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; } } }