Codeforces Round #319 Div1 C: Points on Plane

問題

codeforces.com

解法

縦，横1000の長方形に切る．

長方形内で点をyの値でソートする．ひとつの長方形内では，そこに含まれる点の数をPとすると，x軸方向に1000*P，y軸方向にの長さが最大で必要になる．長方形間ではx軸方向に最大で2000必要になり，これは1000個ある．

よって合計の長さは最大で，である．

コード

import java.io.IOException;
import java.io.InputStream;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.NoSuchElementException;

public class Main {
	private final int BUCKET_NUM = 1010;// バケットの横幅

	public void solve() {
		FastScanner scanner = new FastScanner();
		int N = scanner.nextInt();

		ArrayList<ArrayList<Point>> points = new ArrayList<>();
		for (int i = 0; i < BUCKET_NUM; i++) {
			points.add(new ArrayList<Point>());
		}
		for (int i = 0; i < N; i++) {
			int x = scanner.nextInt();
			int y = scanner.nextInt();
			int bucket = x / BUCKET_NUM;
			points.get(bucket).add(new Point(i + 1, x, y));
		}

		for (int i = 0; i < BUCKET_NUM; i++) {
			if (i % 2 == 0) {
				// 偶数番目の長方形なら昇順にソートする
				Collections.sort(points.get(i), new Comparator<Point>() {

					@Override
					public int compare(Point p1, Point p2) {
						if (p1.y == p2.y) {
							return p1.x - p2.x;
						}
						return p1.y - p2.y;
					}
				});
			} else {
				// 奇数番目の長方形なら降順にソートする
				Collections.sort(points.get(i), new Comparator<Point>() {

					@Override
					public int compare(Point p1, Point p2) {
						if (p1.y == p2.y) {
							return p1.x - p2.x;
						}
						return p2.y - p1.y;
					}
				});
			}
		}

		StringBuilder sb = new StringBuilder();
		for (ArrayList<Point> arrayList : points) {
			for (Point point2 : arrayList) {
				sb.append(point2.id + " ");
			}
		}
		System.out.println(sb.toString());
	}

	public static void main(String[] args) {
		new Main().solve();
	}
}

class Point {
	int id, x, y;

	public Point(int id, int x, int y) {
		this.id = id;
		this.x = x;
		this.y = y;
	}
}

class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}

	private int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}

	private void skipUnprintable() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
	}

	public boolean hasNext() {
		skipUnprintable();
		return hasNextByte();
	}

	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public int nextInt() {
		return (int) nextLong();
	}

	public long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
}