# HDU - 1242 朋友救天使or天使救朋友

本文介绍了一个经典的迷宫救援问题——HDU-1242,通过广度优先搜索(BFS)算法解决如何在包含墙壁、道路及守卫的迷宫中找到从朋友到被囚禁天使的最短路径。文中提供了完整的C++实现代码,展示了如何高效地遍历迷宫并计算最小救援时间。

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HDU - 1242 朋友救天使or天使救朋友

Angel was caught by the MOLIGPY! He was put in prison by Moligpy. The prison is described as a N * M (N, M <= 200) matrix. There are WALLs, ROADs, and GUARDs in the prison.
Angel’s friends want to save Angel. Their task is: approach Angel. We assume that “approach Angel” is to get to the position where Angel stays. When there’s a guard in the grid, we must kill him (or her?) to move into the grid. We assume that we moving up, down, right, left takes us 1 unit time, and killing a guard takes 1 unit time, too. And we are strong enough to kill all the guards.
You have to calculate the minimal time to approach Angel. (We can move only UP, DOWN, LEFT and RIGHT, to the neighbor grid within bound, of course.)
Input
First line contains two integers stand for N and M.
Then N lines follows, every line has M characters. “.” stands for road, “a” stands for Angel, and “r” stands for each of Angel’s friend.
Process to the end of the file.
Output
For each test case, your program should output a single integer, standing for the minimal time needed. If such a number does no exist, you should output a line containing “Poor ANGEL has to stay in the prison all his life.”
Sample Input
7 8
#.#####.
#.a#…r.
#…#x…
…#…#.#
#…##…
.#…

Sample Output
13

#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <queue>
using namespace std;
char a[220][220];
int n,m,book[220][220];
struct node
{
    int x,y;
    int step;
};
void bfs(int tx,int ty)
{
    int next[4][2]= {{-1,0},{1,0},{0,-1},{0,1}};
    queue<node> q;
    struct node t,f;
    t.x=tx;
    t.y=ty;
    t.step=0;
    q.push(t);
    book[t.x][t.y]=1;
    while(!q.empty())
    {
        f=q.front();
        q.pop();
        if(a[f.x][f.y]=='r')
        {
            printf("%d\n",f.step);
            return;
        }
        for(int i=0; i<4; i++)
        {
            t.x=f.x+next[i][0];
            t.y=f.y+next[i][1];
            if(a[t.x][t.y]!='#'&&!book[t.x][t.y]&&t.x>=0&&t.y>=0&&t.x<n&&t.y<m)
            {
                t.step=f.step+1;
//                printf("%c\n",a[t.x][t.y]);
                book[t.x][t.y]=1;
                if(a[t.x][t.y]=='x')
                t.step=t.step+1;
                q.push(t);
            }
        }
    }
    printf("Poor ANGEL has to stay in the prison all his life.\n");
    return;
}
int main()
{
    int i,j,tx,ty;
    while(scanf("%d%d",&n,&m)!=EOF)
    {
        memset(book,0,sizeof(book));
        for(i=0; i<n; i++)
            scanf("%s",a[i]);
        for(i=0; i<n; i++)
            for(j=0; j<m; j++)
            {
                if(a[i][j]=='a')
                {
                    tx=i;
                    ty=j;
                }
            }
            bfs(tx,ty);
    }
    return 0;
}

### 关于HDU - 6609 的题目解析 由于当前未提供具体关于 HDU - 6609 题目的详细描述,以下是基于一般算法竞赛题型可能涉及的内容进行推测和解答。 #### 可能的题目背景 假设该题目属于动态规划类问题(类似于多重背包问题),其核心在于优化资源分配或路径选择。此类问题通常会给出一组物品及其属性(如重量、价值等)以及约束条件(如容量限制)。目标是最优地选取某些物品使得满足特定的目标函数[^2]。 #### 动态转移方程设计 如果此题确实是一个变种的背包问题,则可以采用如下状态定义方法: 设 `dp[i][j]` 表示前 i 种物品,在某种条件下达到 j 值时的最大收益或者最小代价。对于每一种新加入考虑范围内的物体 k ,更新规则可能是这样的形式: ```python for i in range(n): for s in range(V, w[k]-1, -1): dp[s] = max(dp[s], dp[s-w[k]] + v[k]) ``` 这里需要注意边界情况处理以及初始化设置合理值来保证计算准确性。 另外还有一种可能性就是它涉及到组合数学方面知识或者是图论最短路等相关知识点。如果是后者的话那么就需要构建相应的邻接表表示图形结构并通过Dijkstra/Bellman-Ford/Floyd-Warshall等经典算法求解两点间距离等问题了[^4]。 最后按照输出格式要求打印结果字符串"Case #X: Y"[^3]。 #### 示例代码片段 下面展示了一个简单的伪代码框架用于解决上述提到类型的DP问题: ```python def solve(): t=int(input()) res=[] cas=1 while(t>0): n,k=list(map(int,input().split())) # Initialize your data structures here ans=find_min_unhappiness() # Implement function find_min_unhappiness() res.append(f&#39;Case #{cas}: {round(ans)}&#39;) cas+=1 t-=1 print("\n".join(res)) solve() ```
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