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public/c/ch6/tsp/huisu/travelroute.c

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+#include <stdio.h>
+#include <limits.h>
+#define MAX_CITIES 4  // 城市数量
+#define INF INT_MAX
+int n = MAX_CITIES;  // 城市数量
+int dist[MAX_CITIES][MAX_CITIES] = {
+    {0, 30, 6, 4},   {30, 0, 5, 10},  
+    {6, 5, 0, 20},  {4, 10, 20, 0} 
+};
+int visited[MAX_CITIES];  // 标记城市是否访问
+int bestPath[MAX_CITIES];  // 最优路径
+int bestCost = INF;  // 最优路径的总成本
+// 回溯法求解TSP
+void backtrack(int currentCity, int count, int cost, int path[]) {
+    if (count == n) { // 所有城市都已访问，检查是否是最优解 
+        cost += dist[currentCity][0];  // 加上返回起点的距离
+        if (cost < bestCost) {
+            bestCost = cost;
+            for (int i = 0; i < n; i++) 
+                bestPath[i] = path[i]; 
+        }
+        return;
+    } 
+    for (int i = 0; i < n; i++) {// 尝试所有未访问的城市
+        if (!visited[i]) { // 访问城市i 
+            visited[i] = 1; path[count] = i; 
+            // 递归访问下一个城市
+            backtrack(i, count + 1, cost + dist[currentCity][i], path); 
+            visited[i] = 0; // 回溯
+        }
+    }
+}
+int main() {
+    int path[MAX_CITIES];
+    visited[0] = 1;  // 从第一个城市出发
+    path[0] = 0;     // 起点是城市0
+    backtrack(0, 1, 0, path);  // 从城市0开始回溯  
+    printf("\n最优路径是: ");
+    for (int i = 0; i < n; i++) 
+        printf("%d ", bestPath[i]); 
+    printf("\n最小路程: %d\n", bestCost); 
+    return 0;
+}