#![allow(unused_imports)] use std::cmp::*; use std::collections::*; use std::io::Write; use std::ops::Bound::*; #[allow(unused_macros)] macro_rules! debug { ($($e:expr),*) => { #[cfg(debug_assertions)] $({ let (e, mut err) = (stringify!($e), std::io::stderr()); writeln!(err, "{} = {:?}", e, $e).unwrap() })* }; } fn main() { let v = read_vec::(); let (n, q) = (v[0], v[1]); let a = read_vec::(); let mut queries = vec![]; for _ in 0..q { let v = read_vec::(); let (t, l, r) = (v[0], v[1], v[2]); queries.push((t, l, r)); } let mut accum = vec![0; n + 1]; for i in 0..n { accum[i + 1] = accum[i] + a[i]; } let mut seg = LazySegtree::::new(n + 2); seg.apply_range(0, n + 1, 0); seg.apply_range(1, n + 1, 1); /* for i in 1..=n { debug!(get_index1(i, n, &mut seg)); debug!(get_index2(i, n, &mut seg)); } seg.apply_range(3, 3 + 1, 0); for i in 1..n { debug!(get_index1(i, n, &mut seg)); debug!(get_index2(i, n, &mut seg)); } */ for (t, l, r) in queries { let l = get_index1(l, n, &mut seg); let r = get_index2(r, n, &mut seg) - 1; // debug!((l, r)); if t == 1 { seg.apply_range(l + 1, r + 1, 0); } else { let ans = accum[r] - accum[l - 1]; println!("{}", ans); } } } fn get_index1(x: usize, n: usize, seg: &mut LazySegtree) -> usize { let (ok, ng) = binary_search(0, n + 2, |mid: usize| seg.prod(0, mid).0 < x as i64); ok } fn get_index2(x: usize, n: usize, seg: &mut LazySegtree) -> usize { let (ok, ng) = binary_search(0, n + 2, |mid: usize| seg.prod(0, mid).0 < x as i64); ng } fn read() -> T { let mut s = String::new(); std::io::stdin().read_line(&mut s).ok(); s.trim().parse().ok().unwrap() } fn read_vec() -> Vec { read::() .split_whitespace() .map(|e| e.parse().ok().unwrap()) .collect() } type Input = usize; fn binary_search(lb: Input, ub: Input, mut criterion: F) -> (Input, Input) where F: FnMut(Input) -> bool, { assert_eq!(criterion(lb), true); assert_eq!(criterion(ub), false); let mut ok = lb; let mut ng = ub; while ng - ok > 1 { let mid = (ng + ok) / 2; if criterion(mid) { ok = mid; } else { ng = mid; } } (ok, ng) } pub struct Additive2; impl Monoid for Additive2 { type S = (i64, i64); fn identity() -> Self::S { (0, 1) } fn binary_operation(a: &Self::S, b: &Self::S) -> Self::S { (a.0 + b.0, a.1 + b.1) } } struct AdditiveUpdate; impl MapMonoid for AdditiveUpdate { type M = Additive2; type F = i64; fn identity_map() -> Self::F { std::i64::MAX } fn mapping(&f: &i64, &x: &(i64, i64)) -> (i64, i64) { if f == std::i64::MAX { return x; } (f * x.1, x.1) } fn composition(&f: &i64, &g: &i64) -> i64 { if f == std::i64::MAX { return g; } f } } //https://github.com/rust-lang-ja/ac-library-rs pub mod internal_bit { // Skipped: // // - `bsf` = `__builtin_ctz`: is equivalent to `{integer}::trailing_zeros` #[allow(dead_code)] pub(crate) fn ceil_pow2(n: u32) -> u32 { 32 - n.saturating_sub(1).leading_zeros() } #[cfg(test)] mod tests { #[test] fn ceil_pow2() { // https://github.com/atcoder/ac-library/blob/2088c8e2431c3f4d29a2cfabc6529fe0a0586c48/test/unittest/bit_test.cpp assert_eq!(0, super::ceil_pow2(0)); assert_eq!(0, super::ceil_pow2(1)); assert_eq!(1, super::ceil_pow2(2)); assert_eq!(2, super::ceil_pow2(3)); assert_eq!(2, super::ceil_pow2(4)); assert_eq!(3, super::ceil_pow2(5)); assert_eq!(3, super::ceil_pow2(6)); assert_eq!(3, super::ceil_pow2(7)); assert_eq!(3, super::ceil_pow2(8)); assert_eq!(4, super::ceil_pow2(9)); assert_eq!(30, super::ceil_pow2(1 << 30)); assert_eq!(31, super::ceil_pow2((1 << 30) + 1)); assert_eq!(32, super::ceil_pow2(u32::max_value())); } } } pub mod internal_type_traits { use std::{ fmt, iter::{Product, Sum}, ops::{ Add, AddAssign, BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Div, DivAssign, Mul, MulAssign, Not, Rem, RemAssign, Shl, ShlAssign, Shr, ShrAssign, Sub, SubAssign, }, }; // Skipped: // // - `is_signed_int_t` (probably won't be used directly in `modint.rs`) // - `is_unsigned_int_t` (probably won't be used directly in `modint.rs`) // - `to_unsigned_t` (not used in `fenwicktree.rs`) /// Corresponds to `std::is_integral` in C++. // We will remove unnecessary bounds later. // // Maybe we should rename this to `PrimitiveInteger` or something, as it probably won't be used in the // same way as the original ACL. pub trait Integral: 'static + Send + Sync + Copy + Ord + Not + Add + Sub + Mul + Div + Rem + AddAssign + SubAssign + MulAssign + DivAssign + RemAssign + Sum + Product + BitOr + BitAnd + BitXor + BitOrAssign + BitAndAssign + BitXorAssign + Shl + Shr + ShlAssign + ShrAssign + fmt::Display + fmt::Debug + fmt::Binary + fmt::Octal + Zero + One + BoundedBelow + BoundedAbove { } /// Class that has additive identity element pub trait Zero { /// The additive identity element fn zero() -> Self; } /// Class that has multiplicative identity element pub trait One { /// The multiplicative identity element fn one() -> Self; } pub trait BoundedBelow { fn min_value() -> Self; } pub trait BoundedAbove { fn max_value() -> Self; } macro_rules! impl_integral { ($($ty:ty),*) => { $( impl Zero for $ty { #[inline] fn zero() -> Self { 0 } } impl One for $ty { #[inline] fn one() -> Self { 1 } } impl BoundedBelow for $ty { #[inline] fn min_value() -> Self { Self::min_value() } } impl BoundedAbove for $ty { #[inline] fn max_value() -> Self { Self::max_value() } } impl Integral for $ty {} )* }; } impl_integral!(i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, usize); } pub mod lazysegtree { use crate::internal_bit::ceil_pow2; use crate::Monoid; pub trait MapMonoid { type M: Monoid; type F: Clone; // type S = ::S; fn identity_element() -> ::S { Self::M::identity() } fn binary_operation( a: &::S, b: &::S, ) -> ::S { Self::M::binary_operation(a, b) } fn identity_map() -> Self::F; fn mapping(f: &Self::F, x: &::S) -> ::S; fn composition(f: &Self::F, g: &Self::F) -> Self::F; } impl Default for LazySegtree { fn default() -> Self { Self::new(0) } } impl LazySegtree { pub fn new(n: usize) -> Self { vec![F::identity_element(); n].into() } } impl From::S>> for LazySegtree { fn from(v: Vec<::S>) -> Self { let n = v.len(); let log = ceil_pow2(n as u32) as usize; let size = 1 << log; let mut d = vec![F::identity_element(); 2 * size]; let lz = vec![F::identity_map(); size]; d[size..(size + n)].clone_from_slice(&v); let mut ret = LazySegtree { n, size, log, d, lz, }; for i in (1..size).rev() { ret.update(i); } ret } } impl LazySegtree { pub fn set(&mut self, mut p: usize, x: ::S) { assert!(p < self.n); p += self.size; for i in (1..=self.log).rev() { self.push(p >> i); } self.d[p] = x; for i in 1..=self.log { self.update(p >> i); } } pub fn get(&mut self, mut p: usize) -> ::S { assert!(p < self.n); p += self.size; for i in (1..=self.log).rev() { self.push(p >> i); } self.d[p].clone() } pub fn prod(&mut self, mut l: usize, mut r: usize) -> ::S { // println!("{} {}", l, r); assert!(l <= r && r <= self.n); if l == r { return F::identity_element(); } l += self.size; r += self.size; for i in (1..=self.log).rev() { if ((l >> i) << i) != l { self.push(l >> i); } if ((r >> i) << i) != r { self.push(r >> i); } } let mut sml = F::identity_element(); let mut smr = F::identity_element(); while l < r { if l & 1 != 0 { sml = F::binary_operation(&sml, &self.d[l]); l += 1; } if r & 1 != 0 { r -= 1; smr = F::binary_operation(&self.d[r], &smr); } l >>= 1; r >>= 1; } F::binary_operation(&sml, &smr) } pub fn all_prod(&self) -> ::S { self.d[1].clone() } pub fn apply(&mut self, mut p: usize, f: F::F) { assert!(p < self.n); p += self.size; for i in (1..=self.log).rev() { self.push(p >> i); } self.d[p] = F::mapping(&f, &self.d[p]); for i in 1..=self.log { self.update(p >> i); } } pub fn apply_range(&mut self, mut l: usize, mut r: usize, f: F::F) { assert!(l <= r && r <= self.n); if l == r { return; } l += self.size; r += self.size; for i in (1..=self.log).rev() { if ((l >> i) << i) != l { self.push(l >> i); } if ((r >> i) << i) != r { self.push((r - 1) >> i); } } { let l2 = l; let r2 = r; while l < r { if l & 1 != 0 { self.all_apply(l, f.clone()); l += 1; } if r & 1 != 0 { r -= 1; self.all_apply(r, f.clone()); } l >>= 1; r >>= 1; } l = l2; r = r2; } for i in 1..=self.log { if ((l >> i) << i) != l { self.update(l >> i); } if ((r >> i) << i) != r { self.update((r - 1) >> i); } } } pub fn max_right(&mut self, mut l: usize, g: G) -> usize where G: Fn(::S) -> bool, { assert!(l <= self.n); assert!(g(F::identity_element())); if l == self.n { return self.n; } l += self.size; for i in (1..=self.log).rev() { self.push(l >> i); } let mut sm = F::identity_element(); while { // do while l % 2 == 0 { l >>= 1; } if !g(F::binary_operation(&sm, &self.d[l])) { while l < self.size { self.push(l); l *= 2; let res = F::binary_operation(&sm, &self.d[l]); if g(res.clone()) { sm = res; l += 1; } } return l - self.size; } sm = F::binary_operation(&sm, &self.d[l]); l += 1; //while { let l = l as isize; (l & -l) != l } } {} self.n } pub fn min_left(&mut self, mut r: usize, g: G) -> usize where G: Fn(::S) -> bool, { assert!(r <= self.n); assert!(g(F::identity_element())); if r == 0 { return 0; } r += self.size; for i in (1..=self.log).rev() { self.push((r - 1) >> i); } let mut sm = F::identity_element(); while { // do r -= 1; while r > 1 && r % 2 != 0 { r >>= 1; } if !g(F::binary_operation(&self.d[r], &sm)) { while r < self.size { self.push(r); r = 2 * r + 1; let res = F::binary_operation(&self.d[r], &sm); if g(res.clone()) { sm = res; r -= 1; } } return r + 1 - self.size; } sm = F::binary_operation(&self.d[r], &sm); // while { let r = r as isize; (r & -r) != r } } {} 0 } } pub struct LazySegtree where F: MapMonoid, { n: usize, size: usize, log: usize, d: Vec<::S>, lz: Vec, } impl LazySegtree where F: MapMonoid, { fn update(&mut self, k: usize) { self.d[k] = F::binary_operation(&self.d[2 * k], &self.d[2 * k + 1]); } fn all_apply(&mut self, k: usize, f: F::F) { self.d[k] = F::mapping(&f, &self.d[k]); if k < self.size { self.lz[k] = F::composition(&f, &self.lz[k]); } } fn push(&mut self, k: usize) { self.all_apply(2 * k, self.lz[k].clone()); self.all_apply(2 * k + 1, self.lz[k].clone()); self.lz[k] = F::identity_map(); } } // TODO is it useful? use std::fmt::{Debug, Error, Formatter, Write}; impl Debug for LazySegtree where F: MapMonoid, F::F: Debug, ::S: Debug, { fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { for i in 0..self.log { for j in 0..1 << i { f.write_fmt(format_args!( "{:?}[{:?}]\t", self.d[(1 << i) + j], self.lz[(1 << i) + j] ))?; } f.write_char('\n')?; } for i in 0..self.size { f.write_fmt(format_args!("{:?}\t", self.d[self.size + i]))?; } Ok(()) } } #[cfg(test)] mod tests { use crate::{LazySegtree, MapMonoid, Max}; struct MaxAdd; impl MapMonoid for MaxAdd { type M = Max; type F = i32; fn identity_map() -> Self::F { 0 } fn mapping(&f: &i32, &x: &i32) -> i32 { f + x } fn composition(&f: &i32, &g: &i32) -> i32 { f + g } } #[test] fn test_max_add_lazy_segtree() { let base = vec![3, 1, 4, 1, 5, 9, 2, 6, 5, 3]; let n = base.len(); let mut segtree: LazySegtree = base.clone().into(); check_segtree(&base, &mut segtree); let mut segtree = LazySegtree::::new(n); let mut internal = vec![i32::min_value(); n]; for i in 0..n { segtree.set(i, base[i]); internal[i] = base[i]; check_segtree(&internal, &mut segtree); } segtree.set(6, 5); internal[6] = 5; check_segtree(&internal, &mut segtree); segtree.apply(5, 1); internal[5] += 1; check_segtree(&internal, &mut segtree); segtree.set(6, 0); internal[6] = 0; check_segtree(&internal, &mut segtree); segtree.apply_range(3, 8, 2); internal[3..8].iter_mut().for_each(|e| *e += 2); check_segtree(&internal, &mut segtree); } //noinspection DuplicatedCode fn check_segtree(base: &[i32], segtree: &mut LazySegtree) { let n = base.len(); #[allow(clippy::needless_range_loop)] for i in 0..n { assert_eq!(segtree.get(i), base[i]); } for i in 0..=n { for j in i..=n { assert_eq!( segtree.prod(i, j), base[i..j].iter().max().copied().unwrap_or(i32::min_value()) ); } } assert_eq!( segtree.all_prod(), base.iter().max().copied().unwrap_or(i32::min_value()) ); for k in 0..=10 { let f = |x| x < k; for i in 0..=n { assert_eq!( Some(segtree.max_right(i, f)), (i..=n) .filter(|&j| f(base[i..j] .iter() .max() .copied() .unwrap_or(i32::min_value()))) .max() ); } for j in 0..=n { assert_eq!( Some(segtree.min_left(j, f)), (0..=j) .filter(|&i| f(base[i..j] .iter() .max() .copied() .unwrap_or(i32::min_value()))) .min() ); } } } } } pub mod segtree { use crate::internal_bit::ceil_pow2; use crate::internal_type_traits::{BoundedAbove, BoundedBelow, One, Zero}; use std::cmp::{max, min}; use std::convert::Infallible; use std::marker::PhantomData; use std::ops::{Add, Mul}; // TODO Should I split monoid-related traits to another module? pub trait Monoid { type S: Clone; fn identity() -> Self::S; fn binary_operation(a: &Self::S, b: &Self::S) -> Self::S; } pub struct Max(Infallible, PhantomData S>); impl Monoid for Max where S: Copy + Ord + BoundedBelow, { type S = S; fn identity() -> Self::S { S::min_value() } fn binary_operation(a: &Self::S, b: &Self::S) -> Self::S { max(*a, *b) } } pub struct Min(Infallible, PhantomData S>); impl Monoid for Min where S: Copy + Ord + BoundedAbove, { type S = S; fn identity() -> Self::S { S::max_value() } fn binary_operation(a: &Self::S, b: &Self::S) -> Self::S { min(*a, *b) } } pub struct Additive(Infallible, PhantomData S>); impl Monoid for Additive where S: Copy + Add + Zero, { type S = S; fn identity() -> Self::S { S::zero() } fn binary_operation(a: &Self::S, b: &Self::S) -> Self::S { *a + *b } } pub struct Multiplicative(Infallible, PhantomData S>); impl Monoid for Multiplicative where S: Copy + Mul + One, { type S = S; fn identity() -> Self::S { S::one() } fn binary_operation(a: &Self::S, b: &Self::S) -> Self::S { *a * *b } } impl Default for Segtree { fn default() -> Self { Segtree::new(0) } } impl Segtree { pub fn new(n: usize) -> Segtree { vec![M::identity(); n].into() } } impl From> for Segtree { fn from(v: Vec) -> Self { let n = v.len(); let log = ceil_pow2(n as u32) as usize; let size = 1 << log; let mut d = vec![M::identity(); 2 * size]; d[size..(size + n)].clone_from_slice(&v); let mut ret = Segtree { n, size, log, d }; for i in (1..size).rev() { ret.update(i); } ret } } impl Segtree { pub fn set(&mut self, mut p: usize, x: M::S) { assert!(p < self.n); p += self.size; self.d[p] = x; for i in 1..=self.log { self.update(p >> i); } } pub fn get(&self, p: usize) -> M::S { assert!(p < self.n); self.d[p + self.size].clone() } pub fn prod(&self, mut l: usize, mut r: usize) -> M::S { assert!(l <= r && r <= self.n); let mut sml = M::identity(); let mut smr = M::identity(); l += self.size; r += self.size; while l < r { if l & 1 != 0 { sml = M::binary_operation(&sml, &self.d[l]); l += 1; } if r & 1 != 0 { r -= 1; smr = M::binary_operation(&self.d[r], &smr); } l >>= 1; r >>= 1; } M::binary_operation(&sml, &smr) } pub fn all_prod(&self) -> M::S { self.d[1].clone() } pub fn max_right(&self, mut l: usize, f: F) -> usize where F: Fn(&M::S) -> bool, { assert!(l <= self.n); assert!(f(&M::identity())); if l == self.n { return self.n; } l += self.size; let mut sm = M::identity(); while { // do while l % 2 == 0 { l >>= 1; } if !f(&M::binary_operation(&sm, &self.d[l])) { while l < self.size { l *= 2; let res = M::binary_operation(&sm, &self.d[l]); if f(&res) { sm = res; l += 1; } } return l - self.size; } sm = M::binary_operation(&sm, &self.d[l]); l += 1; // while { let l = l as isize; (l & -l) != l } } {} self.n } pub fn min_left(&self, mut r: usize, f: F) -> usize where F: Fn(&M::S) -> bool, { assert!(r <= self.n); assert!(f(&M::identity())); if r == 0 { return 0; } r += self.size; let mut sm = M::identity(); while { // do r -= 1; while r > 1 && r % 2 == 1 { r >>= 1; } if !f(&M::binary_operation(&self.d[r], &sm)) { while r < self.size { r = 2 * r + 1; let res = M::binary_operation(&self.d[r], &sm); if f(&res) { sm = res; r -= 1; } } return r + 1 - self.size; } sm = M::binary_operation(&self.d[r], &sm); // while { let r = r as isize; (r & -r) != r } } {} 0 } fn update(&mut self, k: usize) { self.d[k] = M::binary_operation(&self.d[2 * k], &self.d[2 * k + 1]); } } // Maybe we can use this someday // ``` // for i in 0..=self.log { // for j in 0..1 << i { // print!("{}\t", self.d[(1 << i) + j]); // } // println!(); // } // ``` pub struct Segtree where M: Monoid, { // variable name is _n in original library n: usize, size: usize, log: usize, d: Vec, } #[cfg(test)] mod tests { use crate::segtree::Max; use crate::Segtree; #[test] fn test_max_segtree() { let base = vec![3, 1, 4, 1, 5, 9, 2, 6, 5, 3]; let n = base.len(); let segtree: Segtree> = base.clone().into(); check_segtree(&base, &segtree); let mut segtree = Segtree::>::new(n); let mut internal = vec![i32::min_value(); n]; for i in 0..n { segtree.set(i, base[i]); internal[i] = base[i]; check_segtree(&internal, &segtree); } segtree.set(6, 5); internal[6] = 5; check_segtree(&internal, &segtree); segtree.set(6, 0); internal[6] = 0; check_segtree(&internal, &segtree); } //noinspection DuplicatedCode fn check_segtree(base: &[i32], segtree: &Segtree>) { let n = base.len(); #[allow(clippy::needless_range_loop)] for i in 0..n { assert_eq!(segtree.get(i), base[i]); } for i in 0..=n { for j in i..=n { assert_eq!( segtree.prod(i, j), base[i..j].iter().max().copied().unwrap_or(i32::min_value()) ); } } assert_eq!( segtree.all_prod(), base.iter().max().copied().unwrap_or(i32::min_value()) ); for k in 0..=10 { let f = |&x: &i32| x < k; for i in 0..=n { assert_eq!( Some(segtree.max_right(i, f)), (i..=n) .filter(|&j| f(&base[i..j] .iter() .max() .copied() .unwrap_or(i32::min_value()))) .max() ); } for j in 0..=n { assert_eq!( Some(segtree.min_left(j, f)), (0..=j) .filter(|&i| f(&base[i..j] .iter() .max() .copied() .unwrap_or(i32::min_value()))) .min() ); } } } } } use lazysegtree::*; use segtree::*;