140 lines
3.2 KiB
C
140 lines
3.2 KiB
C
#include <stdio.h>
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#include <stdlib.h>
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#include <stdbool.h>
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#ifdef _WIN32
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#include <windows.h>
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#endif
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// 邻接矩阵存储图
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typedef struct
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{
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int vexnum;
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int **arcs;
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} AMGraphStruct;
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typedef AMGraphStruct *AMGraph;
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// 定义最大顶点数和最大边权值
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#define MaxInt 99999 // 最大边权值，用于初始化距离数组
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#define MAXN 1005 // 最大顶点数
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static bool S[MAXN]; // S[i]为true表示顶点i已加入集合S，否则未加入
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static int D[MAXN]; // D[i]为v0到顶点i的当前最短路径长度
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static int Path[MAXN]; // Path[i]为v0到顶点i的最短路径上的前驱顶点
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// Dijkstra算法求最短路径
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void ShortestPath_DIJ(AMGraph G, int v0)
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{
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// 初始化
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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
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int min;
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n = G->vexnum;
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for (v = 0; v < n; ++v)
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{
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S[v] = false;
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D[v] = G->arcs[v0][v];
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if (D[v] < MaxInt)
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{
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Path[v] = v0;
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}
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else
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{
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Path[v] = -1;
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}
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}
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S[v0] = true;
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D[v0] = 0;
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// 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
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for (i = 1; i < n; ++i)
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{
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// 在V-S中选择距离v0最近的顶点u
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min = MaxInt;
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for (w = 0; w < n; ++w)
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{
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if (!S[w] && D[w] < min)
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{
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v = w;
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min = D[w];
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}
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}
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S[v] = true;
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// 修改当前最短路径及距离
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for (w = 0; w < n; ++w)
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{
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if (!S[w] && (D[v] + G->arcs[v][w] < D[w]))
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{
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D[w] = D[v] + G->arcs[v][w];
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Path[w] = v;
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}
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}
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}
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}
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int main(void)
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{
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#ifdef _WIN32
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system("chcp 65001 > nul");
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SetConsoleOutputCP(65001);
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SetConsoleCP(65001);
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#endif
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// 输入顶点数和边数
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printf("请输入顶点数n和边数m：");
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int n, m;
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if (scanf("%d %d", &n, &m) != 2)
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{
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return 0;
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}
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// 初始化邻接矩阵
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AMGraph g = (AMGraph)malloc(sizeof(*g));
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g->vexnum = n;
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g->arcs = (int **)malloc((size_t)n * sizeof(int *));
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for (int i = 0; i < n; ++i)
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{
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g->arcs[i] = (int *)malloc((size_t)n * sizeof(int));
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for (int j = 0; j < n; ++j)
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{
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g->arcs[i][j] = (i == j) ? 0 : MaxInt;
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}
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}
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// 输入边信息
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for (int i = 0; i < m; ++i)
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{
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printf("请输入第%d条边的顶点x、y和边权z：", i + 1);
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int x, y, z;
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if (scanf("%d %d %d", &x, &y, &z) != 3)
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{
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return 0;
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}
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if (x >= 1 && x <= n && y >= 1 && y <= n)
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{
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if (z < g->arcs[x - 1][y - 1])
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{
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g->arcs[x - 1][y - 1] = z;
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}
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}
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}
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// 调用Dijkstra算法
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ShortestPath_DIJ(g, 0);
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if (D[n - 1] >= MaxInt)
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{
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printf("从顶点0到顶点%d不存在路径\n", n - 1);
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}
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else
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{
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printf("从顶点0到顶点%d的最短路径长度为：%d\n", n - 1, D[n - 1]);
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}
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// 释放内存
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for (int i = 0; i < n; ++i)
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{
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free(g->arcs[i]);
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}
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free(g->arcs);
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free(g);
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return 0;
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} |