更新Dijkstra算法求最短路径

.vscode/settings.json

@@ -4,7 +4,7 @@
   "C_Cpp_Runner.debuggerPath": "gdb",
   "C_Cpp_Runner.cStandard": "c17",
   "C_Cpp_Runner.cppStandard": "c++17",
-  "C_Cpp_Runner.msvcBatchPath": "C:/Program Files/Microsoft Visual Studio/VR_NR/Community/VC/Auxiliary/Build/vcvarsall.bat",
+  "C_Cpp_Runner.msvcBatchPath": "",
   "C_Cpp_Runner.useMsvc": false,
   "C_Cpp_Runner.warnings": [
     "-Wall",

exercise/44.c

@@ -1,11 +1,81 @@
 #include <stdio.h>
 #include <stdlib.h>
+#include <stdbool.h>
 #ifdef _WIN32
 #include <windows.h>
 #endif
 
+// 邻接矩阵存储图
+typedef struct
+{
+    int vexnum;
+    int **arcs;
+} AMGraphStruct;
+typedef AMGraphStruct *AMGraph;
+
+// 定义最大顶点数和最大边权值
+#define MaxInt 0x3f3f3f3f
+#define MAXN 1005      // 最大顶点数
+static bool S[MAXN];   // S[i]为true表示顶点i已加入集合S，否则未加入
+static int D[MAXN];    // D[i]为v0到顶点i的当前最短路径长度
+static int Path[MAXN]; // Path[i]为v0到顶点i的最短路径上的前驱顶点
+
+// Dijkstra算法求最短路径
+void ShortestPath_DIJ(AMGraph G, int v0)
+{
+    // 初始化
+    int n, i, v, w; // n为顶点数，i为循环变量，v为当前顶点，w为邻接顶点
+    int min;
+    n = G->vexnum;
+    for (v = 0; v < n; ++v)
+    {
+        S[v] = false;
+        D[v] = G->arcs[v0][v];
+        if (D[v] < MaxInt)
+        {
+            Path[v] = v0;
+        }
+        else
+        {
+            Path[v] = -1;
+        }
+    }
+    S[v0] = true;
+    D[v0] = 0;
+
+    // 主循环，每次求得v0到某个顶点的最短路径，并将该顶点加入集合S
+    for (i = 1; i < n; ++i)
+    {
+        // 在V-S中选择距离v0最近的顶点u
+        min = MaxInt;
+        for (w = 0; w < n; ++w)
+        {
+            if (!S[w] && D[w] < min)
+            {
+                v = w;
+                min = D[w];
+            }
+        }
+
+        // 如果min为MaxInt，说明v0到其他顶点的路径都不可达
+        if (min == MaxInt)
+        {
+            break;
+        }
+        S[v] = true;
+
+        // 修改当前最短路径及距离
+        for (w = 0; w < n; ++w)
+        {
+            if (!S[w] && (D[v] + G->arcs[v][w] < D[w]))
+            {
+                D[w] = D[v] + G->arcs[v][w];
+                Path[w] = v;
+            }
+        }
+    }
+}
 
-// Dijkstra
 int main(void)
 {
 #ifdef _WIN32
@@ -14,6 +84,75 @@ int main(void)
     SetConsoleCP(65001);
 #endif
 
+    // 输入顶点数和边数
+    int n, m;
+    if (scanf("%d %d", &n, &m) != 2)
+    {
+        return 0;
+    }
+    if (n < 1 || n > MAXN || m < 0)
+    {
+        printf("参数不符合要求\n");
+        return 0;
+    }
+    
+    // 初始化邻接矩阵
+    AMGraph g = (AMGraph)malloc(sizeof(*g));
+    g->vexnum = n;
+    g->arcs = (int **)malloc((size_t)n * sizeof(int *));
+    for (int i = 0; i < n; ++i)
+    {
+        g->arcs[i] = (int *)malloc((size_t)n * sizeof(int));
+        for (int j = 0; j < n; ++j)
+        {
+            g->arcs[i][j] = (i == j) ? 0 : MaxInt;
+        }
+    }
+
+    // 输入边信息
+    for (int i = 0; i < m; ++i)
+    {
+        int x, y, z;
+        if (scanf("%d %d %d", &x, &y, &z) != 3)
+        {
+            for (int k = 0; k < n; ++k) free(g->arcs[k]);
+            free(g->arcs);
+            free(g);
+            printf("参数不符合要求\n");
+            return 0;
+        }
+        if (x < 1 || x > n || y < 1 || y > n || z <= 0 || z > 10000)
+        {
+            for (int k = 0; k < n; ++k) free(g->arcs[k]);
+            free(g->arcs);
+            free(g);
+            printf("参数不符合要求\n");
+            return 0;
+        }
+        if (z < g->arcs[x - 1][y - 1])
+        {
+            g->arcs[x - 1][y - 1] = z;
+        }
+    }
+
+    // 执行Dijkstra算法
+    ShortestPath_DIJ(g, 0);
+    if (D[n - 1] >= MaxInt)
+    {
+        printf("-1\n");
+    }
+    else
+    {
+        printf("%d\n", D[n - 1]);
+    }
+
+    // 释放内存
+    for (int i = 0; i < n; ++i)
+    {
+        free(g->arcs[i]);
+    }
+    free(g->arcs);
+    free(g);
     
     return 0;
 }