#include

#include

#define U    65535

#define PARENT(i)    ((i-1)/2)

#define LEFT(i)        (2*(i)+1)

#define RIGHT(i)    (2*(i)+2)

#define N 5

struct vertex {

int key;

struct vtable *adj;

};

struct vtable {

int key;//这个key是在vertex数组的序号

//struct vertext *v;

int w;

struct vtable *next;

};

struct vassist {

int d;

int p;

int key;

};

int insert(struct vertex *,int,int,int,int);

int walk(struct vertex *,int,int);

struct vassist *initialize_ss(int,int);

int relaxd(int *,int ,int ,int);

int relaxb(struct vassist *,int ,int ,int);

int build_min_heap(struct vassist *,int);

int min_heapify(struct vassist *, int ,int);

int heap_extract_min(struct vassist *,int);

int inheap(struct vassist *,int ,int );

int heap_decrease(struct vassist *,int ,int);

int dijkstra(struct vertex *,int,int,int **);

int bellman_ford(struct vertex *,int*, int,int);

int insert(struct vertex *p,int len,int i,int j,int w) {

struct vtable *q,*prev;

q = p[i].adj;

printf("key:%d\n",p[i].key);

prev = NULL;

while(q!=NULL) {

if (q->key == j) {

printf("error: v %d to %d already exist.\n",i,j);

return 0;

}

else {

prev = q;

q=q->next;

}

}

q = (struct vtable*)malloc(sizeof(struct vtable));

q->key = j;

q->w = w;

q->next = NULL;

if(prev!=NULL)

prev->next = q;

else

p[i].adj = q;

return 1;

}

int walk(struct vertex *p,int len,int i) {

struct vtable *q = p[i].adj;

while(q!=NULL) {

printf(" %d,w is %d\n",q->key,q->w);

q=q->next;

}

printf("\n");

}

struct vassist *initialize_ss(int size,int s) {

int i;

struct vassist *va;

va = (struct vassist *)malloc(size*sizeof(struct vassist));

for(i=0;i

va[i].key = i;//建堆后i!=key

va[i].d = U;

va[i].p = -1;

}

va[s].d = 0;

return va;

}

//relax for dijkstra

int relaxd(int *p,int u,int v,int w) {//w=w(u,v)

if(p[v]>p[u]+w) {

p[v] = p[u]+w;

//为了简单处理,p使用的是数组

//没有父母标记

//如果想用父母标记,请将p改为一个自定义的结构体

}

return 1;

}

//relax for beltman_ford

int relaxb(struct vassist *va,int u,int v,int w) {//w=w(u,v)

if(va[v].d>va[u].d+w) {

va[v].d = va[u].d+w;

va[v].p = u;

}

return 1;

}

int bellman_ford(struct vertex *graph,int *h,int size,int s) {//算法要求不含源点可达的负权回路

int i,j;

struct vtable *p;

struct vassist *va;

va = initialize_ss(size,s);

for(i=1;i

for(j=0;j

p = graph[j].adj;

while(p!=NULL) {

relaxb(va,j,p->key,p->w);

p=p->next;

}

}

printf("from %d,\n",s);

for(j=0;j

printf("to %d: %d\n",j,va[j].d);

for(j=0;j

p = graph[j].adj;

while(p!=NULL) {

if(va[p->key].d>va[j].d+p->w)

return 0;

p = p->next;

}

}

for(j=1;j<=size;j++)

h[j] = va[j].d;

free(va);

h[0] = 0;

return 1;

}

int build_min_heap(struct vassist *va,int size) {//建堆

int i;

for (i =size/2-1; i>=0; i--)

min_heapify(va,i,size);

return 1;

}

int min_heapify(struct vassist *va, int i,int heap_size) {

int l,r,min;

struct vassist temp;

int tmin = U;

l = LEFT(i);

r = RIGHT(i);

if ((l < heap_size) &&(va[l].d

min = l;

tmin = va[l].d;

}

else {

min = i;

tmin = va[i].d;

}

if ((r < heap_size) &&(va[r].d

min = r;

tmin = va[r].d;

}

if (!(min == i)) {

temp.d = va[min].d;

temp.p = va[min].p;

temp.key = va[min].key;

va[min].d = va[i].d;

va[min].p = va[i].p;

va[min].key = va[i].key;

va[i].d = temp.d;

va[i].p = temp.p;

va[i].key = temp.key;

min_heapify(va,min,heap_size);

}

return 1;

}

int heap_extract_min(struct vassist *va,int heap_size) {

int min;

if ( heap_size<1 )

return -1;

min = va[0].key;

va[0].p = va[heap_size -1].p;

va[0].d = va[heap_size -1].d;

va[0].key = va[heap_size -1].key;

heap_size = heap_size -1;

min_heapify(va,0,heap_size);

return min;

}

int inheap(struct vassist *va,int heap_size,int j) {

int i;

for(i=0;i

if(va[i].key == j)

return i;

return -1;

}

int heap_decrease(struct vassist *va,int i,int key_new) {

struct vassist temp;

if(key_new>va[i].d)

return 0;

va[i].d = key_new;

while((i>0)&&(va[PARENT(i)].d > va[i].d)) {

temp.d = va[i].d;

temp.p = va[i].p;

temp.key = va[i].key;

va[i].d = va[PARENT(i)].d;

va[i].p = va[PARENT(i)].p;

va[i].key = va[PARENT(i)].key;

va[PARENT(i)].d = temp.d;

va[PARENT(i)].p = temp.p;

va[PARENT(i)].key = temp.key;

i = PARENT(i);

}

return 1;

}

int dijkstra(struct vertex *graph,int len,int s,int **delta) {

int i,j,heap_size;

struct vtable *q;

struct vassist *va;

int *p;

p = (int *)malloc(len * sizeof(int));

for(i=0;i

p[i] = U;

p[s] = 0;

heap_size = len;

va = initialize_ss(len,s);

build_min_heap(va,heap_size);//va被拿去建堆,后续输出距离时不能再用了

while(heap_size>0) {

i = heap_extract_min(va,heap_size);

printf("node:%d\n",i);

heap_size--;

for(j=0;j

printf("key:%d,d:%d, in array:%d\n",va[j].key,va[j].d,p[va[j].key]);

q = graph[i].adj;

while(q!=NULL) {

j=inheap(va,heap_size,q->key);

if(j>=0)

if(va[j].d>p[i]+q->w)

heap_decrease(va,j,p[i]+q->w);

relaxd(p,i,q->key,q->w);//其实可以合并heap_decreas和relax,不过为了接口简单没有这样做

printf("relax %d to %d ,w is %d\n",i,q->key,q->w);

q = q->next;

}

for(j=0;j

printf("key:%d,d:%d, in array:%d\n",va[j].key,va[j].d,p[va[j].key]);

}

for(i=0;i

printf("from %d to %d, distance is %d\n",s,i,p[i]);

free(va);

for(i=0;i

delta[s][i] = p[i];

}

free(p);

}

int **johnson(struct vertex *g, int n) {

int i,j;

int *h,**delta,**d;

struct vertex *gn;

struct vtable *p;

gn = (struct vertex *)malloc(n*sizeof(struct vertex));

h = (int *)malloc(n*sizeof(int));

delta = (int**)malloc(n*sizeof(int *));

d = (int**)malloc(n*sizeof(int *));

for(i=0;i

delta[i]=(int*)malloc(n*sizeof(int));

d[i]=(int*)malloc(n*sizeof(int));

}

for(i=0;i

gn[i] = g[i];

for(i=1;i

insert(gn,n,0,i,0);

if(!bellman_ford(gn,h,n,0)) {

printf("the input graph contains a negative-weight cycle.\n");

return NULL;

}

for(i=0;i

p = gn[i].adj;

while(p!=NULL) {

p->w = p->w+h[i]-h[p->key];

p=p->next;

}

}

for(i=0;i

walk(gn,n,i);

printf("before dijkstra\n");

for(i=1;i

dijkstra(gn,n,i,delta);

for(j=1;j

d[i][j] = delta[i][j] + h[j] - h[i];

}

for(i=1;i

for(j=1;j

printf("%d\t",d[i][j]);

printf("\n");

}

return d;

}

int main(){

int i,j;

int **d;

struct vertex vt[N+1];//为0结点的加入预留位置

for(i=0;i

vt[i].adj = NULL;

vt[i].key = i;

}

insert(vt,N+1,1,2,3);

insert(vt,N+1,1,3,8);

insert(vt,N+1,1,5,-4);

insert(vt,N+1,2,4,1);

insert(vt,N+1,2,5,7);

insert(vt,N+1,3,2,4);

insert(vt,N+1,4,3,-5);

insert(vt,N+1,4,1,2);

insert(vt,N+1,5,4,6);

d = johnson(vt,N+1);

return 1;

}