HDU 1026 Ignatius and the Princess I(BFS+プライオリティキュー)
HDU1026 Ignatius and the Princess I
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
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
問題の概要
典型的なbfs+印刷パス+優先キューの問題.N*Mサイズの迷路があり、ヒーローは(0,0)から入り、プリンセスは(N-1,M-1)の位置にあり、その中には道の途中に怪物(1-9で表され、hpは1-9で、それらを殺すにはhp秒が必要)があり、「X」は歩けないことを示している.
問題の難点
簡単なbfsに時間の問題を加えているので、bfsを使うときは優先問題を考える必要があります.広さだけで検索すると、必ずしも最短とは限らないからです.だから優先キューで解決して、少ない時間で先に列を出させます.
また、印刷パスの問題ですが、これはdfsで前駆点を検索すればいいです.
はい、次はACコードです
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
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
問題の概要
典型的なbfs+印刷パス+優先キューの問題.N*Mサイズの迷路があり、ヒーローは(0,0)から入り、プリンセスは(N-1,M-1)の位置にあり、その中には道の途中に怪物(1-9で表され、hpは1-9で、それらを殺すにはhp秒が必要)があり、「X」は歩けないことを示している.
問題の難点
簡単なbfsに時間の問題を加えているので、bfsを使うときは優先問題を考える必要があります.広さだけで検索すると、必ずしも最短とは限らないからです.だから優先キューで解決して、少ない時間で先に列を出させます.
struct node{
int x, y, sec, prex, prey;
friend bool operator < (node n1, node n2){
return n2.sec < n1.sec;
}
}note[N][N];また、印刷パスの問題ですが、これはdfsで前駆点を検索すればいいです.
void print(int x, int y)
{
if (x == 0 && y == 0)
return;
int prex = note[x][y].prex;
int prey = note[x][y].prey;
print(prex, prey);
int prel = note[prex][prey].sec;
int len = note[x][y].sec;
printf("%ds:(%d,%d)->(%d,%d)
", prel + 1, prex, prey, x, y);
for (int i = prel + 2; i <= len; i++)
{
printf("%ds:FIGHT AT (%d,%d)
", i, x, y);
}
}はい、次はACコードです
#include q; //
node cur;
note[0][0].x = note[0][0].y = 0; //
note[0][0].sec = 0;
book[0][0] = 1;
q.push(note[0][0]); //
while(!q.empty())
{
cur = q.top(); //
q.pop();
if(cur.x==n-1 && cur.y==m-1){ //
return 1;
}
for(int i=0;i<4;i++){
int nx = cur.x + nxt[i][0];
int ny = cur.y + nxt[i][1];
if( judge(nx,ny) == 0) //
continue;
//
book[nx][ny] = 1;
if( '1'<=a[nx][ny] && a[nx][ny]<='9' ){ //
int hp = a[nx][ny] - '0';
note[nx][ny].sec = cur.sec + hp + 1;
note[nx][ny].prex = cur.x;
note[nx][ny].prey = cur.y;
note[nx][ny].x = nx;
note[nx][ny].y = ny;
}else{ //
note[nx][ny].sec = cur.sec + 1;
note[nx][ny].prex = cur.x;
note[nx][ny].prey = cur.y;
note[nx][ny].x = nx;
note[nx][ny].y = ny;
}
q.push(note[nx][ny]);
}
}
return 0;
}
void print(int x, int y) //dfs
{
if (x == 0 && y == 0)
return;
int prex = note[x][y].prex;
int prey = note[x][y].prey;
print(prex, prey);
int prel = note[prex][prey].sec;
int len = note[x][y].sec;
printf("%ds:(%d,%d)->(%d,%d)
", prel + 1, prex, prey, x, y);
for (int i = prel + 2; i <= len; i++)
{
printf("%ds:FIGHT AT (%d,%d)
", i, x, y);
}
}
int main()
{
while(~scanf("%d%d",&n,&m))
{
memset(book,0,sizeof(book));
for(int i = 0; i < n; i++)
{
for(int j = 0; j < m; j++)
{
scanf(" %c",&a[i][j]);
}
}
int ans = bfs();
if(ans==0) {
printf("God please help our poor hero.
");
} else {
printf("It takes %d seconds to reach the target position, let me show you the way.
",note[n-1][m-1].sec);
print(n-1,m-1);
}
printf("FINISH
");
}
return 0;
}