HZAU_1208_color_circle(dfs)

原题

Problem J: Color Circle

Time Limit: 1 Sec  Memory Limit: 1280 MB

Description

     There are colorful flowers in the parterre in front of the door of college and form many beautiful patterns. Now, you want to find a circle consist of flowers with same color. What should be done ?

     Assuming the flowers arranged as matrix in parterre, indicated by a N*M matrix. Every point in the matrix indicates the color of a flower. We use the same uppercase letter to represent the same kind of color. We think a sequence of points d1, d2, … dk makes up a circle while:

    1. Every point is different.

    2. k >= 4

    3. All points belong to the same color.

    4. For 1 <= i <= k-1, di is adjacent to di+1 and dk is adjacent to d1. ( Point x is adjacent to Point y while they have the common edge).

    N, M <= 50. Judge if there is a circle in the given matrix.

Input

     There are multiply test cases.

     In each case, the first line are two integers n and m, the 2nd ~ n+1th lines is the given n*m matrix. Input m characters in per line.

Output

      Output your answer as “Yes” or ”No” in one line for each case.
Sample Input

3 3
AAA
ABA
AAA

Sample Output

Yes

题意

对于一张地图，判断能否找到一条路线，长度大于4，相同字母，并且回到原点。

思路

找图中的一个环，可以从第一个点进入开始 dfs（深度优先搜索） ，标记已经访问过的点，如果遍历过程中遇到它们，则找到一个环，输出 Yes ，否则继续从未标记点开始继续搜索。如果所有的点标记后未找到环，则输出 No 。

涉及知识及算法

DFS:深度优先搜索属于图算法的一种，英文缩写为DFS即Depth First Search.其过程简要来说是对每一个可能的分支路径深入到不能再深入为止，而且每个节点只能访问一次。

——百度百科

代码实现

#include<stdio.h>#include<string.h>#include<stdlib.h>#include<iostream>using namespace std;#define MAXX 110000int n,m;int mapp[55][55];        //存储字符bool vis[55][55];        //记录是否被访问int mv[4][2]= {{-1,0},{1,0},{0,-1},{0,1}};      //上下左右四个方向bool flag;              //标记是否有环void dfs(int x,int y,int xa,int ya) // (x,y) 为当前点坐标， (xa,ya)为上一点{    for(int i=0; i<4; i++)  // 搜索四个方向    {        int xi=x+mv[i][0];        int yi=y+mv[i][1];         if(xi<0||xi>=n||yi<0||yi>=m||mapp[xi][yi]!=mapp[x][y])continue; // 要求搜索的点相同且不越界        if(!vis[xi][yi])      //如果该点未被访问        {            vis[xi][yi]=true;   //置为已访问            dfs(xi,yi,x,y);                 if(flag) return;   //若有环则跳出        }        else        {            if(xi==xa&&yi==ya)continue; // 忽略上一点，如果还遇到一个已经访问的点，则是一个环            flag=true;            return;    //跳出        }    }}void solve(){    for(int i=0; i<n; i++)        for(int j=0; j<m; j++)            if(!vis[i][j])          //只访问未标记点            {                vis[i][j]=true;                dfs(i,j,-1,-1);                if(flag)                {                    cout<<"Yes"<<endl;                    return;                }            }    cout<<"No"<<endl;}int main(){    while(cin>>n>>m)    {        string c;        memset(vis,false,sizeof(vis));        flag=false;        for(int i=0; i<n; i++)        {            cin>>c;            for(int j=0; j<m; j++)                mapp[i][j]=c[j];        }        solve();    }    return 0;}
/**************************************************************
    Problem: 1208
    Language: C++
    Result: Accepted
    Time:1 ms
    Memory:1520 kb
****************************************************************/

转载自博主小坏蛋_千千，向他表示感谢。