174 lines
3.8 KiB
C
174 lines
3.8 KiB
C
/* file name: shortestPath.c */
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/* 利用 Dijkstra 演算法求最短路徑 */
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#include <stdio.h>
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#include <stdlib.h>
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#define MAX_V 100 /*最大節點數*/
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#define VISITED 1
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#define NOTVISITED 0
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#define Infinite 1073741823
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/* A[1..N][1..N] 為圖形的相鄰矩陣 */
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/* D[i] i=1..N 用來儲存某起始頂點到i節點的最短距離 */
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/* S[1..N] 用來記錄頂點是否已經拜訪過 */
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/* P[1..N] 用來記錄最近經過的中間節點 */
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long int A[MAX_V+1][MAX_V+1];
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long int D[MAX_V+1];
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long int S[MAX_V+1], P[MAX_V+1];
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int source , sink , N;
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int step = 1;
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int top = -1; /*堆疊指標*/
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int Stack[MAX_V+1]; /*堆疊空間*/
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void init(void);
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int minD(void);
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void output_step(void);
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void output_path(void);
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void push(int);
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int pop(void);
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int main(){
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int t,I;
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init();
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output_step();
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printf("\n");
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for (step =2;step <=N; step++) {
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/* minD 傳回一值t使得D[t] 為最小 */
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t = minD();
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S[t] = VISITED;
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/* 找出經過t點會使路徑縮短的節點*/
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for (I=1; I <= N; I++)
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if ((S[I] == NOTVISITED) && (D[t]+A[t][I] <= D[I])) {
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D[I] = D[t] + A[t][I];
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P[I] = t;
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}
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output_step();
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printf("\n");
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}
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output_path();
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return 0;
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}
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void init(){
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FILE *fptr;
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int i,j;
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int weight;
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fptr = fopen("shortestPath1.dat","r");
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if (fptr == NULL) {
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perror("shortestPath.dat");
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exit(1);
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}
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fscanf(fptr, "%d", &N); /*讀取圖形節點數*/
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for (i=1; i<=N; i++ )
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for (j=1; j<=N; j++)
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A[i][j] = Infinite; /*起始A[1..N][1..N]相鄰矩陣*/
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while (fscanf(fptr,"%d %d %d", &i, &j, &weight) != EOF)
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A[i][j] = weight; /*讀取i節點到j節點的權weight */
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fclose(fptr);
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printf("Enter source node : ");
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scanf("%d", &source);
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printf("Enter sink node : ");
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scanf("%d", &sink);
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/* 起始各陣列初值*/
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for (i = 1; i <= N; i++) {
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S[i] = NOTVISITED; /*各頂點設為尚未拜訪*/
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D[i] = A[source][i]; /*記錄起始頂點至各頂點最短距離*/
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P[i] = source;
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}
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S[source] = VISITED; /*始起節點設為已經走訪*/
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D[source] = 0;
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}
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int minD(){
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int i,t;
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long int minimum = Infinite;
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for (i=1; i<=N; i++)
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if ((S[i] == NOTVISITED) && D[i] < minimum) {
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minimum = D[i];
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t = i;
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}
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return t;
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}
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/* 顯示目前的D陣列與P陣列狀況 */
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void output_step(){
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int i;
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printf("\n Step #%d",step);
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printf("\n================================================\n");
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for (i=1; i<=N; i++)
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printf(" D[%d]", i);
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printf("\n");
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for (i=1; i<=N; i++)
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if (D[i] == Infinite)
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printf(" ----");
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else
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printf("%6ld",D[i]);
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printf("\n================================================\n");
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for (i=1; i<=N; i++)
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printf(" P[%d]", i);
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printf("\n");
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for (i=1; i<=N;i++)
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printf("%6ld", P[i]);
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}
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/*顯示最短路徑*/
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void output_path(){
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int node = sink;
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/*判斷是否起始頂點等於終點或無路徑至終點*/
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if ((sink == source) || (D[sink] == Infinite)) {
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printf("\nNode %d has no Path to Node %d", source, sink);
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return;
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}
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printf("\n");
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printf(" The shortest Path from V%d to V%d :", source, sink);
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printf("\n------------------------------------------\n");
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/*由終點開始將上一次經過的中間節點推入堆疊至到起始節點*/
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printf(" V%d", source);
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while (node != source) {
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push(node);
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node = P[node];
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}
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while(node != sink) {
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node = pop();
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printf(" --%ld-->",A[P[node]][node]);
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printf("V%d", node);
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}
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printf("\n Total length : %ld\n", D[sink]);
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}
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void push(int value){
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if (top >= MAX_V) {
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printf("Stack overflow!\n");
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exit(1);
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}
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else
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Stack[++top] = value;
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}
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int pop(){
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if (top < 0) {
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printf("Stack empty!\n");
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exit(1);
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}
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return Stack[top--];
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}
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