180 lines
4.1 KiB
C++
180 lines
4.1 KiB
C++
#include <stdio.h>
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#include <stdlib.h>
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#include <stdbool.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 path[MAX_V+1][MAX_V+1]; // 追蹤路徑的矩陣
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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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bool floydWarshall();
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void output_path();
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void output_step();
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void print_path(int start, int end);
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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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printf("\n警告：圖形中存在負權迴路，計算結果可能不正確！\n");
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output_path();
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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, line_count = 0;
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char line[256];
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fptr = fopen("shortestPath_matrix.dat", "r");
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if (fptr == NULL) {
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perror("shortestPath_matrix.dat");
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exit(1);
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}
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// 計算總頂點數
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while (fgets(line, sizeof(line), fptr)) {
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line_count++;
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}
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N = line_count;
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rewind(fptr);
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// 初始化距離矩陣與路徑矩陣
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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;
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path[i][j] = i;
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} else {
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dist[i][j] = Infinite;
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path[i][j] = -1;
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}
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}
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}
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// 讀取完整矩陣
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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 (fscanf(fptr, "%d", &weight) == 1) {
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if (weight != 0 && i != j) { // 只處理非零且非對角線的權重
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dist[i][j] = weight;
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path[i][j] = i;
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}
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}
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}
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}
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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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bool floydWarshall(){
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int k, i, j;
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bool has_negative_cycle = false;
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long int temp_dist[MAX_V+1][MAX_V+1];
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// 主要的 Floyd-Warshall 演算法
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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 (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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path[i][j] = path[k][j];
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}
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}
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}
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}
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// 複製目前的距離矩陣
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for (i = 1; i <= N; i++) {
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for (j = 1; j <= N; j++) {
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temp_dist[i][j] = dist[i][j];
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}
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}
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// 再執行一次迭代來檢查負權迴路
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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 (dist[i][k] != Infinite &&
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dist[k][j] != Infinite &&
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dist[i][k] + dist[k][j] < temp_dist[i][j]) {
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has_negative_cycle = true;
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goto end_check; // 找到負權迴路後直接跳出
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}
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}
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}
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}
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end_check:
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return has_negative_cycle;
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}
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void print_path(int start, int end) {
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if (start == end) {
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printf("頂點%d", start);
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return;
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}
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if (path[start][end] == -1) {
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printf("無路徑");
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return;
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}
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print_path(start, path[start][end]);
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printf(" → %d", end);
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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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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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printf("\n節點間最短距離矩陣：\n");
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output_step();
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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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printf("最短路徑：");
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print_path(source, sink);
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printf("\n");
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}
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}
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