procon_lib_rs
This documentation is automatically generated by online-judge-tools/verification-helper
crates/flow/maxflow/src/lib.rs
- View this file on GitHub
- Last update: 2025-03-02 17:25:42+09:00
- Link: https://commons.wikimedia.org/wiki/File:Min_cut.png
- Link: https://creativecommons.org/licenses/by-sa/3.0/deed.en
- Link: https://gist.github.com/MiSawa/47b1d99c372daffb6891662db1a2b686
- Link: https://github.com/atcoder/ac-library/issues/5
- Link: https://github.com/rust-lang-ja/ac-library-rs/blob/master/src/maxflow.rs
- Link: https://github.com/rust-lang-ja/ac-library-rs/pull/24#discussion_r485343451
Depends on
Required by
Code
//! From <https://github.com/rust-lang-ja/ac-library-rs/blob/master/src/maxflow.rs>
use internal_type_traits::Integral;
use std::cmp::min;
use std::iter;
#[derive(Default, Debug, Clone, PartialEq, Eq)]
struct SimpleQueue<T> {
payload: Vec<T>,
pos: usize,
}
impl<T> SimpleQueue<T> {
fn empty(&self) -> bool {
self.pos == self.payload.len()
}
fn push(&mut self, t: T) {
self.payload.push(t);
}
// Do we need mutable version?
fn front(&self) -> Option<&T> {
if self.pos < self.payload.len() {
Some(&self.payload[self.pos])
} else {
None
}
}
fn clear(&mut self) {
self.payload.clear();
self.pos = 0;
}
fn pop(&mut self) -> Option<&T> {
if self.pos < self.payload.len() {
self.pos += 1;
Some(&self.payload[self.pos - 1])
} else {
None
}
}
}
impl<Cap> MaxFlow<Cap>
where
Cap: Integral,
{
pub fn new(n: usize) -> MaxFlow<Cap> {
MaxFlow {
_n: n,
pos: Vec::new(),
g: iter::repeat_with(Vec::new).take(n).collect(),
}
}
pub fn add_edge(&mut self, from: usize, to: usize, cap: Cap) -> usize {
assert!(from < self._n);
assert!(to < self._n);
assert!(Cap::zero() <= cap);
let m = self.pos.len();
self.pos.push((from, self.g[from].len()));
let rev = self.g[to].len() + usize::from(from == to);
self.g[from].push(_Edge { to, rev, cap });
let rev = self.g[from].len() - 1;
self.g[to].push(_Edge {
to: from,
rev,
cap: Cap::zero(),
});
m
}
}
#[derive(Debug, PartialEq, Eq)]
pub struct Edge<Cap: Integral> {
pub from: usize,
pub to: usize,
pub cap: Cap,
pub flow: Cap,
}
impl<Cap> MaxFlow<Cap>
where
Cap: Integral,
{
pub fn get_edge(&self, i: usize) -> Edge<Cap> {
let m = self.pos.len();
assert!(i < m);
let _e = &self.g[self.pos[i].0][self.pos[i].1];
let _re = &self.g[_e.to][_e.rev];
Edge {
from: self.pos[i].0,
to: _e.to,
cap: _e.cap + _re.cap,
flow: _re.cap,
}
}
pub fn edges(&self) -> Vec<Edge<Cap>> {
let m = self.pos.len();
(0..m).map(|i| self.get_edge(i)).collect()
}
pub fn change_edge(&mut self, i: usize, new_cap: Cap, new_flow: Cap) {
let m = self.pos.len();
assert!(i < m);
assert!(Cap::zero() <= new_flow && new_flow <= new_cap);
let (to, rev) = {
let _e = &mut self.g[self.pos[i].0][self.pos[i].1];
_e.cap = new_cap - new_flow;
(_e.to, _e.rev)
};
let _re = &mut self.g[to][rev];
_re.cap = new_flow;
}
/// `s != t` must hold, otherwise it panics.
pub fn flow(&mut self, s: usize, t: usize) -> Cap {
self.flow_with_capacity(s, t, Cap::max_value())
}
/// # Parameters
/// * `s != t` must hold, otherwise it panics.
/// * `flow_limit >= 0`
pub fn flow_with_capacity(&mut self, s: usize, t: usize, flow_limit: Cap) -> Cap {
let n_ = self._n;
assert!(s < n_);
assert!(t < n_);
// By the definition of max flow in appendix.html, this function should return 0
// when the same vertices are provided. On the other hand, it is reasonable to
// return infinity-like value too, which is what the original implementation
// (and this implementation without the following assertion) does.
// Since either return value is confusing, we'd rather deny the parameters
// of the two same vertices.
// For more details, see https://github.com/rust-lang-ja/ac-library-rs/pull/24#discussion_r485343451
// and https://github.com/atcoder/ac-library/issues/5 .
assert_ne!(s, t);
// Additional constraint
assert!(Cap::zero() <= flow_limit);
let mut calc = FlowCalculator {
graph: self,
s,
t,
level: vec![0; n_],
iter: vec![0; n_],
que: SimpleQueue::default(),
};
let mut flow = Cap::zero();
while flow < flow_limit {
calc.bfs();
if calc.level[t] == -1 {
break;
}
calc.iter.iter_mut().for_each(|e| *e = 0);
while flow < flow_limit {
let f = calc.dfs(t, flow_limit - flow);
if f == Cap::zero() {
break;
}
flow += f;
}
}
flow
}
pub fn min_cut(&self, s: usize) -> Vec<bool> {
let mut visited = vec![false; self._n];
let mut que = SimpleQueue::default();
que.push(s);
while let Some(&p) = que.pop() {
visited[p] = true;
for e in &self.g[p] {
if e.cap != Cap::zero() && !visited[e.to] {
visited[e.to] = true;
que.push(e.to);
}
}
}
visited
}
}
struct FlowCalculator<'a, Cap> {
graph: &'a mut MaxFlow<Cap>,
s: usize,
t: usize,
level: Vec<i32>,
iter: Vec<usize>,
que: SimpleQueue<usize>,
}
impl<Cap> FlowCalculator<'_, Cap>
where
Cap: Integral,
{
fn bfs(&mut self) {
self.level.iter_mut().for_each(|e| *e = -1);
self.level[self.s] = 0;
self.que.clear();
self.que.push(self.s);
while !self.que.empty() {
let v = *self.que.front().unwrap();
self.que.pop();
for e in &self.graph.g[v] {
if e.cap == Cap::zero() || self.level[e.to] >= 0 {
continue;
}
self.level[e.to] = self.level[v] + 1;
if e.to == self.t {
return;
}
self.que.push(e.to);
}
}
}
fn dfs(&mut self, v: usize, up: Cap) -> Cap {
if v == self.s {
return up;
}
let mut res = Cap::zero();
let level_v = self.level[v];
for i in self.iter[v]..self.graph.g[v].len() {
self.iter[v] = i;
let &_Edge {
to: e_to,
rev: e_rev,
..
} = &self.graph.g[v][i];
if level_v <= self.level[e_to] || self.graph.g[e_to][e_rev].cap == Cap::zero() {
continue;
}
let d = self.dfs(e_to, min(up - res, self.graph.g[e_to][e_rev].cap));
if d <= Cap::zero() {
continue;
}
self.graph.g[v][i].cap += d;
self.graph.g[e_to][e_rev].cap -= d;
res += d;
if res == up {
return res;
}
}
self.iter[v] = self.graph.g[v].len();
res
}
}
/// 最大流を解く
#[derive(Default, Debug, Clone, PartialEq, Eq)]
pub struct MaxFlow<Cap> {
_n: usize,
pos: Vec<(usize, usize)>,
g: Vec<Vec<_Edge<Cap>>>,
}
#[derive(Debug, PartialEq, Eq, Clone)]
struct _Edge<Cap> {
to: usize,
rev: usize,
cap: Cap,
}
#[cfg(test)]
mod test {
use crate::{Edge, MaxFlow};
#[test]
fn test_max_flow_wikipedia() {
// From https://commons.wikimedia.org/wiki/File:Min_cut.png
// Under CC BY-SA 3.0 https://creativecommons.org/licenses/by-sa/3.0/deed.en
let mut graph = MaxFlow::new(6);
assert_eq!(graph.add_edge(0, 1, 3), 0);
assert_eq!(graph.add_edge(0, 2, 3), 1);
assert_eq!(graph.add_edge(1, 2, 2), 2);
assert_eq!(graph.add_edge(1, 3, 3), 3);
assert_eq!(graph.add_edge(2, 4, 2), 4);
assert_eq!(graph.add_edge(3, 4, 4), 5);
assert_eq!(graph.add_edge(3, 5, 2), 6);
assert_eq!(graph.add_edge(4, 5, 3), 7);
assert_eq!(graph.flow(0, 5), 5);
let edges = graph.edges();
{
#[rustfmt::skip]
assert_eq!(
edges,
vec![
Edge { from: 0, to: 1, cap: 3, flow: 3 },
Edge { from: 0, to: 2, cap: 3, flow: 2 },
Edge { from: 1, to: 2, cap: 2, flow: 0 },
Edge { from: 1, to: 3, cap: 3, flow: 3 },
Edge { from: 2, to: 4, cap: 2, flow: 2 },
Edge { from: 3, to: 4, cap: 4, flow: 1 },
Edge { from: 3, to: 5, cap: 2, flow: 2 },
Edge { from: 4, to: 5, cap: 3, flow: 3 },
]
);
}
assert_eq!(
graph.min_cut(0),
vec![true, false, true, false, false, false]
);
}
#[test]
fn test_max_flow_wikipedia_multiple_edges() {
// From https://commons.wikimedia.org/wiki/File:Min_cut.png
// Under CC BY-SA 3.0 https://creativecommons.org/licenses/by-sa/3.0/deed.en
let mut graph = MaxFlow::new(6);
for &(u, v, c) in &[
(0, 1, 3),
(0, 2, 3),
(1, 2, 2),
(1, 3, 3),
(2, 4, 2),
(3, 4, 4),
(3, 5, 2),
(4, 5, 3),
] {
for _ in 0..c {
graph.add_edge(u, v, 1);
}
}
assert_eq!(graph.flow(0, 5), 5);
assert_eq!(
graph.min_cut(0),
vec![true, false, true, false, false, false]
);
}
#[test]
#[allow(clippy::many_single_char_names)]
fn test_max_flow_misawa() {
// Originally by @MiSawa
// From https://gist.github.com/MiSawa/47b1d99c372daffb6891662db1a2b686
let n = 100;
let mut graph = MaxFlow::new((n + 1) * 2 + 5);
let (s, a, b, c, t) = (0, 1, 2, 3, 4);
graph.add_edge(s, a, 1);
graph.add_edge(s, b, 2);
graph.add_edge(b, a, 2);
graph.add_edge(c, t, 2);
for i in 0..n {
let i = 2 * i + 5;
for j in 0..2 {
for k in 2..4 {
graph.add_edge(i + j, i + k, 3);
}
}
}
for j in 0..2 {
graph.add_edge(a, 5 + j, 3);
graph.add_edge(2 * n + 5 + j, c, 3);
}
assert_eq!(graph.flow(s, t), 2);
}
#[test]
fn test_dont_repeat_same_phase() {
let n = 100_000;
let mut graph = MaxFlow::new(3);
graph.add_edge(0, 1, n);
for _ in 0..n {
graph.add_edge(1, 2, 1);
}
assert_eq!(graph.flow(0, 2), n);
}
}Traceback (most recent call last):
File "/opt/hostedtoolcache/Python/3.13.9/x64/lib/python3.13/site-packages/onlinejudge_verify/documentation/build.py", line 71, in _render_source_code_stat
bundled_code = language.bundle(stat.path, basedir=basedir, options={'include_paths': [basedir]}).decode()
~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/opt/hostedtoolcache/Python/3.13.9/x64/lib/python3.13/site-packages/onlinejudge_verify/languages/rust.py", line 288, in bundle
raise NotImplementedError
NotImplementedError