CS Academy Round #36 BBox Count

コード

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

public class Main {

  private static final int MAX = 2500;

  // 直線と直線の隙間にある点で作ることが出来る組合せを計算する
  private long intervalCount(ArrayList<Integer> lines, FenwickTree bit) {
    long ans = 0;
    for (int i = -1; i < lines.size(); i++) {
      int x1 = i >= 0 ? lines.get(i) + 1 : 0;
      int x2 = i + 1 < lines.size() ? lines.get(i + 1) : MAX;

      // lines[i] を下辺としたときの上辺の数
      // (lines.get(i), x2)
      if (x2 - x1 >= 2) {
        // (lines.get(i), lines.get(i+1)) の区間の点を選ぶ組み合わせの数
        long k = bit.sum(x1, x2);
        ans += k * (k - 1) / 2;
      }
    }
    return ans;
  }

  private void solve(FastScanner in, PrintWriter out) {
    int N = in.nextInt();
    ArrayList<Integer>[] xs = new ArrayList[MAX];
    for (int i = 0; i < MAX; i++) {
      xs[i] = new ArrayList<>();
    }
    for (int i = 0; i < N; i++) {
      int y = in.nextInt() - 1;
      int x = in.nextInt() - 1;
      xs[y].add(x);
    }

    for (ArrayList<Integer> list : xs) {
      Collections.sort(list);
    }

    long ans = 0;
    for (int left = 0; left < MAX; left++) {
      if (xs[left].isEmpty()) {
        continue;
      }
      boolean[] added = new boolean[MAX];
      FenwickTree bit = new FenwickTree(MAX);
      int addedCount = 0;
      for (int right = left; right < MAX; right++) {
        if (xs[right].isEmpty()) {
          continue;
        }

        for (int x : xs[right]) {
          if (!added[x]) {
            added[x] = true;
            bit.add(x, 1);
            addedCount++;
          }
        }

        if (right == left) {
          continue;
        }

        // xs[right] と xs[left] をマージしてソートしたリストを作る
        ArrayList<Integer> merged = new ArrayList<>(xs[left].size() + xs[right].size());
        for (int i = 0, j = 0; i < xs[left].size() || j < xs[right].size(); ) {
          int leftTop = i < xs[left].size() ? xs[left].get(i) : MAX;
          int rightTop = j < xs[right].size() ? xs[right].get(j) : MAX;

          if (leftTop == rightTop) {
            merged.add(leftTop);
            i++;
            j++;
          } else if (leftTop < rightTop) {
            merged.add(leftTop);
            i++;
          } else {
            merged.add(rightTop);
            j++;
          }
        }

        // 今あるやつ全部
        ans += addedCount * (addedCount - 1) / 2;

        // right が端点とならないものを全て抜く
        ans -= intervalCount(xs[left], bit);

        // left が端点とならないものを全て抜く
        ans -= intervalCount(xs[right], bit);

        // right および left が端点とならないもの (重複して引いた分) を足し込む
        ans += intervalCount(merged, bit);
      }
    }
    out.println(ans);
  }

  class FenwickTree {

    int N;
    long[] data;

    FenwickTree(int N) {
      this.N = N + 1;
      data = new long[N + 1];
    }

    void add(int k, long val) {
      for (int x = k; x < N; x |= x + 1) {
        data[x] += val;
      }
    }

    // [0, k)
    long sum(int k) {
      if (k >= N) {
        k = N - 1;
      }
      long ret = 0;
      for (int x = k - 1; x >= 0; x = (x & (x + 1)) - 1) {
        ret += data[x];
      }
      return ret;
    }

    // [l, r)
    long sum(int l, int r) {
      return sum(r) - sum(l);
    }
  }

  public static void main(String[] args) {
    PrintWriter out = new PrintWriter(System.out);
    new Main().solve(new FastScanner(), out);
    out.close();
  }

  private static class FastScanner {

    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int bufferLength = 0;

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

    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();
    }

    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();
      }
    }

    double nextDouble() {
      return Double.parseDouble(next());
    }

    double[] nextDoubleArray(int n) {
      double[] array = new double[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextDouble();
      }
      return array;
    }

    double[][] nextDoubleMap(int n, int m) {
      double[][] map = new double[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextDoubleArray(m);
      }
      return map;
    }

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

    public int[] nextIntArray(int n) {
      int[] array = new int[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextInt();
      }
      return array;
    }

    public long[] nextLongArray(int n) {
      long[] array = new long[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextLong();
      }
      return array;
    }

    public String[] nextStringArray(int n) {
      String[] array = new String[n];
      for (int i = 0; i < n; i++) {
        array[i] = next();
      }
      return array;
    }

    public char[][] nextCharMap(int n) {
      char[][] array = new char[n][];
      for (int i = 0; i < n; i++) {
        array[i] = next().toCharArray();
      }
      return array;
    }

    public int[][] nextIntMap(int n, int m) {
      int[][] map = new int[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextIntArray(m);
      }
      return map;
    }
  }
}