最短路径

第一步

 状态已知距离上游A已知0AC 邻接1AD邻接6 A E邻接9 A P未知 无穷 

第二步

 状态已知距离上游A已知0AC 已知1AD邻接6 A E邻接9 A P邻接4C

第二步

 状态已知距离上游A已知0AC 已知1AD邻接6 A E邻接7PP已知 4C

第三步

 状态已知距离上游A已知0AC 已知1AD已知6 A E邻接7PP已知 4C

最后，E成为已知。倒退，可以知道路径为E, P, C, A。正过来，就是从A到E的最短路径了。

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注解：不断的把未知变已知，从邻接中选取最小的。如上图中的第二步有两个，一个是P未知变邻接，然后重新看距离，到D的距离是此次的最短距离6（A到P的距离反而为7），更新D为已知点。

#include <stdio.h>#include <stdlib.h>#define NUM_V 5#define INFINITY 10000typedef struct node *position;typedef struct record *label;/* node */struct node {    int element;    position next;    int weight;};/* table element, keep record */struct record {    int status;    int distance;    int previous;};/*  * operations (stereotype) */void insert_edge(position, int, int, int);void print_graph(position, int);int new_neighbors(position, label, int, int);void shortest_path(position, label, int, int, int);/* for testing purpose */void main(){    struct node graph[NUM_V];    struct record records[NUM_V];    int i;    // initialize the vertices    for(i=0; i<NUM_V; i++) {        (graph+i)->element = i;        (graph+i)->next    = NULL;        (graph+i)->weight  = -1;    }    // insert edges    insert_edge(graph,0,1,1);    insert_edge(graph,0,2,6);    insert_edge(graph,0,3,9);    insert_edge(graph,1,4,3);    insert_edge(graph,4,3,3);    print_graph(graph,NUM_V);        // initialize the book    for (i=0; i<NUM_V; i++){        (records+i)->status   = -1;        (records+i)->distance = INFINITY;        (records+i)->previous = -1;    }        shortest_path(graph, records, NUM_V, 0, 3);        // }void shortest_path(position graph, label records, int nv, int start, int end) {    int current;        (records+start)->status   = 1;    (records+start)->distance = 0;    (records+start)->previous = 0;        current = start;    while(current != end) {        current = new_neighbors(graph, records, nv, current);    }        while(current != start) {        printf("%d <- ", current);        current = (records+current)->previous;    }    printf("%d\n", current);}int new_neighbors(position graph, label records, int nv, int current) {    int newDist;    int v;    int i;    int d;        position p;        // update the current known    (records + current)->status = 1;        // UPDATE new neighbors    p = (graph+current)->next;    while(p != NULL) {        v = p->element;        (records + v)->status = 0;        newDist = p->weight + (records + current)->distance;        if ((records + v)->distance > newDist) {            (records + v)->distance = newDist;            (records + v)->previous = current;        }        p = p->next;    }        // find the next known    d = INFINITY;    for (i=0; i<nv; i++) {        if ((records + i)->status==0 && (records + i)->distance < d){            d = (records + i)->distance;            v = i;        }    }    return v;}/* print the graph */void print_graph(position graph, int nv) {    int i;    position p;    for(i=0; i<nv; i++) {        p = (graph + i)->next;        printf("From %3d: ", i);        while(p != NULL) {            printf("%d->%d; w:%d ", i, p->element, p->weight);            p = p->next;        }        printf("\n");    }}/* * insert an edge * with weight */void insert_edge(position graph,int from, int to, int weight){    position np;    position nodeAddr;    np = graph + from;    nodeAddr = (position) malloc(sizeof(struct node));    nodeAddr->element = to;    nodeAddr->next    = np->next;    nodeAddr->weight  = weight;    np->next = nodeAddr;}

参考文章：http://www.cnblogs.com/vamei/p/3604629.html