#[doc = " https://github.com/hatoo/competitive-rust-snippets"] #[allow(unused_imports)] use std::cmp::{max, min, Ordering}; #[allow(unused_imports)] use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque}; #[allow(unused_imports)] use std::io::{stdin, stdout, BufWriter, Write}; #[allow(unused_imports)] use std::iter::FromIterator; #[allow(unused_macros)] macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } } #[macro_export] macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut parser = Parser :: from_str ( $ s ) ; input_inner ! { parser , $ ( $ r ) * } } ; ( parser = $ parser : ident , $ ( $ r : tt ) * ) => { input_inner ! { $ parser , $ ( $ r ) * } } ; ( new_stdin_parser = $ parser : ident , $ ( $ r : tt ) * ) => { let stdin = std :: io :: stdin ( ) ; let reader = std :: io :: BufReader :: new ( stdin . lock ( ) ) ; let mut $ parser = Parser :: new ( reader ) ; input_inner ! { $ parser , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { input ! { new_stdin_parser = parser , $ ( $ r ) * } } ; } #[macro_export] macro_rules ! input_inner { ( $ parser : ident ) => { } ; ( $ parser : ident , ) => { } ; ( $ parser : ident , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ parser , $ t ) ; input_inner ! { $ parser $ ( $ r ) * } } ; } #[macro_export] macro_rules ! read_value { ( $ parser : ident , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ parser , $ t ) ) ,* ) } ; ( $ parser : ident , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ parser , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ parser : ident , chars ) => { read_value ! ( $ parser , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ parser : ident , usize1 ) => { read_value ! ( $ parser , usize ) - 1 } ; ( $ parser : ident , $ t : ty ) => { $ parser . next ::<$ t > ( ) . expect ( "Parse error" ) } ; } use std::io; use std::io::BufRead; use std::str; pub struct Parser { reader: R, buf: Vec, pos: usize, } impl Parser { pub fn from_str(s: &str) -> Parser { Parser { reader: io::empty(), buf: s.as_bytes().to_vec(), pos: 0, } } } impl Parser { pub fn new(reader: R) -> Parser { Parser { reader: reader, buf: vec![], pos: 0, } } pub fn update_buf(&mut self) { self.buf.clear(); self.pos = 0; loop { let (len, complete) = { let buf2 = self.reader.fill_buf().unwrap(); self.buf.extend_from_slice(buf2); let len = buf2.len(); if len == 0 { break; } (len, buf2[len - 1] <= 0x20) }; self.reader.consume(len); if complete { break; } } } pub fn next(&mut self) -> Result { loop { let mut begin = self.pos; while begin < self.buf.len() && (self.buf[begin] <= 0x20) { begin += 1; } let mut end = begin; while end < self.buf.len() && (self.buf[end] > 0x20) { end += 1; } if begin != self.buf.len() { self.pos = end; return str::from_utf8(&self.buf[begin..end]).unwrap().parse::(); } else { self.update_buf(); } } } } #[allow(unused_macros)] macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } } #[doc = " https://github.com/hatoo/competitive-rust-snippets"] const BIG_STACK_SIZE: bool = true; #[allow(dead_code)] fn main() { use std::thread; if BIG_STACK_SIZE { thread::Builder::new() .stack_size(32 * 1024 * 1024) .name("solve".into()) .spawn(solve) .unwrap() .join() .unwrap(); } else { solve(); } } fn solve() { input!{ N:usize, a:[usize;N], Q:usize, x:[usize;Q], } let mut set = skiplist::Multiset::new(); let mut sum = 0; for i in 0..N { sum+=a[i]; set.insert(a[i]); } for i in 0..Q { let xi=x[i]; // xi以上のものを集める let geit=set.unwrap().ge_iter(&xi); let mut biggers = vec![]; for g in geit { for _ in 0..set.counting(&g) { biggers.push(g); } } // 消去する for &b in &biggers { set.remove(&b); } let mut pushback=vec![]; let mut diff = 0; for &b in &biggers { assert!(b.clone()>=xi); let newv = b%xi; diff+=b-newv; pushback.push(newv); } sum-=diff; println!("{}",sum); for p in pushback { set.insert(p); } } } mod skiplist { use std; use std::collections::{BTreeMap, BTreeSet}; use std::rc::Rc; use std::cell::{Cell, RefCell}; // use std::ops::RangeBounds; use std::fmt; struct RandGen { x: u64, } impl RandGen { fn new(seed: u64) -> RandGen { RandGen { x: seed, } } fn next(&mut self) -> u64 { const a: u64 = 1103515245; const b: u64 = 12345; const m: u64 = 1<<32; self.x = (a*self.x+b)%m; self.x } } pub struct Skiplist { max_height: Option, left_sentinel: Rc>>, right_sentinel: Rc>>, rand_gen: RandGen, traverse_stat: Cell, connect_stat: Cell, } impl Skiplist { fn print_graph(&self) { for level in (0..self.height()).rev() { let mut line=vec![]; let mut cur = self.left_sentinel.clone(); loop { let next0 = cur.borrow().next[level].clone(); let next = next0.unwrap().clone(); if next.borrow().value.is_none() { break; } else { cur = next.clone(); let v = cur.borrow().value.clone().unwrap(); line.push(v); } } let mut ss = vec![]; for x in line { while ss.len() < x { ss.push("--".to_string()); } ss.push(format!("{:>02}", x)); } println!("{}",ss.connect(",")); } println!(""); } } impl Skiplist where T: std::cmp::Ord + fmt::Debug + Clone { pub fn new() -> Skiplist { let left_sentinel = Rc::new(RefCell::new(SkipNode::sentinel())); let right_sentinel = Rc::new(RefCell::new(SkipNode::sentinel())); let sentinel_height = left_sentinel.borrow().height(); for level in 0..sentinel_height { left_sentinel.borrow_mut().next[level] = Some(right_sentinel.clone()); right_sentinel.borrow_mut().prev[level] = Some(left_sentinel.clone()); } Skiplist { max_height: None, left_sentinel: left_sentinel, right_sentinel: right_sentinel, rand_gen: RandGen::new(0), traverse_stat: Cell::new(0), connect_stat: Cell::new(0), } } fn height(&self) -> usize { self.max_height.unwrap_or(33) } fn pick_height(&mut self) -> usize { let z = self.rand_gen.next(); let mut k = 0; let mut m = 1; while z&m!=0 { k+=1; m<<=1; } k+1 } pub fn insert(&mut self, x: T) -> bool { let mut paths = self.traverse(&x); // println!("insert {:?}: {:?}", x, &paths); if !paths.is_empty() { let next0 = paths[0].borrow().next[0].clone(); let next = next0.unwrap(); let found = next.borrow().value.as_ref() == Some(&x); if found { return false; } } let new_height = self.pick_height(); self.max_height = Some(std::cmp::max(self.max_height.unwrap_or(0), new_height)); while paths.len() < new_height { paths.push(self.left_sentinel.clone()); } let new_node = Rc::new(RefCell::new(SkipNode::new(x, new_height))); for level in 0..new_height { let prev = &paths[level]; self.connect_stat.set(self.connect_stat.get()+1); SkipNode::connect(prev, &new_node, level); } true } fn find_node(&self, x: &T) -> Option>>> { let paths = self.traverse(x); // println!("find {:?}: {:?}", x, &paths); if paths.is_empty() { return None } let next0 = paths[0].borrow().next[0].clone(); let next = next0.unwrap(); if next.borrow().value.as_ref() == Some(x) { Some(next) } else { None } } pub fn find(&self, x: &T) -> bool { self.find_node(x).is_some() } pub fn reset_stat(&self) { self.traverse_stat.set(0); self.connect_stat.set(0); } pub fn show_stat(&self) { println!("traverse: {}", self.traverse_stat.get()); println!("connect: {}", self.connect_stat.get()); } fn traverse(&self, x: &T) -> Vec>>> { if self.height() == 0 { return vec![] } let mut cur = self.left_sentinel.clone(); let mut acc = vec![self.left_sentinel.clone(); self.height()]; let mut level = self.height() - 1; loop { if level == 0 { loop { acc[level] = cur.clone(); let next0 = cur.borrow().next[level].clone(); let next = next0.unwrap(); if next.borrow().value.is_none() || next.borrow().value.as_ref().unwrap() >= x { break; } else { cur = next.clone(); self.traverse_stat.set(self.traverse_stat.get()+1); } } break; } let next0 = cur.borrow().next[level].clone(); let next = next0.unwrap(); if next.borrow().value.is_none() || next.borrow().value.as_ref().unwrap() >= x { acc[level] = cur.clone(); level -= 1; continue; } else { cur = next; self.traverse_stat.set(self.traverse_stat.get()+1); } } acc } fn traverse_rev(&self, x: &T) -> Vec>>> { if self.height() == 0 { return vec![] } let mut cur = self.right_sentinel.clone(); let mut acc = vec![self.right_sentinel.clone(); self.height()]; let mut level = self.height() - 1; loop { if level == 0 { loop { acc[level] = cur.clone(); let next = cur.borrow().prev[level].clone().unwrap(); if next.borrow().value.is_none() || next.borrow().value.as_ref().unwrap() <= x { break; } else { cur = next.clone(); } } break; } let next = cur.borrow().prev[level].clone().unwrap(); if next.borrow().value.is_none() || next.borrow().value.as_ref().unwrap() <= x { acc[level] = cur.clone(); level -= 1; continue; } else { cur = next; } } acc } pub fn remove(&mut self, x: &T) -> bool { let node = self.find_node(x); if node.is_none() { return false } let node = node.unwrap(); node.borrow_mut().remove(); true } #[doc = "iterator in range [x,]"] pub fn ge_iter(&self, x: &T) -> Range { let f = self.traverse(x)[0].clone(); Range { forward: true, f: f, b: self.right_sentinel.clone(), } } #[doc = "iterator in range [,x]"] pub fn le_iter(&self, x: &T) -> Range { let b = self.traverse_rev(x)[0].clone(); Range { forward: false, f: self.left_sentinel.clone(), b: b, } } #[doc = "iterator in range [..]"] pub fn iter(&self) -> Range { Range { forward: true, f: self.left_sentinel.clone(), b: self.right_sentinel.clone(), } } } pub struct Range { forward: bool, f: Rc>>, b: Rc>>, } impl Iterator for Range { type Item = T; fn next(&mut self) -> Option { let next0 = if self.forward { self.f.borrow().next[0].clone() } else { self.b.borrow().prev[0].clone() }; if next0.is_none() { return None } let next = next0.unwrap(); if self.forward { self.f = next; self.f.borrow().value.clone() } else { self.b = next; self.b.borrow().value.clone() } } } impl DoubleEndedIterator for Range { fn next_back(&mut self) -> Option { let next0 = if self.forward { self.b.borrow().prev[0].clone() } else { self.f.borrow().next[0].clone() }; if next0.is_none() { return None } let next = next0.unwrap(); if self.forward { self.b = next; self.b.borrow().value.clone() } else { self.f = next; self.f.borrow().value.clone() } } } impl fmt::Debug for Skiplist where T: fmt::Debug + Clone + std::cmp::Ord { fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { let v: Vec = self.iter().collect(); writeln!(f, "{:?}", v); Ok(()) } } struct SkipNode { value: Option, prev: Vec>>>>, next: Vec>>>>, } impl fmt::Debug for SkipNode where T: fmt::Debug + std::cmp::Ord { fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { writeln!(f, "{:?}, {:?}", self.value, self.height()); Ok(()) } } impl SkipNode where T: std::cmp::Ord + fmt::Debug { fn sentinel() -> SkipNode { SkipNode { value: None, prev: vec![None; 33], next: vec![None; 33], } } fn new(value: T, height: usize) -> SkipNode { SkipNode { value: Some(value), prev: vec![None; height], next: vec![None; height], } } fn height(&self) -> usize { self.next.len() } fn remove(&mut self) { for level in 0..self.height() { let prev_node = self.prev[level].clone().unwrap(); let next_node = self.next[level].clone().unwrap(); next_node.borrow_mut().prev[level] = Some(prev_node.clone()); prev_node.borrow_mut().next[level] = Some(next_node.clone()); } } // x -> z => x -> y -> z // z = some or none fn connect(x: &Rc>, y: &Rc>, level: usize) { let x_next = x.borrow().next[level].clone().unwrap(); x.borrow_mut().next[level] = Some(y.clone()); y.borrow_mut().prev[level] = Some(x.clone()); y.borrow_mut().next[level] = Some(x_next.clone()); x_next.borrow_mut().prev[level] = Some(y.clone()); } } #[test] fn test_iter() { let mut sl = Skiplist::new(); for i in 1..6 { sl.insert(i); } for x in sl.iter() { println!("{}",x); } // for x in sl.iter().rev() { // println!("{}",x); // } for x in sl.ge_iter(&2) { println!("{}",x); } // for x in sl.ge_iter(&2).rev() { // println!("{}",x); // } for x in sl.le_iter(&2) { println!("{}",x); } // for x in sl.le_iter(&2).rev() { // println!("{}",x); // } } #[test] fn test_pick_height() { let mut sl = Skiplist::::new(); let mut cnt = vec![0;60]; for _ in 0..1_000 { cnt[sl.pick_height()] += 1; } println!("{:?}",cnt); } #[test] fn test_insert() { let mut s = Skiplist::new(); assert_eq!(s.find(&10), false); s.insert(10); assert_eq!(s.find(&8), false); assert_eq!(s.find(&10), true); } #[test] fn test_debug0() { let mut s = Skiplist::new(); let mut data = vec![920,265,659]; for x in data { s.insert(x); assert!(s.find(&x)); } s.insert(660); dbg!(&s); assert!(s.find(&660)); } #[test] fn test_debug1() { let mut s = Skiplist::new(); s.insert(0); assert!(s.find(&0)); s.insert(5); assert!(s.find(&5)); } #[test] fn test_debug2() { let mut s = Skiplist::new(); s.insert(0); s.insert(5); s.print_graph(); s.insert(9); s.print_graph(); assert_eq!(s.find(&5),true); s.remove(&4); assert_eq!(s.find(&5),true); s.remove(&5); s.print_graph(); assert_eq!(s.find(&5),false); s.remove(&9); s.print_graph(); assert_eq!(s.find(&9),false); assert_eq!(s.find(&0),true); } #[test] fn test_compare_reference_insert_and_find() { use rand::{Rng, SeedableRng, StdRng}; let mut rng = StdRng::from_seed(&[3, 2, 1]); let mut ts = BTreeSet::new(); let mut sl = Skiplist::new(); let size = 10000; let mut data1 = vec![]; for _ in 0..size { let x = rng.next_u64()%size; data1.push(x as usize); } let mut data2 = vec![]; for _ in 0..size { let x = rng.next_u64()%size; data2.push(x as usize); } let mut data3 = vec![]; for _ in 0..size { let x = rng.next_u64()%size; data3.push(x as usize); } println!("insert and find phase"); for x in data1 { // dbg!(x); ts.insert(x); sl.insert(x); assert_eq!(sl.find(&x), ts.contains(&x)); // sl.print_graph(); } sl.print_graph(); println!("find phase"); for x in data2 { assert_eq!(sl.find(&x), ts.contains(&x)); } println!("remove phase"); for x in data3 { assert_eq!(sl.remove(&x), ts.remove(&x)); assert_eq!(sl.find(&x), ts.contains(&x)); } } #[test] fn test_skiplist_stat() { use rand::{Rng, SeedableRng, StdRng}; let size = 1000; let mut rng = StdRng::from_seed(&[3, 2, 1]); let mut s = Skiplist::new(); println!("insert"); for _ in 0..size { s.insert(rng.next_u64()); } s.show_stat(); s.reset_stat(); println!("connect"); for _ in 0..size { s.find(&rng.next_u64()); } s.show_stat(); } #[bench] fn bench_skiplist_insert_random(b: &mut test::Bencher) { use rand::{Rng, SeedableRng, StdRng}; let size = 10000; let mut s = Skiplist::new(); let mut rng = StdRng::from_seed(&[3, 2, 1]); b.iter(|| for _ in 0..size { s.insert(rng.next_u64()); } ); } #[bench] fn bench_skiplist_find_random(b: &mut test::Bencher) { use rand::{Rng, SeedableRng, StdRng}; let size = 10000; let mut s = Skiplist::new(); let mut rng = StdRng::from_seed(&[3, 2, 1]); for _ in 0..size { s.insert(rng.next_u64()); } b.iter(|| for _ in 0..size { s.find(&rng.next_u64()); } ); } #[bench] fn bench_skiplist_insert_forward(b: &mut test::Bencher) { let mut s = Skiplist::new(); let size = 10000; let mut data = vec![]; for i in 0..size { data.push(i); } b.iter(|| for &x in &data { s.insert(x); } ); } #[bench] fn bench_skiplist_insert_reverse(b: &mut test::Bencher) { let mut s = Skiplist::new(); let size = 10000; let mut data = vec![]; for i in 0..size { data.push(i); } data.reverse(); b.iter(|| for &x in &data { s.insert(x); } ); } #[bench] fn bench_skiplist_connect_simple(b: &mut test::Bencher) { let left=Rc::new(RefCell::new(SkipNode::new(0,2))); let right=Rc::new(RefCell::new(SkipNode::new(10000000,2))); for l in 0..2 { left.borrow_mut().next[l]=Some(right.clone()); right.borrow_mut().prev[l]=Some(left.clone()); } let mut data = vec![]; for i in 0..10000 { let n=Rc::new(RefCell::new(SkipNode::new(i+1,2))); data.push(n) } b.iter(|| for n in &data { for l in 0..2 { SkipNode::connect(&left, n, l); } } ) } #[bench] fn bench_skiplist_connect_random(b: &mut test::Bencher) { use rand::{Rng, SeedableRng, StdRng}; let mut rng = StdRng::from_seed(&[3, 2, 1]); let left=Rc::new(RefCell::new(SkipNode::new(0,2))); let right=Rc::new(RefCell::new(SkipNode::new(10000000,2))); for l in 0..2 { left.borrow_mut().next[l]=Some(right.clone()); right.borrow_mut().prev[l]=Some(left.clone()); } let mut prev_cands = vec![left.clone()]; let mut data = vec![]; for i in 0..10000 { let n=Rc::new(RefCell::new(SkipNode::new(i+1,2))); let i=rng.next_u64() as usize % prev_cands.len(); let prev = prev_cands[i].clone(); data.push((prev,n.clone())); prev_cands.push(n.clone()); } b.iter(|| for (prev,n) in &data { for l in 0..2 { SkipNode::connect(&prev, &n, l); } } ) } #[bench] fn bench_skiplist_alloc_new_node(b: &mut test::Bencher) { b.iter(|| for _ in 0..10000 { Rc::new(RefCell::new(SkipNode::new(0,2))); } ) } #[bench] fn bench_skiplist_pick_height(b: &mut test::Bencher) { let mut sl=Skiplist::::new(); b.iter(|| for _ in 0..10000 { sl.pick_height(); } ) } #[bench] fn bench_btree_insert_random(b: &mut test::Bencher) { use rand::{Rng, SeedableRng, StdRng}; let size = 10000; let mut s = BTreeSet::new(); let mut rng = StdRng::from_seed(&[3, 2, 1]); b.iter(|| for _ in 0..size { s.insert(rng.next_u64()); } ); } #[bench] fn bench_btree_find_random(b: &mut test::Bencher) { use rand::{Rng, SeedableRng, StdRng}; let size = 10000; let mut s = BTreeSet::new(); let mut rng = StdRng::from_seed(&[3, 2, 1]); for _ in 0..size { s.insert(rng.next_u64()); } b.iter(|| for _ in 0..size { s.contains(&rng.next_u64()); } ); } use std::collections::HashMap; pub struct Multiset { sl: Skiplist, counting: HashMap, } impl Multiset where T: Ord + fmt::Debug + Clone + std::hash::Hash { pub fn new() -> Multiset { Multiset { sl: Skiplist::new(), counting: HashMap::new(), } } pub fn insert(&mut self, x: T) { self.sl.insert(x.clone()); *self.counting.entry(x).or_insert(0) += 1; } pub fn counting(&self, x: &T) -> usize { self.counting.get(x).cloned().unwrap_or(0) } pub fn remove(&mut self, x: &T) -> bool { let cnt = self.counting(x); if cnt == 0 { return false } if cnt >= 2 { *self.counting.get_mut(x).unwrap() -= 1; } else if cnt == 1 { self.counting.remove(x); self.sl.remove(x); } return true } pub fn unwrap(&self) -> &Skiplist { &self.sl } } #[test] fn test_multiset() { let mut s = Multiset::new(); assert_eq!(s.counting(&1),0); s.insert(1); assert_eq!(s.counting(&1),1); s.insert(1); assert_eq!(s.counting(&1),2); assert!(s.remove(&1)); assert_eq!(s.unwrap().ge_iter(&1).next().unwrap(),1); assert_eq!(s.counting(&1),1); assert!(s.remove(&1)); assert_eq!(s.counting(&1),0); assert_eq!(s.unwrap().ge_iter(&1).next(),None); } }