#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; use std::io::{Write, BufWriter}; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes.by_ref().map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr, ) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, [graph1; $len:expr]) => {{ let mut g = vec![vec![]; $len]; let ab = read_value!($next, [(usize1, usize1)]); for (a, b) in ab { g[a].push(b); g[b].push(a); } g }}; ($next:expr, ( $($t:tt),* )) => { ( $(read_value!($next, $t)),* ) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, chars) => { read_value!($next, String).chars().collect::>() }; ($next:expr, usize1) => (read_value!($next, usize) - 1); ($next:expr, [ $t:tt ]) => {{ let len = read_value!($next, usize); read_value!($next, [$t; len]) }}; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } #[allow(unused)] macro_rules! debug { ($($format:tt)*) => (write!(std::io::stderr(), $($format)*).unwrap()); } #[allow(unused)] macro_rules! debugln { ($($format:tt)*) => (writeln!(std::io::stderr(), $($format)*).unwrap()); } const INF: i64 = 1 << 60; fn monotone_minima(l: usize, r: usize, a: usize, b: usize, frm: &[i64], lat: &mut [i64], cost_fun: &F) where F: Fn(usize, usize) -> i64 { let n = r - l; let m = b - a; if n == 0 || m == 0 { return; } let mid = (a + b) / 2; let mut mi = (INF, n); for i in l..r { let cost = cost_fun(i, mid); mi = min(mi, (cost + frm[i], i)); } let idx = mi.1; assert!(l <= idx && idx < r); lat[mid] = min(lat[mid], mi.0); monotone_minima(l, idx + 1, a, mid, frm, lat, cost_fun); monotone_minima(idx, r, mid + 1, b, frm, lat, cost_fun); } fn induce(l: usize, mid: usize, r: usize, dp: &mut [i64], cost_fun: &F) where F: Fn(usize, usize) -> i64 { let (frm, lat) = dp.split_at_mut(mid); let frm = &frm[l..]; let lat = &mut lat[..r - mid]; let inner_cost_fun = |i: usize, j: usize| cost_fun(i + l, j + mid); monotone_minima(0, mid - l, 0, r - mid, frm, lat, &inner_cost_fun); } // Performs online dp with divide and conquer. // Converted from the following off-line dp: // dp[i + 1][j] <--min-- dp[i][k] + cost_fun(k, j) (k < j) fn online_dc(l: usize, r: usize, dp: &mut [i64], cost_fun: &F) where F: Fn(usize, usize) -> i64 { if l + 1 >= r { return; } let mid = (l + r) / 2; online_dc(l, mid, dp, cost_fun); induce(l, mid, r, dp, cost_fun); online_dc(mid, r, dp, cost_fun); } // Tags: online-dp, divide-and-conquer, online-divide-and-conquer // https://qiita.com/tmaehara/items/0687af2cfb807cde7860 // https://ei1333.github.io/luzhiled/snippets/dp/monotone-minima.html // O(n log^2 n) fn solve() { let out = std::io::stdout(); let mut out = BufWriter::new(out.lock()); macro_rules! puts { ($($format:tt)*) => (let _ = write!(out,$($format)*);); } #[allow(unused)] macro_rules! putvec { ($v:expr) => { for i in 0..$v.len() { puts!("{}{}", $v[i], if i + 1 == $v.len() {"\n"} else {" "}); } } } input! { n: usize, a: [i64; n], x: [i64; n], y: [i64; n], } // padding let mut a = a; a.insert(0, 0); let mut x = x; x.push(0); let mut y = y; y.push(0); let cost_fun = |i: usize, j: usize| { (a[j] - x[i]).abs() + y[i].abs() }; let mut dp = vec![INF; n + 1]; dp[0] = 0; online_dc(0, n + 1, &mut dp, &cost_fun); puts!("{}\n", dp[n]); } fn main() { // In order to avoid potential stack overflow, spawn a new thread. let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); thd.spawn(|| solve()).unwrap().join().unwrap(); }