HDOJ 1026 BFS
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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
Author
Ignatius.L
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一直知道有BFS和DFS不过平时用的都是DFS,所以这道题一开始也反应不过来BFS。然后上网查了别人的代码,然后再研究一下BFS和DFS的区别。
DFS深度搜索,强调的是深度,用递归,所以会先向一个方向走到头。然后返回上个节点开始继续。
BFS广度搜索,强调的是广度,一般用queue队列进行。四个方向都走完,然后进行下一层。
BFS所用的内存远大于DFS。但是BFS记录的信息更多把。这道题难在打印,而BFS储存大量信息就很好的可以解决用一个pre就行了。反馈到上一个节点然后用栈进行输出。
#include <iostream> #include <queue> #include <stack> using namespace std; const int N = 102; typedef struct { int x,y; int cost; int prex,prey; }Node; int dir[4][2] = {{-1, 0},{1, 0},{0, -1},{0, 1}}; int m, n; Node path[N][N]; char graph[N][N]; void init() { int i, j; for(i = 0; i < m; i++) cin>>graph[i]; for(i = 0; i < m; i++) for(j = 0; j < n; j++) path[i][j].cost = -1; } bool isBound(int x,int y) { if(x < 0 || y < 0) return false; if(x >= m || y >= n) return false; return true; } void bfs() { queue<Node> Q; Node a, b; a.x = 0; a.y = 0; a.cost = 0; a.prex = 0; a.prey = 0; if(graph[0][0] != '.') a.cost = graph[0][0] - '0'; path[0][0] = a; Q.push(a); while(!Q.empty()) { a = Q.front(); Q.pop(); for(int i = 0; i < 4; i++) { b.x = a.x + dir[i][0]; b.y = a.y + dir[i][1]; if(!isBound(b.x, b.y)) continue; if(graph[b.x][b.y] == 'X') continue; if(graph[b.x][b.y] == '.') b.cost = a.cost + 1; else b.cost = a.cost + graph[b.x][b.y] - '0' + 1; if(b.cost < path[b.x][b.y].cost || path[b.x][b.y].cost == -1) { b.prex = a.x; b.prey = a.y; path[b.x][b.y] = b; Q.push(b); } } } if(path[m - 1][n - 1].cost == -1) { cout<<"God please help our poor hero."<<endl; cout<<"FINISH"<<endl; return ; } stack<Node> S; int cc = 1, tmp; cout<<"It takes "<<path[m - 1][n - 1].cost<<" seconds to reach the target position, let me show you the way."<<endl; a = path[m - 1][n - 1]; while(1) { if(a.x == 0 && a.y == 0) break; S.push(a); a = path[a.prex][a.prey]; } a = path[0][0]; while(!S.empty()) { b = S.top(); S.pop(); if(graph[b.x][b.y] == '.') cout<<cc++<<"s:("<<a.x<<","<<a.y<<")->("<<b.x<<","<<b.y<<")"<<endl; else { cout<<cc++<<"s:("<<a.x<<","<<a.y<<")->("<<b.x<<","<<b.y<<")"<<endl; tmp = graph[b.x][b.y] - '0'; while(tmp--) cout<<cc++<<"s:FIGHT AT ("<<b.x<<","<<b.y<<")"<<endl; } a = b; } cout<<"FINISH"<<endl; } int main() { while(cin>>m>>n) { init(); bfs(); } return 0; }
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