fn main() { let mut io = IO::new(); input!{ from io, n: usize, m: usize, st: usize, go: usize, ed: [(usize, usize, i64); m] } let mut g = UndirectedGraph::new(n); for &(u, v, c) in &ed { g.add_edge(u, v, c); } let (_dist, parent) = dijkstra_heap(&g, st); let mut v = go; let mut stack = Vec::new(); while v != st { stack.push(v); v = parent[v]; } stack.push(st); stack.reverse(); io.iterln(stack.into_iter(), " "); } // ------------ Dijkstra's algorithm start ------------ #[allow(clippy::many_single_char_names)] pub fn dijkstra_heap>(g: &G, s: usize) -> (Vec, Vec) { let n = g.size(); let mut dist = vec![C::MAX; n]; let mut depth = vec![std::usize::MAX; n]; let mut parent = vec![std::usize::MAX; n]; let mut que = std::collections::BinaryHeap::new(); dist[s] = C::zero(); depth[s] = 0; que.push((C::zero(), s)); while let Some((d, u)) = que.pop() { let d = -d; if dist[u] < d { continue; } for e in g.edges_from(u) { let v = e.to; let d2 = d + e.cost; if dist[v] > d2 { dist[v] = d2; depth[v] = depth[u] + 1; parent[v] = u; que.push((-d2, v)); } else if dist[v] == d2 { if parent[v] > u { parent[v] = u } } } } (dist, parent) } // ------------ Dijkstra's algorithm end ------------ // ------------ Graph impl start ------------ pub trait Cost: Element + Clone + Copy + std::fmt::Display + Eq + Ord + Zero + One + Add + AddAssign + Sub + Neg { const MAX: Self; } #[derive(Copy, Clone)] pub struct Edge { // pub from: usize, pub to: usize, pub cost: C, pub id: usize } pub struct UndirectedGraph(pub Vec>>, pub usize); pub struct DirectedGraph{ pub forward: Vec>>, pub backward: Vec>>, pub count: usize, } pub trait Graph { fn new(size: usize) -> Self; fn size(&self) -> usize; fn add_edge(&mut self, u: usize, v: usize, cost: C); fn edges_from(&self, v: usize) -> std::slice::Iter>; } impl Graph for UndirectedGraph { fn new(size: usize) -> Self { Self(vec![Vec::>::new(); size], 0) } fn size(&self) -> usize { self.0.len() } fn add_edge(&mut self, u: usize, v: usize, cost: C) { self.0[u].push(Edge{ to: v, cost: cost.clone(), id: self.1 }); self.0[v].push(Edge{ to: u, cost: cost.clone(), id: self.1 }); self.1 += 1; } fn edges_from(&self, v: usize) -> std::slice::Iter> { self.0[v].iter() } } impl Graph for DirectedGraph { fn new(size: usize) -> Self { Self { forward: vec![Vec::>::new(); size], backward: vec![Vec::>::new(); size], count: 0 } } fn size(&self) -> usize { self.forward.len() } fn add_edge(&mut self, u: usize, v: usize, cost: C) { self.forward[u].push(Edge{ to: v, cost: cost.clone(), id: self.count }); self.backward[v].push(Edge{ to: u, cost: cost.clone(), id: self.count }); self.count += 1; } fn edges_from(&self, v: usize) -> std::slice::Iter> { self.forward[v].iter() } } impl DirectedGraph { pub fn edges_to(&self, u: usize) -> std::slice::Iter> { self.backward[u].iter() } pub fn reverse(&self) -> Self { Self { forward: self.backward.clone(), backward: self.forward.clone(), count: self.count, } } } macro_rules! impl_cost { ($($T:ident,)*) => { $( impl Cost for $T { const MAX: Self = std::$T::MAX; } )* }; } impl_cost! { i8, i16, i32, i64, i128, isize, } #[derive(Clone, Copy, PartialEq, Eq, PartialOrd, Ord)] pub struct Void(); impl std::fmt::Display for Void { fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result { write!(f, "") } } impl Zero for Void { fn zero() -> Self { Void() } fn is_zero(&self) -> bool { true } } impl One for Void { fn one() -> Self { Void() } fn is_one(&self) -> bool { true } } impl Add for Void { type Output = Self; fn add(self, _: Self) -> Self { Void() } } impl AddAssign for Void { fn add_assign(&mut self, _: Self) {} } impl Sub for Void { type Output = Self; fn sub(self, _: Self) -> Self { Void() } } impl Neg for Void { type Output = Self; fn neg(self) -> Self { Void() } } impl Cost for Void { const MAX: Self = Void(); } // ------------ Graph impl end ------------ // ------------ algebraic traits start ------------ use std::marker::Sized; use std::ops::*; /// 元 pub trait Element: Sized + Clone + PartialEq {} impl Element for T {} /// 結合性 pub trait Associative: Magma {} /// マグマ pub trait Magma: Element + Add {} impl> Magma for T {} /// 半群 pub trait SemiGroup: Magma + Associative {} impl SemiGroup for T {} /// モノイド pub trait Monoid: SemiGroup + Zero {} impl Monoid for T {} pub trait ComMonoid: Monoid + AddAssign {} impl ComMonoid for T {} /// 群 pub trait Group: Monoid + Neg {} impl> Group for T {} pub trait ComGroup: Group + ComMonoid {} impl ComGroup for T {} /// 半環 pub trait SemiRing: ComMonoid + Mul + One {} impl + One> SemiRing for T {} /// 環 pub trait Ring: ComGroup + SemiRing {} impl Ring for T {} pub trait ComRing: Ring + MulAssign {} impl ComRing for T {} /// 体 pub trait Field: ComRing + Div + DivAssign {} impl + DivAssign> Field for T {} /// 加法単元 pub trait Zero: Element { fn zero() -> Self; fn is_zero(&self) -> bool { *self == Self::zero() } } /// 乗法単元 pub trait One: Element { fn one() -> Self; fn is_one(&self) -> bool { *self == Self::one() } } macro_rules! impl_integer { ($($T:ty,)*) => { $( impl Associative for $T {} impl Zero for $T { fn zero() -> Self { 0 } fn is_zero(&self) -> bool { *self == 0 } } impl<'a> Zero for &'a $T { fn zero() -> Self { &0 } fn is_zero(&self) -> bool { *self == &0 } } impl One for $T { fn one() -> Self { 1 } fn is_one(&self) -> bool { *self == 1 } } impl<'a> One for &'a $T { fn one() -> Self { &1 } fn is_one(&self) -> bool { *self == &1 } } )* }; } impl_integer! { i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, usize, } // ------------ algebraic traits end ------------ // ------------ io module start ------------ use std::io::{stdout, BufWriter, Read, StdoutLock, Write}; pub struct IO { iter: std::str::SplitAsciiWhitespace<'static>, buf: BufWriter>, } impl IO { pub fn new() -> Self { let mut input = String::new(); std::io::stdin().read_to_string(&mut input).unwrap(); let input = Box::leak(input.into_boxed_str()); let out = Box::new(stdout()); IO { iter: input.split_ascii_whitespace(), buf: BufWriter::new(Box::leak(out).lock()), } } fn scan_str(&mut self) -> &'static str { self.iter.next().unwrap() } pub fn scan(&mut self) -> ::Output { ::scan(self) } pub fn scan_vec(&mut self, n: usize) -> Vec<::Output> { (0..n).map(|_| self.scan::()).collect() } pub fn print(&mut self, x: T) { ::print(self, x); } pub fn println(&mut self, x: T) { self.print(x); self.print("\n"); } pub fn iterln>(&mut self, mut iter: I, delim: &str) { if let Some(v) = iter.next() { self.print(v); for v in iter { self.print(delim); self.print(v); } } self.print("\n"); } pub fn flush(&mut self) { self.buf.flush().unwrap(); } } impl Default for IO { fn default() -> Self { Self::new() } } pub trait Scan { type Output; fn scan(io: &mut IO) -> Self::Output; } macro_rules! impl_scan { ($($t:tt),*) => { $( impl Scan for $t { type Output = Self; fn scan(s: &mut IO) -> Self::Output { s.scan_str().parse().unwrap() } } )* }; } impl_scan!(i16, i32, i64, isize, u16, u32, u64, usize, String, f32, f64); impl Scan for char { type Output = char; fn scan(s: &mut IO) -> Self::Output { s.scan_str().chars().next().unwrap() } } pub enum Bytes {} impl Scan for Bytes { type Output = &'static [u8]; fn scan(s: &mut IO) -> Self::Output { s.scan_str().as_bytes() } } pub enum Chars {} impl Scan for Chars { type Output = Vec; fn scan(s: &mut IO) -> Self::Output { s.scan_str().chars().collect() } } pub enum Usize1 {} impl Scan for Usize1 { type Output = usize; fn scan(s: &mut IO) -> Self::Output { s.scan::().wrapping_sub(1) } } impl Scan for (T, U) { type Output = (T::Output, U::Output); fn scan(s: &mut IO) -> Self::Output { (T::scan(s), U::scan(s)) } } impl Scan for (T, U, V) { type Output = (T::Output, U::Output, V::Output); fn scan(s: &mut IO) -> Self::Output { (T::scan(s), U::scan(s), V::scan(s)) } } impl Scan for (T, U, V, W) { type Output = (T::Output, U::Output, V::Output, W::Output); fn scan(s: &mut IO) -> Self::Output { (T::scan(s), U::scan(s), V::scan(s), W::scan(s)) } } pub trait Print { fn print(w: &mut IO, x: Self); } macro_rules! impl_print_int { ($($t:ty),*) => { $( impl Print for $t { fn print(w: &mut IO, x: Self) { w.buf.write_all(x.to_string().as_bytes()).unwrap(); } } )* }; } impl_print_int!(i16, i32, i64, isize, u16, u32, u64, usize, f32, f64); impl Print for u8 { fn print(w: &mut IO, x: Self) { w.buf.write_all(&[x]).unwrap(); } } impl Print for &[u8] { fn print(w: &mut IO, x: Self) { w.buf.write_all(x).unwrap(); } } impl Print for &str { fn print(w: &mut IO, x: Self) { w.print(x.as_bytes()); } } impl Print for String { fn print(w: &mut IO, x: Self) { w.print(x.as_bytes()); } } impl Print for (T, U) { fn print(w: &mut IO, (x, y): Self) { w.print(x); w.print(" "); w.print(y); } } impl Print for (T, U, V) { fn print(w: &mut IO, (x, y, z): Self) { w.print(x); w.print(" "); w.print(y); w.print(" "); w.print(z); } } mod neboccoio_macro { #[macro_export] macro_rules! input { (@start $io:tt @read @rest) => {}; (@start $io:tt @read @rest, $($rest: tt)*) => { input!(@start $io @read @rest $($rest)*) }; (@start $io:tt @read @rest mut $($rest:tt)*) => { input!(@start $io @read @mut [mut] @rest $($rest)*) }; (@start $io:tt @read @rest $($rest:tt)*) => { input!(@start $io @read @mut [] @rest $($rest)*) }; (@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [[$kind:tt; $len1:expr]; $len2:expr] $($rest:tt)*) => { let $($mut)* $var = (0..$len2).map(|_| $io.scan_vec::<$kind>($len1)).collect::>>(); input!(@start $io @read @rest $($rest)*) }; (@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [$kind:tt; $len:expr] $($rest:tt)*) => { let $($mut)* $var = $io.scan_vec::<$kind>($len); input!(@start $io @read @rest $($rest)*) }; (@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: $kind:tt $($rest:tt)*) => { let $($mut)* $var = $io.scan::<$kind>(); input!(@start $io @read @rest $($rest)*) }; (from $io:tt $($rest:tt)*) => { input!(@start $io @read @rest $($rest)*) }; } } // ------------ io module end ------------