132 lines
2.7 KiB
C++
132 lines
2.7 KiB
C++
#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 Infinite 1073741823
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long int dist[MAX_V+1][MAX_V+1];
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int N; // 節點數量
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int source, sink; // 起點和終點
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void init();
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int floydWarshall();
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void output_path();
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void output_step();
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int main() {
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init();
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// 檢查是否存在負權迴路
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if (floydWarshall()) {
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output_path();
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printf("\n圖形中存在負權迴路，無法計算最短路徑\n");
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} else {
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output_path();
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}
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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, weight;
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fptr = fopen("shortestPath.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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// 初始化距離矩陣
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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 (i == j)
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dist[i][j] = 0; // 自身到自身的距離為0
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else
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dist[i][j] = Infinite; // 其他預設為無窮大
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}
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}
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// 讀取邊的權重
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while (fscanf(fptr, "%d %d %d", &i, &j, &weight) != EOF)
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dist[i][j] = weight; // 設置直接相連邊的權重
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fclose(fptr);
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printf("檔案內權重如下\n");
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output_step();
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printf("\n輸入起始節點 (1~%d): ", N);
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scanf("%d", &source);
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printf("輸入目標節點 (1~%d): ", N);
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scanf("%d", &sink);
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}
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int floydWarshall(){
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int k, i, j;
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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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// 如果經過 k 點的路徑比直接路徑短，更新距離
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if (dist[i][k] != Infinite &&
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dist[k][j] != Infinite &&
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dist[i][k] + dist[k][j] < dist[i][j]) {
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dist[i][j] = dist[i][k] + dist[k][j];
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}
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}
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}
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}
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// 檢查是否存在負權迴路
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for (i = 1; i <= N; i++) {
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if (dist[i][i] < 0) {
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return 1; // 存在負權迴路
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}
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}
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return 0; // 不存在負權迴路
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}
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void output_step(){
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int i, j;
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printf("\t");
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for (j = 1; j <= N; j++) {
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printf("V%d\t", j);
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}
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printf("\n");
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// 輸出距離矩陣
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for (i = 1; i <= N; i++) {
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printf("V%d\t", i);
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for (j = 1; j <= N; j++) {
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if (dist[i][j] == Infinite)
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printf("∞\t");
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else
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printf("%2ld\t", dist[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 output_path(){
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int i, j;
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// 輸出標題列
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printf("\n節點間最短距離矩陣：\n");
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output_step();
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// 檢查起點到終點的路徑
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if (dist[source][sink] == Infinite) {
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printf("\n節點 V%d 到節點 V%d 沒有路徑\n", source, sink);
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} else {
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printf("\n從節點 V%d 到節點 V%d 的最短距離為：%ld\n",
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source, sink, dist[source][sink]);
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}
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}
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