#[macro_use] mod io { use std::io::*; pub trait Scan { fn scan(sc: &mut Scanner) -> T; } macro_rules! scan_primitive { ($t: ty) => { impl Scan<$t> for $t { fn scan(sc: &mut Scanner) -> $t { sc.next_token().expect("EOF?").parse() .unwrap_or_else(|e| panic!("Cannot parse {}", e)) } } }; ($t: ty, $($u: ty),+) => { scan_primitive!($t); scan_primitive!($($u),+); }; } macro_rules! scan_tuple { ($($t: ident),*) => { impl< $($t: Scan<$t>),* > Scan< ( $($t),* ) > for ( $($t),* ) { fn scan(sc: &mut Scanner) -> ( $($t),* ) { ( $( $t::scan(sc)),* ) } } }; } scan_primitive!(u8, u16, u32, u64, i8, i16, i32, i64, f32, f64, usize, isize, bool, String); scan_tuple!(T, U); scan_tuple!(T, U, V); scan_tuple!(T, U, V, W); #[allow(dead_code)] pub fn cin() -> Scanner { Scanner::new(stdin()) } #[allow(dead_code)] pub struct Scanner { buf: Vec, len: usize, idx: usize, reader: T, } #[allow(dead_code)] impl Scanner { pub fn new(r: Reader) -> Scanner { Scanner { buf: vec![0; 8192], len: 0, idx: 0, reader: r, } } pub fn next>(&mut self) -> T { T::scan::(self) } fn next_token(&mut self) -> Option { let mut res = String::with_capacity(16); while let Some(c) = self.get_u8() { let d = c as char; if !d.is_whitespace() { res.push(d); } else if res.len() != 0 { self.unget_u8(c); break; } } if res.len() == 0 { None } else { Some(res) } } pub fn next_line(&mut self) -> String { self.next_line_wrapped().unwrap() } pub fn next_line_wrapped(&mut self) -> Option { let c = self.get_u8(); if c.is_none() { return None; } let mut line = String::with_capacity(20); line.push(c.unwrap() as char); loop { let c = self.get_u8(); if c.is_none() || c.unwrap() == b'\n' { // コメントはC++等での仕様 // if c.is_some() { // self.unget_u8(b'\n'); // } return Some(line); } line.push(c.unwrap() as char); } } pub fn has_next(&mut self) -> bool { loop { let c = self.get_u8(); if c.is_none() { return false; } let c = c.unwrap(); if !(c as char).is_whitespace() { self.unget_u8(c); return true; } } } fn get_u8(&mut self) -> Option { if self.idx == self.len { match self.reader.read(&mut self.buf[..]) { Ok(l) if l > 0 => { self.idx = 0; self.len = l; } _ => return None, } } self.idx += 1; Some(self.buf[self.idx - 1]) } fn unget_u8(&mut self, c: u8) { self.idx = self.idx - 1; self.buf[self.idx] = c; } } // Output macro_rules! dump { ($($a: expr),+) => {{ use std::io::*; write!(stderr(), "{}:{}\t", file!(), line!()).unwrap(); dump!(A $($a),+); write!(stderr(), " = ").unwrap(); dump!(B $($a),+); writeln!(stderr(), "").unwrap(); }}; (A $x: expr) => { write!(stderr(), "{}", stringify!($x)).unwrap(); }; (A $x: expr, $($y: expr),+) => { write!(stderr(), "{}, ", stringify!($x)).unwrap(); dump!(A $($y),+); }; (B $x: expr) => { write!(stderr(), "{:?}", $x).unwrap(); }; (B $x: expr, $($y: expr),+) => { write!(stderr(), "{:?}, ", $x).unwrap(); dump!(B $($y),+); }; } macro_rules! p { ($x:expr) => { println!("{:.10}", $x); }; ($x:expr, $($y:expr),+) => { print!("{:.10} ", $x); p!($($y),+); }; } } #[allow(unused_imports)] use io::*; #[allow(dead_code)] mod avl_tree { use std; use std::cmp::Ordering::*; use std::fmt::*; type Link = Option>>; pub struct AVLTree { pub root: Link, } impl AVLTree { pub fn new() -> Self { AVLTree { root: None } } pub fn at(&self, k: usize) -> Option<&T> { if let Some(n) = at(&self.root, k) { Some(&n.val) } else { None } } pub fn remove_at(&mut self, k: usize) -> Option { let (root, kth) = remove_at(self.root.take(), k); self.root = root; kth } pub fn merge(&mut self, right: &mut AVLTree) { self.root = merge(self.root.take(), right.root.take()); } pub fn split_at(&mut self, k: usize) -> (AVLTree, AVLTree) { let (left, right) = split_at(self.root.take(), k); (AVLTree { root: left }, AVLTree { root: right }) } } impl AVLTree { pub fn insert(&mut self, val: T) { self.root = insert(self.root.take(), val); } pub fn remove(&mut self, val: &T) -> bool { let (root, flg) = remove(self.root.take(), val); self.root = root; flg } pub fn find(&self, val: &T) -> Option<&T> { if let Some(n) = find(&self.root, &val) { Some(&n.val) } else { None } } pub fn split(&mut self, val: &T) -> (AVLTree, AVLTree) { let (left, right) = split(self.root.take(), val); (AVLTree { root: left }, AVLTree { root: right }) } // get the number of elements which is less than val pub fn count_less(&mut self, val: &T) -> usize { count_less(&self.root, &val) } } impl AVLTree { pub fn check(&self) { if let Some(ref root) = self.root { debug_assert!(balance_factor(&self.root).abs() < 2); root.verify(); } } } #[derive(Debug)] pub struct Node { left: Link, val: T, right: Link, size: usize, height: isize, } impl Node { fn new(val: T) -> Link { Some(Box::new(Node { val: val, left: None, right: None, size: 1, height: 1, })) } #[inline(always)] fn update(&mut self) { self.size = size(&self.left) + size(&self.right) + 1; self.height = std::cmp::max(height(&self.left), height(&self.right)) + 1; } } impl Node { fn verify(&self) { debug_assert_eq!(self.size, size(&self.left) + size(&self.right) + 1); debug_assert_eq!(self.height, std::cmp::max(height(&self.left), height(&self.right)) + 1); debug_assert!(balance_factor(&self.left).abs() < 2); if let Some(ref l) = self.left { debug_assert!(l.val < self.val); l.verify(); } debug_assert!(balance_factor(&self.right).abs() < 2); if let Some(ref r) = self.right { debug_assert!(self.val < r.val); r.verify(); } } } // verified fn insert(n: Link, val: T) -> Link { match n { None => Node::new(val), Some(mut n) => { match val.partial_cmp(&n.val).unwrap() { Less => n.left = insert(n.left.take(), val), Equal => (), // TODO: optional Greater => n.right = insert(n.right.take(), val), } n.update(); balance(Some(n)) } } } // verified fn remove(n: Link, val: &T) -> (Link, bool) { match n { None => (n, false), Some(mut n) => { match val.partial_cmp(&n.val).unwrap() { Less => { let (left, flg) = remove(n.left.take(), val); n.left = left; n.update(); (balance(Some(n)), flg) } Equal => { let (q, r) = (n.left.take(), n.right.take()); match r { None => (q, true), Some(r) => { let (r, mut min) = remove_leftmost(Some(r)); min.left = q; min.right = r; min.update(); (balance(Some(min)), true) } } } Greater => { let (right, flg) = remove(n.right.take(), val); n.right = right; n.update(); (balance(Some(n)), flg) } } } } } // verified // delete the leftmost (minimum) Node from n. returns (modified n, removed Node) fn remove_leftmost(n: Link) -> (Link, Box>) { let mut n = n.unwrap(); match n.left { None => { let right = n.right.take(); n.update(); (right, n) } _ => { let (left, min) = remove_leftmost(n.left.take()); n.left = left; n.update(); (balance(Some(n)), min) } } } // (new n, deleted max) // delete the rightmost (maximum) Node from n. returns (modified n, removed Node) fn remove_rightmost(n: Link) -> (Link, Box>) { let mut n = n.unwrap(); match n.right { None => { let left = n.left.take(); n.update(); (left, n) } _ => { let (right, max) = remove_rightmost(n.right.take()); n.right = right; n.update(); (balance(Some(n)), max) } } } fn merge(left: Link, right: Link) -> Link { match (left, right) { (None, right) => right, (left, None) => left, (mut left, mut right) => { if size(&left) > size(&right) { let (right, x) = remove_leftmost(right.take()); merge_into_left(left, Some(x), right) } else { let (left, x) = remove_rightmost(left.take()); merge_into_right(left, Some(x), right) } } } } // merge left, par, and right. size of par must be one. fn merge3(left: Link, par: Link, right: Link) -> Link { debug_assert!(size(&par) == 1); if size(&left) > size(&right) { merge_into_left(left, par, right) } else { merge_into_right(left, par, right) } } fn merge_into_left(left: Link, par: Link, right: Link) -> Link { debug_assert_eq!(size(&par), 1); debug_assert!(size(&left) >= size(&right)); if height(&left) > height(&right) + 1 { let mut left = left.unwrap(); left.right = merge_into_left(left.right.take(), par, right); left.update(); balance(Some(left)) } else { let mut par = par.unwrap(); par.left = left; par.right = right; par.update(); balance(Some(par)) } } fn merge_into_right(left: Link, par: Link, right: Link) -> Link { debug_assert_eq!(size(&par), 1); debug_assert!(size(&left) <= size(&right)); if height(&left) + 1 < height(&right) { let mut right = right.unwrap(); right.left = merge_into_right(left, par, right.left.take()); right.update(); balance(Some(right)) } else { let mut par = par.unwrap(); par.left = left; par.right = right; par.update(); balance(Some(par)) } } fn split(n: Link, val: &T) -> (Link, Link) { match n { None => (None, None), Some(mut n) => { let (l, r) = (n.left.take(), n.right.take()); n.update(); match val.partial_cmp(&n.val).unwrap() { Less => { let (ll, lr) = split(l, val); (ll, merge3(lr, Some(n), r)) } Equal => (l, merge(Some(n), r)), Greater => { let (rl, rr) = split(r, val); (merge3(l, Some(n), rl), rr) } } } } } // verified fn split_at(n: Link, k: usize) -> (Link, Link) { debug_assert!(k <= size(&n)); match n { None => (None, None), Some(mut n) => { let (l, r) = (n.left.take(), n.right.take()); n.update(); let sl = size(&l); match k.cmp(&sl) { Less => { let (ll, lr) = split_at(l, k); (ll, merge3(lr, Some(n), r)) } Equal => (l, merge(Some(n), r)), Greater => { let (rl, rr) = split_at(r, k - sl - 1); (merge3(l, Some(n), rl), rr) } } } } } fn find<'a, T: PartialOrd>(n: &'a Link, val: &T) -> Option<&'a Node> { match *n { None => None, Some(ref n) => { match val.partial_cmp(&n.val).unwrap() { Less => find(&n.left, val), Equal => Some(n), Greater => find(&n.right, val), } } } } // verified fn at(n: &Link, k: usize) -> Option<&Node> { match *n { None => None, Some(ref n) => { let ls = size(&n.left); match k.cmp(&ls) { Less => at(&n.left, k), Equal => Some(n), Greater => at(&n.right, k - ls - 1), } } } } // verified fn remove_at(n: Link, k: usize) -> (Link, Option) { match n { None => (n, None), Some(mut n) => { match k.cmp(&size(&n.left)) { Less => { let (left, kth) = remove_at(n.left.take(), k); n.left = left; n.update(); (balance(Some(n)), kth) } Equal => { let (q, r) = (n.left.take(), n.right.take()); match r { None => (q, Some(n.val)), Some(r) => { let (r, mut min) = remove_leftmost(Some(r)); min.left = q; min.right = r; min.update(); (balance(Some(min)), Some(n.val)) } } } Greater => { let sl = size(&n.left); let (right, kth) = remove_at(n.right.take(), k - sl - 1); n.right = right; n.update(); (balance(Some(n)), kth) } } } } } fn count_less(n: &Link, val: &T) -> usize { match *n { None => 0, Some(ref n) => { let sl = size(&n.left); match val.partial_cmp(&n.val).unwrap() { Less => count_less(&n.left, val), Equal => sl, Greater => sl + 1 + count_less(&n.right, val), } } } } // verified fn balance(n: Link) -> Link { match balance_factor(&n) { -1 | 0 | 1 => n, 2 => { let mut n = n.unwrap(); if balance_factor(&n.right) < 0 { n.right = rotate_right(n.right.take()); } rotate_left(Some(n)) } -2 => { let mut n = n.unwrap(); if balance_factor(&n.left) > 0 { n.left = rotate_left(n.left.take()); } rotate_right(Some(n)) } _ => panic!(), } } // verified #[inline(always)] fn rotate_left(q: Link) -> Link { let mut q = q.unwrap(); let mut p = q.right.take().unwrap(); q.right = p.left.take(); q.update(); p.left = Some(q); p.update(); Some(p) } // verified #[inline(always)] fn rotate_right(p: Link) -> Link { let mut p = p.unwrap(); let mut q = p.left.take().unwrap(); p.left = q.right.take(); p.update(); q.right = Some(p); q.update(); Some(q) } // verified #[inline(always)] fn size(n: &Link) -> usize { match *n { None => 0, Some(ref n) => n.size, } } // verified #[inline(always)] fn height(n: &Link) -> isize { match *n { None => 0, Some(ref n) => n.height, } } // verified #[inline(always)] fn balance_factor(n: &Link) -> isize { match *n { None => panic!(), Some(ref n) => height(&n.right) - height(&n.left), } } // verified pub fn insert_ms(n: Link, x: T) -> Link { let (l, r) = split(n, &x); merge3(l, Node::new(x), r) } // verified pub fn remove_at_ms(n: Link, k: usize) -> (Link, Option) { if k < size(&n) { let (l, r) = split_at(n, k); let (right, kth) = remove_leftmost(r); (merge(l, right), Some(kth.val)) } else { (n, None) } } // verified pub fn remove_ms(n: Link, val: &T) -> (Link, bool) { if find(&n, &val).is_some() { let (l, r) = split(n, val); let (right, _) = remove_leftmost(r); (merge(l, right), true) } else { (n, false) } } } fn main() { use avl_tree::*; let mut sc = cin(); while sc.has_next() { let n = sc.next(); let mut t = AVLTree::<(i32, usize)>::new(); let mut x = 0; for i in 0..n { let a = -sc.next::(); if x == 0 { x = a; } t.insert((a, i)); p!(t.count_less(&(x, 0)) + 1); } } }