Dijkstra算法簡單實現（C++）

時間 2020-06-02

標籤 dijkstra 算法簡單實現 c++ 欄目 C&C++ 简体版

原文原文鏈接

圖的最短路徑問題主要包括三種算法：

（1）Dijkstra (沒有負權邊的單源最短路徑）html

（2）Floyed (多源最短路徑)ios

（3）Bellman (含有負權邊的單源最短路徑）算法

本文主要講使用C++實現簡單的Dijkstra算法數據結構

Dijkstra算法簡單實現（C++）

 1 #include<iostream>
 2 #include<stack>
 3 using namespace std;  4 
 5 #define MAXVEX 9
 6 #define INFINITY 65535
 7 
 8 typedef int Patharc[MAXVEX];  9 typedef int ShortPathTable[MAXVEX];  10 
 11 typedef struct {  12     int vex[MAXVEX];  13     int arc[MAXVEX][MAXVEX];  14     int numVertexes;  15 } MGraph;  16 
 17 // 構建圖
 18 void CreateMGraph(MGraph *G){  19     int i, j, k;  20     // 初始化圖
 21     G->numVertexes = 9;  22     for(i = 0; i < G->numVertexes; ++i){  23         G->vex[i] = i;  24  }  25     for(i = 0; i < G->numVertexes; ++i){  26         for(j = 0; j < G->numVertexes; ++j){  27             if(i == j)  28                 G->arc[i][j] = 0;  29             else
 30                 G->arc[i][j] = G->arc[j][i] = INFINITY;  31  }  32  }  33 
 34     G->arc[0][1] = 1;  35     G->arc[0][2] = 5;  36 
 37     G->arc[1][2] = 3;  38     G->arc[1][3] = 7;  39     G->arc[1][4] = 5;  40 
 41     G->arc[2][4] = 1;  42     G->arc[2][5] = 7;  43 
 44     G->arc[3][4] = 2;  45     G->arc[3][6] = 3;  46 
 47     G->arc[4][5] = 3;  48     G->arc[4][6] = 6;  49     G->arc[4][7] = 9;  50 
 51     G->arc[5][7] = 5;  52 
 53     G->arc[6][7] = 2;  54     G->arc[6][8] = 7;  55 
 56     G->arc[7][8] = 4;  57 
 58     // 設置對稱位置元素值
 59     for(i = 0; i < G->numVertexes; ++i){  60         for(j = i; j < G->numVertexes; ++j){  61             G->arc[j][i] = G->arc[i][j];  62  }  63  }  64 }  65 
 66 void ShortPath_Dijkstra(MGraph G, int v0, Patharc P, ShortPathTable D){  67     int final[MAXVEX];  68     int i;  69     for(i = 0; i < G.numVertexes; ++i){  70         final[i] = 0;  71         D[i] = G.arc[v0][i];  72         P[i] = 0;  73  }  74     D[v0] = 0;  75     final[v0] = 1;  76     for(i = 0; i < G.numVertexes; ++i){  77         int min = INFINITY;  78         int j, k, w;  79 
 80         for(j = 0; j < G.numVertexes; ++j){// 查找距離V0最近的頂點
 81             if(!final[j] && D[j] < min){  82                 k = j;  83                 min = D[j];  84  }  85  }  86         final[k] = 1;  87         for(w = 0; w < G.numVertexes; ++w){// 更新各個頂點的距離
 88             if(!final[w] && (min + G.arc[k][w]) < D[w]){  89                 D[w] = min + G.arc[k][w];  90                 P[w] = k;  91  }  92  }  93  }  94 }  95 
 96 // 打印最短路徑
 97 void PrintShortPath(MGraph G, int v0, Patharc P, ShortPathTable D){  98     int i, k;  99     stack<int> path; 100     cout<<"頂點v"<<v0<<"到其餘頂點之間的最短路徑以下: "<<endl; 101     for(i = 0; i < G.numVertexes; ++i){ 102         if(i == v0) continue; 103         cout<<"v"<<v0<<"--"<<"v"<<i<<" weight: "<<D[i]<<" Shortest path: "; 104  path.push(i); 105         int k = P[i]; 106         while(k != 0){ 107  path.push(k); 108             k = P[k]; 109  } 110  path.push(v0); 111         while(!path.empty()){ 112             if(path.size() != 1) 113                 cout<<path.top()<<"->"; 114             else
115                 cout<<path.top()<<endl; 116  path.pop(); 117  } 118  } 119 } 120 
121 int main(int argc, char const *argv[]) { 122     int v0 = 0; // 源點
123  MGraph G; 124  Patharc P; 125  ShortPathTable D; 126     CreateMGraph(&G); 127  ShortPath_Dijkstra(G, v0, P, D); 128  PrintShortPath(G, v0, P, D); 129     return 0; 130 }

運行結果

頂點v0到其餘頂點之間的最短路徑以下: v0--v1 weight: 1  Shortest path: 0->1 v0--v2 weight: 4  Shortest path: 0->1->2 v0--v3 weight: 7  Shortest path: 0->1->2->4->3 v0--v4 weight: 5  Shortest path: 0->1->2->4 v0--v5 weight: 8  Shortest path: 0->1->2->4->5 v0--v6 weight: 10  Shortest path: 0->1->2->4->3->6 v0--v7 weight: 12  Shortest path: 0->1->2->4->3->6->7 v0--v8 weight: 16  Shortest path: 0->1->2->4->3->6->7->8 [Finished in 1.8s]