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【Codeforces 1063B】Labyrinth

off writer rst empty isempty poll nth run buffer

【鏈接】 我是鏈接,點我呀:)
【題意】


你可以往左最多x次,往右最多y次
問你從x,y出發最多能到達多少個格子
只能往上下左右四個方向走到沒有障礙的格子

【題解】


假設我們從(r,c)出發想要到固定某個點(i,j)的最短距離
我們設x0為向左走動的次數,y0為向右走動的次數
顯然(j-c)=y0-x0
即y0 = (j-c) + x0
這裏j-c是一個常數
也就是說當我們讓x0最小的時候到達每一個點的對應的y0也一定是最優的,因為和x0成正相關
因此我們只要求出來(r,c)到所有點所用的x0的最小值就好了
會發現沒個點到達相鄰的點的花費要麽就是1(往左走),要麽就是0(往其他方向走)
符合01bfs的特點

(01bfs:如果向左走的話,那麽就把新得到的狀態加入到末尾,否則加入到隊頭,因為花費為0的話,和之前的dis值相同,依然是當前所有的情況裏最低花費
(所以可以用來繼續更新最小值,因此是放在隊頭,這樣的話能始終維持隊列從頭到尾的dis值依次遞增的順序
(因此能保證每次嘗試用來更新的狀態都是當前狀況下最優的狀態,不會造成錯解或者漏解

【代碼】

import java.io.*;
import java.util.*;

public class Main {
    
    
    static InputReader in;
    static PrintWriter out;
        
    public static void main(String[] args) throws IOException{
        //InputStream ins = new FileInputStream("E:\\rush.txt");
        InputStream ins = System.in;
        in = new InputReader(ins);
        out = new PrintWriter(System.out);
        //code start from here
        new Task().solve(in, out);
        out.close();
    }
    
    static class Pair{
        int x,y,d;
        public Pair(int x,int y,int d){
            this.x = x;
            this.y = y;
            this.d = d;
        }
    }
    
    static int N = 2000;
    static class Task{
        int n,m,r,c,x,y;
        String s[];
        int dis[][];
        int dx[]= {0,0,1,-1},dy[]= {1,-1,0,0};
        Deque<Pair> queue;
        
        public void solve(InputReader in,PrintWriter out) {
            queue = new LinkedList<Pair>();
            dis = new int[N+10][N+10];
            s = new String[N+10];
            n = in.nextInt();m = in.nextInt();
            r = in.nextInt();c = in.nextInt();
            x = in.nextInt();y = in.nextInt();
            for (int i = 1;i <= n;i++)  {
                s[i] = in.next();
                StringBuilder sb = new StringBuilder(s[i]);
                sb.insert(0, ' ');
                s[i] = sb.toString();
            }
            for (int i = 1;i <= N;i++)
                for (int j = 1;j <= N;j++)
                    dis[i][j] = -1;
            
            dis[r][c] = 0;
            queue.offerFirst(new Pair(r,c,0));
            while (!queue.isEmpty()) {
                Pair temp = queue.pollFirst();
                int x0 = temp.x,y0 = temp.y,d = temp.d;
                for (int i = 0;i < 4;i++) {
                    int x1 = x0 + dx[i];int y1 = y0 + dy[i];
                    int td = d;
                    if (i==1) td++;
                    if (x1>=1 && x1<=n && y1>=1 && y1<=m && s[x1].charAt(y1)!='*') {
                        if (dis[x1][y1]==-1 ||dis[x1][y1]>td) {
                            dis[x1][y1] = td;
                            if (i==1) {
                                queue.offerLast(new Pair(x1,y1,td));
                            }else {
                                queue.offerFirst(new Pair(x1,y1,td));
                            }
                        }
                    }
                }
            }
            int ans = 0;
            for (int i = 1;i <= n;i++)
                for (int j = 1;j <= m;j++) {
                    if (dis[i][j]==-1) continue;
                    int x0 = dis[i][j];
                    int y0 = j-c + x0;
                    if (x0<=x && y0<=y) {
                        ans++;
                    }
                }
            out.println(ans);
        }
    }

    

    static class InputReader{
        public BufferedReader br;
        public StringTokenizer tokenizer;
        
        public InputReader(InputStream ins) {
            br = new BufferedReader(new InputStreamReader(ins));
            tokenizer = null;
        }
        
        public String next(){
            while (tokenizer==null || !tokenizer.hasMoreTokens()) {
                try {
                tokenizer = new StringTokenizer(br.readLine());
                }catch(IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        
        public int nextInt() {
            return Integer.parseInt(next());
        }
    }
}

【Codeforces 1063B】Labyrinth