Problem:
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Maximum Flow

A flow network is a directed graph which has a $source$ and a $sink$. In a flow network, each edge $(u, v)$ has a capacity $c(u, v)$. Each edge receives a flow, but the amount of flow on the edge can not exceed the corresponding capacity. Find the maximum flow from the $source$ to the $sink$.

Input

A flow network is given in the following format.

$|V|\;|E|$

$u_0\;v_0\;c_0$

$u_1\;v_1\;c_1$

:

$u_{|E|-1}\;v_{|E|-1}\;c_{|E|-1}$

$|V|$, $|E|$ is the number of vertices and edges of the flow network respectively. The vertices in $G$ are named with the numbers 0, 1,..., $|V|-1$. The source is 0 and the sink is $|V|-1$.

$u_i$, $v_i$, $c_i$ represent $i$-th edge of the flow network.
A pair of $u_i$ and $v_i$ denotes that there is an edge from $u_i$ to $v_i$ and $c_i$ is the capacity of $i$-th edge.

Output

Print the maximum flow.

Constraints

$2 \leq |V| \leq 100$

$1 \leq |E| \leq 1000$

$0 \leq c_i \leq 10000$

Sample Input 1

4 5
0 1 2
0 2 1
1 2 1
1 3 1
2 3 2

Sample Output 1

3

Solution in Rust (judge verdict: Accepted)

//  ____            _                  _                       _       _
// |  _ \ _   _ ___| |_    ___ _ __   | |_ ___ _ __ ___  _ __ | | __ _| |_ ___
// | |_) | | | / __| __|  / __| '_ \  | __/ _ \ '_ ` _ \| '_ \| |/ _` | __/ _ \
// |  _ <| |_| \__ \ |_  | (__| |_) | | ||  __/ | | | | | |_) | | (_| | ||  __/
// |_| \_\\__,_|___/\__|  \___| .__/___\__\___|_| |_| |_| .__/|_|\__,_|\__\___|
//                            |_| |_____|               |_|

//https://github.com/manta1130/Competitive_Programming_Template_Rust

#[macro_use]
mod input {

    use std;
    use std::io;

    const SPLIT_DELIMITER: char = ' ';

    #[macro_export]
    #[allow(unused_macros)]
    macro_rules! input {
    ( $($x:expr ),*) => {
        {
            let temp_str = input_line_str();
            let mut split_result_iter = temp_str.split_whitespace();
                $(
                let buf_split_result = split_result_iter.next();
                let buf_split_result = buf_split_result.unwrap();
                    ($x) = buf_split_result.parse().unwrap();
                )*
        }
    };
}

    #[allow(dead_code)]
    pub fn input_line_str() -> String {
        let mut s = String::new();
        io::stdin().read_line(&mut s).unwrap();
        s.trim().to_string()
    }

    #[allow(dead_code)]
    pub fn p<T>(t: T)
    where
        T: std::fmt::Display,
    {
        println!("{}", t);
    }

    #[allow(dead_code)]
    pub fn input_vector2d<T>(line: usize) -> Vec<Vec<T>>
    where
        T: std::str::FromStr,
    {
        let mut v: Vec<Vec<T>> = Vec::new();

        for _ in 0..line {
            let vec_line = input_vector();
            v.push(vec_line);
        }
        v
    }

    #[allow(dead_code)]
    pub fn input_vector<T>() -> Vec<T>
    where
        T: std::str::FromStr,
    {
        let mut v: Vec<T> = Vec::new();

        let s = input_line_str();
        let split_result = s.split(SPLIT_DELIMITER);
        for z in split_result {
            let buf = match z.parse() {
                Ok(r) => r,
                Err(_) => panic!("Parse Error"),
            };
            v.push(buf);
        }
        v
    }

    #[allow(dead_code)]
    pub fn input_vector_row<T>(n: usize) -> Vec<T>
    where
        T: std::str::FromStr,
    {
        let mut v = Vec::with_capacity(n);
        for _ in 0..n {
            let buf = match input_line_str().parse() {
                Ok(r) => r,
                Err(_) => panic!("Parse Error"),
            };
            v.push(buf);
        }
        v
    }

    pub trait ToCharVec {
        fn to_charvec(&self) -> Vec<char>;
    }

    impl ToCharVec for String {
        fn to_charvec(&self) -> Vec<char> {
            self.to_string().chars().collect::<Vec<_>>()
        }
    }
}

mod flow {
use std;
use std::collections::VecDeque;

type CapValue = u64;
const INF: CapValue = 999999999;

#[derive(Clone, Copy)]
struct Edge {
    to: usize,
    cap: CapValue,
    rev: usize,
}

///最大流を計算(Dinicのアルゴリズム)
pub struct Dinic {
    n: usize,
    g: Vec<Vec<Edge>>,
    iter: Vec<usize>,
    level: Vec<isize>,
}

impl Dinic {
    ///要素数nのグラフを構築する。
    #[warn(dead_code)]
    pub fn new(n: usize) -> Dinic {
        let res = Dinic {
            n: n,
            g: vec![vec![]; n],
            iter: vec![],
            level: vec![],
        };
        res
    }
    #[warn(dead_code)]
    fn bfs(&mut self, s: usize) {
        self.level = vec![-1; self.n];
        let mut que = VecDeque::new();
        self.level[s] = 0;
        que.push_back(s);
        while !que.is_empty() {
            let v = que.pop_front().unwrap();
            for i in 0..self.g[v].len() {
                let e = &self.g[v][i];
                if e.cap > 0 && self.level[e.to] < 0 {
                    self.level[e.to] = self.level[v] + 1;
                    que.push_back(e.to);
                }
            }
        }
    }
    #[warn(dead_code)]
    fn dfs(&mut self, k: usize, t: usize, f: CapValue) -> CapValue {
        if k == t {
            return f;
        }
        for i in self.iter[k]..self.g[k].len() {
            let e = self.g[k][i];
            if e.cap > 0 && self.level[k] < self.level[e.to] {
                let r = self.dfs(e.to, t, std::cmp::min(f, e.cap));
                if r > 0 {
                    self.g[k][i].cap -= r;
                    self.g[e.to][e.rev].cap += r;
                    return r;
                }
            }
        }

        0
    }
    ///最大フローを求める。
    #[warn(dead_code)]
    pub fn get_maxflow(&mut self, s: usize, t: usize) -> CapValue {
        let mut res = 0;
        loop {
            self.bfs(s);
            if self.level[t] < 0 {
                return res;
            }
            self.iter = vec![0; self.n];
            loop {
                let f = self.dfs(s, t, INF);
                if f == 0 {
                    break;
                }
                res += f;
            }
        }
    }
    ///辺の追加
    ///
    /// f->tにvalueの容量を持つ辺を追加する。
    #[warn(dead_code)]
    pub fn add_edge(&mut self, f: usize, t: usize, value: CapValue) {
        let idx_t = self.g[t].len();
        let idx_f = self.g[f].len();
        self.g[f].push(Edge {
            to: t,
            cap: value,
            rev: idx_t,
        });
        self.g[t].push(Edge {
            to: f,
            cap: 0,
            rev: idx_f,
        });
    }
}

///最大流を計算(Ford-Fulkersonのアルゴリズム)
pub struct FordFulkerson {
    n: usize,
    g: Vec<Vec<Edge>>,
    used: Vec<bool>,
}

impl FordFulkerson {
    ///要素数nのグラフを構築する。
    #[warn(dead_code)]
    pub fn new(n: usize) -> FordFulkerson {
        let res = FordFulkerson {
            n: n,
            g: vec![vec![]; n],
            used: vec![],
        };
        res
    }
    #[warn(dead_code)]
    fn dfs(&mut self, k: usize, t: usize, f: CapValue) -> CapValue {
        if k == t {
            return f;
        }
        self.used[k] = true;
        for i in 0..self.g[k].len() {
            let e = self.g[k][i];
            if !self.used[e.to] && e.cap > 0 {
                let r = self.dfs(e.to, t, std::cmp::min(f, e.cap));
                if r > 0 {
                    self.g[k][i].cap -= r;
                    self.g[e.to][e.rev].cap += r;
                    return r;
                }
            }
        }

        0
    }
    ///最大フローを求める。
    #[warn(dead_code)]
    pub fn get_maxflow(&mut self, s: usize, t: usize) -> CapValue {
        let mut res = 0;
        loop {
            self.used = vec![false; self.n];
            let f = self.dfs(s, t, INF);
            if f == 0 {
                return res;
            }
            res += f;
        }
    }
    ///辺の追加
    ///
    /// f->tにvalueの容量を持つ辺を追加する。
    #[warn(dead_code)]
    pub fn add_edge(&mut self, f: usize, t: usize, value: CapValue) {
        let idx_t = self.g[t].len();
        let idx_f = self.g[f].len();
        self.g[f].push(Edge {
            to: t,
            cap: value,
            rev: idx_t,
        });
        self.g[t].push(Edge {
            to: f,
            cap: 0,
            rev: idx_f,
        });
    }
}
}

use flow::*;
#[allow(unused_imports)]
use input::*;

fn main() {
    let (v, e): (usize, usize);
    input!(v, e);
    let mut f = FordFulkerson::new(v);
    for _ in 0..e {
        let (a, b, c): (usize, usize, u64);
        input!(a, b, c);
        f.add_edge(a, b, c);
    }
    println!("{}", f.get_maxflow(0, v - 1));
}