[ACM训练] 算法初级 之 搜索算法 之 深度优先算法DFS (POJ 2251+2488+3083+3009+1321)

对于深度优先算法，第一个直观的想法是只要是要求输出最短情况的详细步骤的题目基本上都要使用深度优先来解决。比较常见的题目类型比如寻路等，可以结合相关的经典算法进行分析。

常用步骤：

---

第一道题目：Dungeon Master  http://poj.org/problem?id=2251

Input

The input consists of a number of dungeons. Each dungeon description starts with a line containing three integers L, R and C (all limited to 30 in size). 
L is the number of levels making up the dungeon. 
R and C are the number of rows and columns making up the plan of each level. 
Then there will follow L blocks of R lines each containing C characters. Each character describes one cell of the dungeon. A cell full of rock is indicated by a '#' and empty cells are represented by a '.'. Your starting position is indicated by 'S' and the exit by the letter 'E'. There's a single blank line after each level. Input is terminated by three zeroes for L, R and C.

Output

Each maze generates one line of output. If it is possible to reach the exit, print a line of the form 

Escaped in x minute(s).

where x is replaced by the shortest time it takes to escape. 
If it is not possible to escape, print the line 

Trapped!

Sample Input

3 4 5
S....
.###.
.##..
###.#

#####
#####
##.##
##...

#####
#####
#.###
####E

1 3 3
S##
#E#
###

0 0 0

---

此题目只要求了求出最短的路径步骤，肯定适合使用广度优先算法来处理，但是如果再要求输出对应最短路径下的具体路径，则只能使用深度优先来处理了。

先来一个广度优先算法的参考代码：

#include <iostream>
#include <cstdio>
#include <queue>
#include <cmath>
#include <cstring>

using namespace std;

int l,r,c;

struct node
{
    int i;
    int j;
    int k;
    int s;
};

string road[30][30];
int visited[30*30*30];//i*r*c+j*c+k为索引值

void getroad(int es)
{
    int i,j,k;
    node first,next;
    bool flag=false;

    for(i=0;i<l;i++)
    {
        for(j=0;j<r;j++)
        {
            for(k=0;k<c;k++)
            {
                if(road[i][j][k] == 'S')//找到初始点，标记
                {
                    first.i=i;
                    first.j=j;
                    first.k=k;
                    first.s=0;
                    flag=true;
                    break;
                }
            }
            if(flag)
                break;
        }
        if(flag)
            break;
    }

    queue<node> q;
    q.push(first);
    visited[first.i*r*c+first.j*c+first.k]=es;

    while(!q.empty())
    {
        first=q.front();
        q.pop();

        //需要设计上下左右前后6个方向，1维只有上下j左右k，2维以上再添加前后i
        //同时需要考虑是否处在边界的情况
        next=first;
        next.s+=1;
        int index=0;

        next.j-=1;//上
        index=next.i*r*c+next.j*c+next.k;
        if(next.j>=0 && road[next.i][next.j][next.k] == '.')
        {
            if(visited[index] != es)
            {
                q.push(next);
                visited[index]=es;
            }
        }
        if(next.j>=0 && road[next.i][next.j][next.k] == 'E')
        {
            cout<<"Escaped in "<<next.s<<" minute(s)."<<endl;
            return;
        }

        next.j+=2;//下
        index=next.i*r*c+next.j*c+next.k;
        //cout<<str[next.i][next.j][next.k]<<endl;
        if(next.j<r && road[next.i][next.j][next.k] == '.')
        {
            if(visited[index] != es)
            {
                q.push(next);
                visited[index]=es;
            }
        }
        if(next.j<r && road[next.i][next.j][next.k] == 'E')
        {
            cout<<"Escaped in "<<next.s<<" minute(s)."<<endl;
            return;
        }

        next.j-=1;//复原

        next.k-=1;//左
        index=next.i*r*c+next.j*c+next.k;
        if(next.k>=0 && road[next.i][next.j][next.k] == '.')
        {
            if(visited[index] != es)
            {
                q.push(next);
                visited[index]=es;
            }
        }
        if(next.k>=0 && road[next.i][next.j][next.k] == 'E')
        {
            cout<<"Escaped in "<<next.s<<" minute(s)."<<endl;
            return;
        }

        next.k+=2;//右
        index=next.i*r*c+next.j*c+next.k;
        if(next.k<c && road[next.i][next.j][next.k] == '.')
        {
            if(visited[index] != es)
            {
                q.push(next);
                visited[index]=es;
            }
        }
        if(next.k<c && road[next.i][next.j][next.k] == 'E')
        {
            cout<<"Escaped in "<<next.s<<" minute(s)."<<endl;
            return;
        }

        next.k-=1;//复原

        if(l>1)
        {
            next.i-=1;//前
            index=next.i*r*c+next.j*c+next.k;
            if(next.i>=0 && road[next.i][next.j][next.k] == '.')
            {
                if(visited[index] != es)
                {
                    q.push(next);
                    visited[index]=es;
                }
            }
            if(next.i>=0 && road[next.i][next.j][next.k] == 'E')
            {
                cout<<"Escaped in "<<next.s<<" minute(s)."<<endl;
                return;
            }

            next.i+=2;//后
            index=next.i*r*c+next.j*c+next.k;
            if(next.i<l && road[next.i][next.j][next.k] == '.')
            {
                if(visited[index] != es)
                {
                    q.push(next);
                    visited[index]=es;
                }
            }
            if(next.i<l && road[next.i][next.j][next.k] == 'E')
            {
                cout<<"Escaped in "<<next.s<<" minute(s)."<<endl;
                return;
            }
        }
    }
    cout<<"Trapped!"<<endl;
}


int main()
{
    int count=1;

    while(true)
    {
        cin>>l>>r>>c;

        if(l==0 && r==0 && c==0)
            break;


        int i=0;
        int j=0;
        string tmp;
        for(i=0;i<l;i++)
        {
            for(j=0;j<r;j++)
                cin>>road[i][j];
            getline(cin,tmp);
        }
        getroad(count);

        for(i=0;i<l;i++)
            for(j=0;j<r;j++)
                road[i][j].clear();

        count++;
    }

    return 0;
}

题目更改一下，要求输出最短步数，并且输出对应的具体路径。

考虑一下：