营商的挑战
备选方案
Prim算法
代码
Prim.c
<strong><span style="font-size:18px;">#include <stdio.h>
#include <stdlib.h>
/* run this program using the console pauser or add your own getch, system("pause") or input loop */
#define VNUM 9
#define MV 65536
int P[VNUM];//结点
int Cost[VNUM];//边的耗费
int Mark[VNUM];
int Matrix[VNUM][VNUM] =
{
{0, 10, MV, MV, MV, 11, MV, MV, MV},
{10, 0, 18, MV, MV, MV, 16, MV, 12},
{MV, 18, 0, 22, MV, MV, MV, MV, 8},
{MV, MV, 22, 0, 20, MV, MV, 16, 21},
{MV, MV, MV, 20, 0, 26, MV, 7, MV},
{11, MV, MV, MV, 26, 0, 17, MV, MV},
{MV, 16, MV, MV, MV, 17, 0, 19, MV},
{MV, MV, MV, 16, 7, MV, 19, 0, MV},
{MV, 12, 8, 21, MV, MV, MV, MV, 0},
};
void Prim(int sv) // O(n*n)
{
int i = 0;
int j = 0;
if( (0 <= sv) && (sv < VNUM) )
{
for(i=0; i<VNUM; i++)
{
Cost[i] = Matrix[sv][i];
P[i] = sv;
Mark[i] = 0;
}
Mark[sv] = 1;
for(i=0; i<VNUM; i++)
{
int min = MV;
int index = -1;
for(j=0; j<VNUM; j++)
{
if( !Mark[j] && (Cost[j] < min) )
{
min = Cost[j];
index = j;
}
}
if( index > -1 )
{
Mark[index] = 1;
printf("(%d, %d, %d)\n", P[index], index, Cost[index]);
}
for(j=0; j<VNUM; j++)
{//以index为结点查找最小权值
if( !Mark[j] && (Matrix[index][j] < Cost[j]) )
{
Cost[j] = Matrix[index][j];
P[j] = index;
}
}
}
}
}
int main(int argc, char *argv[])
{
Prim(0);
return 0;
}</span></strong>Kruskal算法
小结
最短路径
解决步骤描述
算法精髓
代码 类似Prim
Dijkstra.c
<strong><span style="font-size:18px;">#include <stdio.h>
#include <stdlib.h>
/* run this program using the console pauser or add your own getch, system("pause") or input loop */
#define VNUM 5
#define MV 65536
int P[VNUM];
int Dist[VNUM];
int Mark[VNUM];
int Matrix[VNUM][VNUM] =
{
{0, 10, MV, 30, 100},
{MV, 0, 50, MV, MV},
{MV, MV, 0, MV, 10},
{MV, MV, 20, 0, 60},
{MV, MV, MV, MV, 0},
};
void Dijkstra(int sv) // O(n*n)
{
int i = 0;
int j = 0;
if( (0 <= sv) && (sv < VNUM) )
{
for(i=0; i<VNUM; i++)
{
Dist[i] = Matrix[sv][i];
P[i] = sv;
Mark[i] = 0;
}
Mark[sv] = 1;
for(i=0; i<VNUM; i++)
{
int min = MV;
int index = -1;
for(j=0; j<VNUM; j++)
{
if( !Mark[j] && (Dist[j] < min) )
{
min = Dist[j];
index = j;
}
}
if( index > -1 )
{
Mark[index] = 1;
}
for(j=0; j<VNUM; j++)
{
if( !Mark[j] && (min + Matrix[index][j] < Dist[j]) )
{
Dist[j] = min + Matrix[index][j];
P[j] = index;
}
}
}
for(i=0; i<VNUM; i++)
{
int p = i;
printf("%d -> %d: %d\n", sv, p, Dist[p]);
do
{
printf("%d <- ", p);
p = P[p];
} while( p != sv );
printf("%d\n", p);
}
}
}
int main(int argc, char *argv[])
{
Dijkstra(0);
return 0;
}
</span></strong>
A矩阵的意义
代码
Floyd.c
#include <stdio.h>
#include <stdlib.h>
/* run this program using the console pauser or add your own getch, system("pause") or input loop */
#define VNUM 5
#define MV 65536
int P[VNUM][VNUM];
int A[VNUM][VNUM];
int Matrix[VNUM][VNUM] =
{
{0, 10, MV, 30, 100},
{MV, 0, 50, MV, MV},
{MV, MV, 0, MV, 10},
{MV, MV, 20, 0, 60},
{MV, MV, MV, MV, 0},
};
void Floyd() // O(n*n*n)
{
int i = 0;
int j = 0;
int k = 0;
for(i=0; i<VNUM; i++)
{
for(j=0; j<VNUM; j++)
{
A[i][j] = Matrix[i][j];
P[i][j] = j;
//保存正序的第二个顶点
}
}
for(i=0; i<VNUM; i++)
{
for(j=0; j<VNUM; j++)
{
for(k=0; k<VNUM; k++)
{
if( (A[j][i] + A[i][k]) < A[j][k] )
{
A[j][k] = A[j][i] + A[i][k];
P[j][k] = P[j][i];
//通过中转
}
}
}
}
for(i=0; i<VNUM; i++)
{
for(j=0; j<VNUM; j++)
{
int p = -1;
printf("%d -> %d: %d\n", i, j, A[i][j]);
printf("%d", i);
p = i;
do
{
p = P[p][j];
printf(" -> %d", p);
} while( p != j);
printf("\n");
}
}
}
int main(int argc, char *argv[])
{
Floyd();
return 0;
}
小结
思考：
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