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Codeforces Round #390 (Div. 2) D. Fedor and coupons

問題

http://codeforces.com/contest/754/problem/D

[l, r] のような範囲の組が N 個あります。このうちK個を選び、K個すべてが重なる範囲を最大にしたいです。最大値と、その時選ぶ範囲のidを出力してください。

解法

非想定解法っぽい Treap

コード

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.Random;

public class D {
  private void solve(FastScanner in, PrintWriter out) {
    int N = in.nextInt();
    int K = in.nextInt();

    long[] l = new long[N];
    long[] r = new long[N];
    long min = 0;
    for (int i = 0; i < N; i++) {
      l[i] = in.nextInt();
      r[i] = in.nextInt();
      min = Math.min(min, l[i]);
    }
    for (int i = 0; i < N; i++) {
      l[i] -= min;
      r[i] -= min;
      l[i] = l[i] * 2 * N + i;
      r[i] = r[i] * 2 * N + i + N;
    }

    long[][] events = new long[2 * N][2];
    for (int i = 0; i < N; i++) {
      events[2 * i][0] = l[i];
      events[2 * i][1] = i;
      events[2 * i + 1][0] = r[i];
      events[2 * i + 1][1] = -i - 1;
    }
    Arrays.sort(events, (o1, o2) -> {
      if (o1[0] == o2[0]) return Long.compare(o1[1], o2[1]);
      return Long.compare(o1[0], o2[0]);
    });

    Treap treap = new Treap();
    long from = -1;
    long max = 0;
    long[] range = null;
    int coupons = 0;
    for (long[] e : events) {
      int i = (int) e[1];
      if (i >= 0) {
        coupons++;
        treap.insert(l[i]);
        if (coupons == K) {
          from = l[i] / (2 * N);
        }
      } else {
        i = -(i + 1);
        long tr = r[i] / (2 * N);
        long tl = l[i] / (2 * N);
        if (tl <= from && coupons >= K) {
          long curRange = tr - from + 1;
          if (max < curRange) {
            max = curRange;
            range = new long[]{from, tr};
          }
          treap.erase(l[i]);
          if (coupons > K) {
            long kth = treap.rank(K - 1);
            from = kth / (2 * N);
          }
        } else {
          treap.erase(l[i]);
        }
        coupons--;
      }
    }
    out.println(max);
    if (max == 0) {
      for (int i = 0; i < K; i++) {
        out.print((i + 1) + " ");
      }
      out.println();
      return;
    }

    for (int i = 0; i < N; i++) {
      long L = l[i] / (2 * N);
      long R = r[i] / (2 * N);
      if (L <= range[0] && range[1] <= R) {
        out.print((i + 1) + " ");
        K--;
        if (K == 0) break;
      }
    }
    out.println();
  }

  public class Treap {
    Random random = new Random();

    private class Node {
      Node left, right;
      long key;
      int priority;
      int count;

      Node(long key) {
        this.key = key;
        priority = random.nextInt();
        left = null;
        right = null;
        count = 1;
      }
    }

    private Node root = null;

    public void clear() {
      root = null;
    }

    public boolean isEmpty() {
      return count(root) == 0;
    }

    private int count(Node n) {
      return n == null ? 0 : n.count;
    }

    private void update(Node c) {
      c.count = 1 + count(c.left) + count(c.right);
    }

    private Node leftRotate(Node c) {
      Node r = c.right;
      c.right = r.left;
      r.left = c;
      update(c);
      return r;
    }

    private Node rightRotate(Node c) {
      Node l = c.left;
      c.left = l.right;
      l.right = c;
      update(c);
      return l;
    }

    private Node insert(Node c, long key) {
      if (c == null) return new Node(key);
      if (c.key < key) {
        c.right = insert(c.right, key);
        if (c.right.priority < c.priority) c = leftRotate(c);
      } else {
        c.left = insert(c.left, key);
        if (c.left.priority < c.priority) c = rightRotate(c);
      }
      update(c);
      return c;
    }

    private Node getMinNode(Node c) {
      while (c.left != null) c = c.left;
      return c;
    }

    private Node erase(Node c, long key) {
      if (key == c.key) {
        if (c.left == null) return c.right;
        if (c.right == null) return c.left;

        Node minNode = getMinNode(c.right);
        c.key = minNode.key;
        c.right = erase(c.right, minNode.key);
      } else {
        if (c.key < key) c.right = erase(c.right, key);
        else c.left = erase(c.left, key);
      }
      update(c);
      return c;
    }

    public void insert(long key) {
      if (contains(key)) return;
      root = insert(root, key);
    }

    public void erase(long key) {
      root = erase(root, key);
    }

    public int size() {
      return count(root);
    }

    public boolean contains(long key) {
      return find(root, key) >= 0;
    }

    public int find(long key) {
      return find(root, key);
    }

    private int find(Node c, long key) {
      if (c == null) return -1;
      if (c.key == key) return count(c.left);
      if (key < c.key) return find(c.left, key);
      int pos = find(c.right, key);
      if (pos < 0) return pos;
      return count(c.left) + 1 + pos;
    }

    private Node rank(Node c, int rank) {
      while (c != null) {
        int leftCount = count(c.left);
        if (leftCount == rank) return c;
        if (leftCount < rank) {
          rank -= leftCount + 1;
          c = c.right;
        } else {
          c = c.left;
        }
      }
      return null;
    }

    public long rank(int rank) {
      if (root == null)
        throw new NullPointerException();
      Node r = rank(root, rank);
      if (r == null)
        throw new NullPointerException();
      return r.key;
    }

  }

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