131 lines
2.9 KiB
C
131 lines
2.9 KiB
C
/*
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Program: all-pairs-shortest-path-v2.c (Report comments/bugs to chikh@yuntech.edu.tw)
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Function: 修改all-pairs-shortest-path-v1.c使得A與Y矩陣能依圖內的頂點總數作配置，避免
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預先配置過大的100x100陣列空間而形成浪費
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*/
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#include <stdio.h>
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#include <stdlib.h> /* for exit() */
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#define Inf 1073741823 /* 此為2^30-1的大數字，為本程式假設的無限大值；可改用limits.h定義的INT_MAX */
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void init(int ***A, int ***Y) /* 讀取輸入資料檔、設定相鄰矩陣，把相關資料結構作初始化 */
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{
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FILE *fptr;
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int i, j;
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int weight, N;
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if ((fptr=fopen("shortestPath.dat","r")) == NULL) { /* 開啟資料檔 */
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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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*A = (int **)malloc((N+1)*sizeof(int *));
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*Y = (int **)malloc((N+1)*sizeof(int *));
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for (i = 0; i <= N; i++) {
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(*A)[i] = (int *)malloc((N+1)*sizeof(int));
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(*Y)[i] = (int *)malloc((N+1)*sizeof(int));
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}
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(*A)[0][0] = N;
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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] = (i==j)? 0: Inf; /* 初始化A[1..N][1..N]相鄰矩陣，所有元素均先預設為∞ */
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(*Y)[i][j] = (i==j)? i: -1;
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}
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while (fscanf(fptr,"%d %d %d",&i,&j,&weight) != EOF) {
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(*A)[i][j] = weight; /* 讀取連接頂點i與j的邊的權重值 */
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(*Y)[i][j] = i;
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}
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fclose(fptr);
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}
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void floydWarshall(int ***A, int ***Y)
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{
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int i, j, k;
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int N = (*A)[0][0]; //無法使用sizeof(A[0])/sizeof(A[0][0])判讀維度，因以malloc()配置所得記憶體空間不具結構
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for (k = 1; k <= N; k++)
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for (i = 1; i <= N; i++)
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for (j = 1; j <= N; j++)
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if ((*A)[i][k] + (*A)[k][j] < (*A)[i][j]) {
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(*A)[i][j] = (*A)[i][k] + (*A)[k][j];
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(*Y)[i][j] = (*Y)[k][j];
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}
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//上面二層for迴圈用於檢視/修正每二頂點(i,j)之間有否經由k(中繼頂點)能得更小距離值
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}
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void printMatrix(int **A)
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{
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int i, j;
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int N = A[0][0];
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for (i = 1; i <= N; i++) {
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for (j = 1; j <= N; j++) {
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if (A[i][j] == Inf)
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printf("%5s","∞");
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else
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printf("%4d",A[i][j]);
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}
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printf("\n");
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}
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}
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void backtrack(int **Y, int source, int dest)
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{
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int k = Y[source][dest];
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if (source == dest) {
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printf("頂點%d →",source);
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return;
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}
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if (Y[source][dest] == -1) {
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printf("頂點%d與%d之間沒有路徑存在 ",source,dest);
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return;
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}
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backtrack(Y,source,k);
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printf(" %d →",dest);
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}
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void traverseMatrix(int **Y)
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{
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int i, j, k, source, sink;
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printf("\n源點 => ");
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scanf("%d",&source);
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printf("終點 => ");
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scanf("%d",&sink);
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printf("最短路徑：");
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backtrack(Y,source,sink);
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printf("\b\b ");
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}
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void freeMemory(int **A, int **Y)
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{
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int i, N = A[0][0];
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for (i = 0; i <= N; i++) {
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free(A[i]);
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free(Y[i]);
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}
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free(A);
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free(Y);
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}
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int main() {
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int **A, **Y;
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init(&A,&Y); /* 讀取輸入資料檔、設定相鄰矩陣，並把相關資料結構作初始化 */
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floydWarshall(&A,&Y);
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printMatrix(A);
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traverseMatrix(Y);
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freeMemory(A,Y);
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return 0;
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}
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