pathfinder2/src/flow/flow.rs
2022-09-11 17:44:15 +02:00

177 lines
5.9 KiB
Rust

use crate::flow::adjacencies::Adjacencies;
use crate::flow::{node_as_address, node_as_token_edge, Node};
use crate::types::{Address, Edge, U256};
use std::cmp::min;
use std::collections::HashMap;
use std::collections::VecDeque;
pub fn compute_flow(
source: &Address,
sink: &Address,
edges: &HashMap<Address, Vec<Edge>>,
) -> String {
let mut adjacencies = Adjacencies::new(edges);
let mut used_edges: HashMap<Node, HashMap<Node, U256>> = HashMap::new();
let mut flow = U256::default();
loop {
let (new_flow, parents) = augmenting_path(source, sink, &mut adjacencies);
if new_flow == U256::default() {
break;
}
flow += new_flow;
for window in parents.windows(2) {
if let [node, prev] = window {
adjacencies.adjust_capacity(prev, node, -new_flow);
adjacencies.adjust_capacity(node, prev, new_flow);
if adjacencies.is_adjacent(node, prev) {
*used_edges
.entry(node.clone())
.or_default()
.entry(prev.clone())
.or_default() -= new_flow;
} else {
*used_edges
.entry(prev.clone())
.or_default()
.entry(node.clone())
.or_default() -= new_flow;
}
} else {
panic!();
}
}
}
println!("Max flow: {flow}");
let transfers = extract_transfers(source, sink, &flow, used_edges);
println!("Num transfers: {}", transfers.len());
flow.to_string()
}
fn augmenting_path(
source: &Address,
sink: &Address,
adjacencies: &mut Adjacencies,
) -> (U256, Vec<Node>) {
let mut parent = HashMap::new();
if *source == *sink {
return (U256::default(), vec![]);
}
let mut queue = VecDeque::<(Node, U256)>::new();
queue.push_back((Node::Node(*source), U256::default() - U256::from(1)));
while let Some((node, flow)) = queue.pop_front() {
for (target, capacity) in adjacencies.outgoing_edges_sorted_by_capacity(&node) {
if !parent.contains_key(&target) && capacity > U256::default() {
parent.insert(target.clone(), node.clone());
let new_flow = min(flow, capacity);
if target == Node::Node(*sink) {
return (
new_flow,
trace(parent, &Node::Node(*source), &Node::Node(*sink)),
);
}
queue.push_back((target, new_flow));
}
}
}
(U256::default(), vec![])
}
fn trace(parent: HashMap<Node, Node>, source: &Node, sink: &Node) -> Vec<Node> {
let mut t = vec![sink.clone()];
let mut node = sink;
loop {
node = parent.get(node).unwrap();
t.push(node.clone());
if *node == *source {
break;
}
}
t
}
fn extract_transfers(
source: &Address,
sink: &Address,
amount: &U256,
mut used_edges: HashMap<Node, HashMap<Node, U256>>,
) -> Vec<Edge> {
let mut transfers: Vec<Edge> = Vec::new();
let mut account_balances: HashMap<Address, U256> = HashMap::new();
account_balances.insert(*source, amount.clone());
while !account_balances.is_empty()
&& (account_balances.len() > 1 || *account_balances.iter().nth(0).unwrap().0 != *sink)
{
let next = extract_next_transfers(&mut used_edges, &mut account_balances);
assert!(!next.is_empty());
transfers.extend(next.into_iter());
}
transfers
}
/// Extract the next list of transfers until we get to a situation where
/// we cannot transfer the full balance and start over.
fn extract_next_transfers(
used_edges: &mut HashMap<Node, HashMap<Node, U256>>,
account_balances: &mut HashMap<Address, U256>,
) -> Vec<Edge> {
let mut transfers = Vec::new();
loop {
let first_edge = transfers.is_empty();
if let Some(edge) = next_nonzero_edge(used_edges, account_balances, first_edge) {
account_balances
.entry(edge.from)
.and_modify(|balance| *balance -= edge.capacity);
account_balances
.entry(edge.to)
.and_modify(|balance| *balance += edge.capacity);
account_balances.retain(|_account, balance| balance > &mut U256::from(0));
used_edges
.entry(Node::Node(edge.from))
.and_modify(|outgoing| {
outgoing.remove(&Node::TokenEdge(edge.from, edge.token));
});
transfers.push(edge);
} else {
return transfers;
}
}
}
fn next_nonzero_edge(
used_edges: &HashMap<Node, HashMap<Node, U256>>,
account_balances: &HashMap<Address, U256>,
first_edge: bool,
) -> Option<Edge> {
for (account, balance) in account_balances {
for (intermediate, _) in &used_edges[&Node::Node(*account)] {
let (from, token) = node_as_token_edge(intermediate);
for (to_node, capacity) in &used_edges[intermediate] {
let to = node_as_address(to_node);
if *capacity == U256::from(0) {
continue;
}
if *balance < *capacity {
// We do not have enough balance yet, there will be another transfer along this edge.
if first_edge {
continue;
} else {
return None;
}
} else {
return Some(Edge {
from: *from,
to: *to,
token: *token,
capacity: *capacity,
});
}
}
}
}
None
}