Ignatius and the Princess I

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

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

题解：给定一个地图，让你从左上角走到右下角，只能上下左右四个方向，有的格子有怪兽，移动格子和打怪都要消耗时间，求到达终点所消耗的最短时间和路径。

题解：最短时间可以用优先队列求出来，路径用二维结构体数组来记录。每个节点保存它从哪儿来，该点消耗的时间。

#include <cstdio>
#include <queue>
#include <cstring>
#define maxn 102
using std::priority_queue;

struct Node{
    int x, y, time;
    friend bool operator<(Node a, Node b){
        return a.time > b.time;
    }
};
struct node{
    int x, y, time;
} path[maxn][maxn];
char map[maxn][maxn];
int n, m, mov[][2] = {0, 1, 0, -1, -1, 0, 1, 0};

bool check(int x, int y)
{
    return x >= 0 && y >= 0 && x < n && y < m && map[x][y] != 'X';
}

bool BFS(int& times)
{
    Node now, next;
    now.x = now.y = now.time = 0;
    priority_queue<Node> Q;
    Q.push(now);
    while(!Q.empty()){
        now = Q.top(); Q.pop();
        if(now.x == n - 1 && now.y == m - 1){
            times = now.time; return true;
        }
        for(int i = 0; i < 4; ++i){
            next = now;
            next.x += mov[i][0]; next.y += mov[i][1];
            if(!check(next.x, next.y)) continue;
            ++next.time;
            path[next.x][next.y].x = now.x;
            path[next.x][next.y].y = now.y;
            path[next.x][next.y].time = 0;
            if(map[next.x][next.y] != '.'){
                next.time += map[next.x][next.y] - '0';
                path[next.x][next.y].time = map[next.x][next.y] - '0';
            }
            map[next.x][next.y] = 'X'; Q.push(next);
        }
    }
    return false;
}

void printPath(int times, int x, int y)
{
    if(times == 0) return;
    times -= path[x][y].time;
    printPath(times - 1, path[x][y].x, path[x][y].y);
    printf("%ds:(%d,%d)->(%d,%d)\n",
        times++, path[x][y].x, path[x][y].y, x, y);
    while(path[x][y].time--)
        printf("%ds:FIGHT AT (%d,%d)\n", times++, x, y);
}

int main()
{
    int times, i;
    while(scanf("%d%d", &n, &m) != EOF){
        for(i = 0; i < n; ++i)
            scanf("%s", map[i]);
        memset(path, 0, sizeof(path));
        if(BFS(times)){
            printf("It takes %d seconds to reach the target position, let me show you the way.\n", times);
            printPath(times, n - 1, m - 1);
        }else puts("God please help our poor hero.");
        puts("FINISH");
    }
    return 0;
}