图Graph--农夫过河问题（BFS/DFS应用）

农夫过河问题：
在这里插入图片描述

/*** @description: 农夫过河问题（羊，白菜，狼），一次最多带一个东西过河，*                  农夫不在的情况下羊会吃白菜，狼会吃羊，如何平安过河* @author: michael ming* @date: 2019/6/13 20:06* @modified by: */
#include <iostream>
#include <queue>
#include <memory.h>#define MaxVertexNum 10 //最多10种情况（顶点）
using namespace std;
struct vertexType
{int farmer;int wolf;int sheep;int vegetable;
};
class MGraph_Farmer //邻接矩阵图类
{
public:vertexType vertex[MaxVertexNum];    //顶点表int edges[MaxVertexNum][MaxVertexNum];//边的邻接矩阵int vN, eN;   //顶点和边的数量int visited[MaxVertexNum];  //访问标志int prev[MaxVertexNum];     //存储搜索路径MGraph_Farmer():vN(0),eN(0){memset(visited,0, sizeof(int)*MaxVertexNum);}void clearPrev(){for(int i = 0; i < MaxVertexNum; ++i)prev[i] = -1;}int findPos(int F, int W, int S, int V)//查找顶点在图中的位置{for(int i = 0; i < vN; ++i)if(vertex[i].farmer == F && vertex[i].wolf == W &&vertex[i].sheep == S && vertex[i].vegetable == V)return i;return -1;}int is_safe(int F, int W, int S, int V)//判断是否安全{if(F != S && (W == S || S == V))//人和羊不在一起时，狼羊或者羊菜在一起，不安全return 0;return 1;}int is_connected(int i, int j)//判断状态之间是否可以转换{int k = 0;if(vertex[i].wolf != vertex[j].wolf)k++;if(vertex[i].sheep != vertex[j].sheep)k++;if(vertex[i].vegetable != vertex[j].vegetable)k++;if(vertex[i].farmer != vertex[j].farmer && k <= 1)//农夫每次需要过河，只能带一件东西return 1;return 0;}void creatGraph()//建立图的存储矩阵{int i = 0, j, F, W, S, V;for(F = 0; F <= 1; F++)//生成所有安全状态的顶点for(W = 0; W <= 1; W++)for(S = 0; S <= 1; S++)for(V = 0; V <= 1; V++)if(is_safe(F, W, S, V)){vertex[i].farmer = F;vertex[i].wolf = W;vertex[i].sheep = S;vertex[i].vegetable = V;i++;}vN = i;//安全顶点个数for(i = 0; i < vN; ++i)for(j = 0; j < vN; ++j)if(is_connected(i,j))//i,j两种状态可以转换，他们的边置1，否则置0{edges[i][j] = edges[j][i] = 1;//无向图eN++;}elseedges[i][j] = edges[j][i] = 0;//无向图eN /= 2;}void dfs(int s, int t){memset(visited,0, sizeof(int)*MaxVertexNum);clearPrev();dfs_path(s, t);if(visited[t])printPath(s,t,t);}void dfs_path(int s, int t)//dfs搜索s到t的路径{int j;visited[s] = true;for(j = 0; j < vN; ++j)if(edges[s][j] == 1 && !visited[j] && !visited[t]){prev[j] = s;//记录路径dfs_path(j, t);}}void printPath(int s, int t, int k){if(k != s){printPath(s,t,prev[k]);}cout << endl;cout << "(" << vertex[k].farmer << vertex[k].wolf<< vertex[k].sheep << vertex[k].vegetable << ")";}void bfs(int s, int t)//bfs搜索s到t的路径{memset(visited,0, sizeof(int)*MaxVertexNum);clearPrev();queue<int> q;q.push(s);visited[s] = true;int j, w;while(!q.empty()){int w = q.front();q.pop();for(j = 0; j < vN; ++j){if(edges[w][j] == 1 && !visited[j]){prev[j] = w;if(j == t){printPath(s,t,j);return;}visited[j] = true;q.push(j);}}}}
};int main()
{int s, t;MGraph_Farmer farmerCrossRiver;farmerCrossRiver.creatGraph();s = farmerCrossRiver.findPos(0,0,0,0);t = farmerCrossRiver.findPos(1,1,1,1);cout << "dfs搜索:";farmerCrossRiver.dfs(s,t);cout << endl << "bfs搜索:";farmerCrossRiver.bfs(s,t);return 0;
}