E - Divide Points

​​link​​

题意：让你将点的集合划分成两个，然后两集合之间的距离没有在集合内部出现。

思路：

一开始以为是二分图啥的，结果是思维，考虑把点划分成4类，00,01,10,11，

0代表奇点，1代表偶点，然后如果存在两个不同类的点就可以划分，把00,11放在一起，01，10放在一起，如果符合的话，如果只存在一个集合的点，那么我们就把所有点就/2，改变其奇偶性，直到出现解位置。

复杂度n*log2e6

(写个jvavhhh)代码：

import java.math.*;
import java.util.*;

import java.io.*;

//import org.graalvm.compiler.lir.alloc.lsra.ssa.SSALinearScan;

public class Main{
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
    static int x[]=new int [1010];
    static int y[]=new int [1010];
    static int num[][]=new int [2][2];
    public  static void main(String[] args)
    {   
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        int n=in.nextInt();
        for(int i=1;i<=n;i++)
        {
            x[i]=in.nextInt();
            y[i]=in.nextInt();
            x[i]+=1000000;
            y[i]+=1000000;
        }

        while(true)
        {
            out.flush();
            for(int i=0;i<2;i++)
                for(int j=0;j<2;j++)
                    num[i][j]=0;
            for(int i=1;i<=n;i++)
                num[x[i]%2][y[i]%2]++;
            Vector ans=new Vector(0);
            boolean flag=false;
            if(((num[0][0]+num[1][1]>0)&(num[1][0]+num[0][1])>0))
            {
                for(int i=1;i<=n;i++)
                {
                    if(x[i]%2==0 && y[i]%2==0 || x[i]%2==1 && y[i]%2==1)    ans.add(i);
                }
                out.println(ans.size());
                Iterator it = ans.iterator();
                while(it.hasNext())
                    out.printf("%d ", it.next());
                out.flush();
                break;
            }
            if(num[0][0]>0 && num[1][1]>0)
            {
                for(int i=1;i<=n;i++)
                {
                    if(x[i]%2==0 && y[i]%2==0 ) ans.add(i);
                }
                out.println(ans.size());
                Iterator it = ans.iterator();
                while(it.hasNext())
                    out.printf("%d ", it.next());
                out.flush();
                break;
            }
            if(num[1][0]>0 && num[0][1]>0)
            {
                for(int i=1;i<=n;i++)
                {
                    if(x[i]%2==0 && y[i]%2==1 ) ans.add(i);
                }
                out.println(ans.size());
                Iterator it = ans.iterator();
                while(it.hasNext())
                    out.printf("%d ", it.next());
                out.flush();
                break;
            }
            if(flag==true)  break;
            for(int i=1;i<=n;i++)
            {
                x[i]/=2;y[i]/=2;
            }
        }

        out.flush();
    }
}