HDU1026 Ignatius and the Princess I BFS

Ignatius and the Princess I

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 22883 Accepted Submission(s): 7378
Special Judge

Problem Description
The Princess has been abducted by the BEelzebub feng5166, our hero Ignatius has to rescue our pretty Princess. Now he gets into feng5166’s castle. The castle is a large labyrinth. To make the problem simply, we assume the labyrinth is a N*M two-dimensional array which left-top corner is (0,0) and right-bottom corner is (N-1,M-1). Ignatius enters at (0,0), and the door to feng5166’s room is at (N-1,M-1), that is our target. There are some monsters in the castle, if Ignatius meet them, he has to kill them. Here is some rules:

1.Ignatius can only move in four directions(up, down, left, right), one step per second. A step is defined as follow: if current position is (x,y), after a step, Ignatius can only stand on (x-1,y), (x+1,y), (x,y-1) or (x,y+1).
2.The array is marked with some characters and numbers. We define them like this:
. : The place where Ignatius can walk on.
X : The place is a trap, Ignatius should not walk on it.
n : Here is a monster with n HP(1<=n<=9), if Ignatius walk on it, it takes him n seconds to kill the monster.

Your task is to give out the path which costs minimum seconds for Ignatius to reach target position. You may assume that the start position and the target position will never be a trap, and there will never be a monster at the start position.

Input
The input contains several test cases. Each test case starts with a line contains two numbers N and M(2<=N<=100,2<=M<=100) which indicate the size of the labyrinth. Then a N*M two-dimensional array follows, which describe the whole labyrinth. The input is terminated by the end of file. More details in the Sample Input.

Output
For each test case, you should output “God please help our poor hero.” if Ignatius can’t reach the target position, or you should output “It takes n seconds to reach the target position, let me show you the way.”(n is the minimum seconds), and tell our hero the whole path. Output a line contains “FINISH” after each test case. If there are more than one path, any one is OK in this problem. More details in the Sample Output.

Sample Input
5 6
.XX.1.
…X.2.
2…X.
…XX.
XXXXX.
5 6
.XX.1.
…X.2.
2…X.
…XX.
XXXXX1
5 6
.XX…
…XX1.
2…X.
…XX.
XXXXX.

Sample Output
It takes 13 seconds to reach the target position, let me show you the way.
1s:(0,0)->(1,0)
2s:(1,0)->(1,1)
3s:(1,1)->(2,1)
4s:(2,1)->(2,2)
5s:(2,2)->(2,3)
6s:(2,3)->(1,3)
7s:(1,3)->(1,4)
8s:FIGHT AT (1,4)
9s:FIGHT AT (1,4)
10s:(1,4)->(1,5)
11s:(1,5)->(2,5)
12s:(2,5)->(3,5)
13s:(3,5)->(4,5)
FINISH
It takes 14 seconds to reach the target position, let me show you the way.
1s:(0,0)->(1,0)
2s:(1,0)->(1,1)
3s:(1,1)->(2,1)
4s:(2,1)->(2,2)
5s:(2,2)->(2,3)
6s:(2,3)->(1,3)
7s:(1,3)->(1,4)
8s:FIGHT AT (1,4)
9s:FIGHT AT (1,4)
10s:(1,4)->(1,5)
11s:(1,5)->(2,5)
12s:(2,5)->(3,5)
13s:(3,5)->(4,5)
14s:FIGHT AT (4,5)
FINISH
God please help our poor hero.
FINISH

问题连接

问题描述

迷宫是个二维数组，英雄要从(0,0)走到(n-1,m-1)。其中’X’不能通过，数字是怪物的HP,HP有多少英雄就要花多少时间打怪，找到最短时间，并把路径表示出来。

问题分析

迷宫问题稍微改编了下。怪物是影响时间的因素之一，所以不是简单的用bool visited数组记录了，我的处理方式是换成int visited数组记录英雄到这点用的最短时间。把每个元素都设置成足够大的值，注意:不能用memset函数，因为它是按一个字节处理的。路径我是记录方向，而没有直接记录对应的点，因为这种处理方式地图一大就会出错。

c++程序如下

#include
#include
#include
#include
using namespace std;
const int N=105;
int n,m,time;
int dir[4][2]={{0,1},{1,0},{0,-1},{-1,0}};
int visited[N][N];
char map[N][N];
string ss;
struct state
{
	int x,y,time;
	string road;
}q,p;
void bfs();
void reset();
int main()
{
	while(cin>>n>>m)
	{
		int i,len,count;
		for(i=0;i<n;i++)
		cin>>map[i];
		ss="";
		bfs();
		if(!ss.empty())
		{
			len=ss.size();
		printf("It takes %d seconds to reach the target position, let me show you the way.\n",time);
		int y,x,my,mx,mi;
		for(i=y=x=count=0;i<len;i++)
		{
			count++;
			if(ss[i]=='F')
			{
				int tx=map[y][x]-'0';
				while(tx--)
				{
					printf("%ds:FIGHT AT (%d,%d)\n",count,y,x);
					count++;
				}
				count--;
			}
			else
			{
				mi=ss[i]-'0';
				my=y+dir[mi][1];
				mx=x+dir[mi][0];
				printf("%ds:(%d,%d)->(%d,%d)\n",count,y,x,my,mx);
				y=my;
				x=mx;
			}
		}
		}
		else printf("God please help our poor hero.\n");
		printf("FINISH\n");
	}
	return 0;
}
void bfs()
{
	time=100000;
	reset();
	q.x=q.y=q.time=0;
	q.road="";
	queue<state>Q;
	Q.push(q);
	visited[0][0]=1;
	while(!Q.empty())
	{
		q=Q.front();
		Q.pop();
		if(q.y==n-1&&q.x==m-1&&q.time<time)
		{
			time=q.time;
			ss=q.road;
		}
		int i;
		for(i=0;i<4;i++)
		{
			p=q;
			p.x+=dir[i][0];
			p.y+=dir[i][1];
			p.time++;
			if(p.x>=0&&p.x<m&&p.y>=0&&p.y<n&&map[p.y][p.x]!='X'&&visited[p.y][p.x]>p.time)
			{
				visited[p.y][p.x]=p.time;
				p.road+=i+'0';
				if(map[p.y][p.x]!='.')
				{
					p.road+='F';
					p.time+=map[p.y][p.x]-'0';
				}
				Q.push(p);
			}
		}
	}
}
void reset()
{
	int i,j;
	for(i=0;i<n;i++)
	{
		for(j=0;j<m;j++)
		{
			visited[i][j]=10000000;
		}
	}
}