#[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; #[macro_export] macro_rules ! dvec { ( $ t : expr ; $ len : expr ) => { vec ! [ $ t ; $ len ] } ; ( $ t : expr ; $ len : expr , $ ( $ rest : expr ) ,* ) => { vec ! [ dvec ! ( $ t ; $ ( $ rest ) ,* ) ; $ len ] } ; } #[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(); } } // O(n logk) fn calc_mid(a: &[i64], k: usize) -> Vec { let mut res = vec![]; let mut n = a.len(); let mut cur = 0; let mut aa = vec![]; // n/k while n >= k { aa.clear(); for _ in 0..k { aa.push(a[cur]); cur += 1; n -= 1; } // klogk aa.sort(); let x = if k%2==0 { aa[(k/2)-1] } else { aa[((k+1)/2)-1] }; res.push(x) } res } fn dp(a: &[i64], k: usize) -> i64 { let maxn = a.len() / k; // O(n logk) let left = calc_mid(&a, k); assert!(left.len() == maxn); let mut leftcum = CumSum1::new(maxn); for i in 0..maxn { leftcum.set(i, left[i]); } leftcum.build(); // O(n) let mut a = a.to_owned(); a.reverse(); // O(n logk) let right = calc_mid(&a, k); assert!(right.len() == maxn); let mut rightcum = CumSum1::new(maxn); for i in 0..maxn { rightcum.set(i, right[i]); } rightcum.build(); let mut rightseg: SEG = SEG::new(maxn+1); for r in 0..maxn+1 { rightseg.update(r, rightcum.query(0, r)); } let mut maxv = std::i64::MIN; // O((n/k)^2) for l in 0..maxn+1 { let r = maxn - l; let v = leftcum.query(0, l) + rightseg.query(0, r+1); maxv = max(maxv, k as i64 * v); } maxv } fn solve() { input!{ n: usize, a: [i64; n], } // k=1 (kadane) let mut sum = 0; let mut b = vec![]; for i in 0..n { sum += a[i]; b.push(-1 * a[i]); // 逆転 } let maxsub = kadane(&b); let mut maxv = 0; let mut v = sum; if maxsub > 0 { v += maxsub; } maxv = max(maxv, v); // k>=2 // n^2 (1/4+1/9+1/16+...1/n^2) // だめそうだがやってみましょう for k in 2..n+1 { maxv = max(maxv, dp(&a, k)); } println!("{}", maxv); } #[doc = "return the sum of the maximum subarray. (Kadane's algorithm). O(N)"] fn kadane(xs: &[i64]) -> i64 { let mut max_ending_here = xs[0]; let mut max_so_far = xs[0]; for i in 1..xs.len() { let x = xs[i]; max_ending_here = max(x, max_ending_here + x); max_so_far = max(max_so_far, max_ending_here); } max_so_far } struct CumSum1 { base: Vec, dp: Vec, } impl CumSum1 { fn new(n: usize) -> CumSum1 { CumSum1 { base: vec![0; n], dp: vec![], } } fn add(&mut self, i: usize, x: i64) { self.base[i] += x; } fn set(&mut self, i: usize, x: i64) { self.base[i] = x; } fn build(&mut self) { let n = self.base.len(); let mut dp = vec![0; n + 1]; let mut acc = 0; for i in 0..n { acc += self.base[i]; dp[i + 1] = acc; } self.dp = dp; } #[doc = "[i,j)"] fn query(&self, i: usize, j: usize) -> i64 { self.dp[j] - self.dp[i] } } #[allow(dead_code)] pub trait Monoid { type T: Clone; fn id() -> Self::T; fn op(a: &Self::T, b: &Self::T) -> Self::T; } #[allow(dead_code)] pub struct SEG { n: usize, buf: Vec, } impl SEG { #[allow(dead_code)] pub fn new(n: usize) -> SEG { let mut m = 1; while m < n { m *= 2; } SEG { n: m, buf: vec![M::id().clone(); 2 * m], } } #[allow(dead_code)] pub fn update(&mut self, k: usize, a: M::T) { let mut k = k + self.n; self.buf[k] = a; while k > 1 { k = k >> 1; self.buf[k] = M::op(&self.buf[k * 2], &self.buf[k * 2 + 1]); } } #[allow(dead_code)] pub fn get(&self, k: usize) -> M::T { self.buf[k + self.n].clone() } pub fn do_query(&self, a: usize, b: usize, k: usize, l: usize, r: usize) -> M::T { if r <= a || b <= l { return M::id(); } if a <= l && r <= b { return self.buf[k].clone(); } else { let vl = self.do_query(a, b, k * 2, l, (l + r) / 2); let vr = self.do_query(a, b, k * 2 + 1, (l + r) / 2, r); return M::op(&vl, &vr); } } #[allow(dead_code)] pub fn query(&self, a: usize, b: usize) -> M::T { self.do_query(a, b, 1, 0, self.n) } } struct MAX; impl Monoid for MAX { type T = i64; fn id() -> Self::T { 0 } fn op(a: &Self::T, b: &Self::T) -> Self::T { std::cmp::max(*a, *b) } }