Problem:
Minimum Spanning Tree

Find the sum of weights of edges of the Minimum Spanning Tree for a given weighted undirected graph G = (V, E).

Input

|V| |E|
s0 t0 w0
s1 t1 w1
:
s|E|-1 t|E|-1 w|E|-1

, where |V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively.

si and ti represent source and target verticess of i-th edge (undirected) and wi represents the weight of the i-th edge.

Output

Print the sum of the weights of the Minimum Spanning Tree.

Constraints

1 ≤ |V| ≤ 10,000

0 ≤ |E| ≤ 100,000

0 ≤ wi ≤ 10,000

The graph is connected

There are no parallel edges

There are no self-loops

Sample Input 1

4 6
0 1 2
1 2 1
2 3 1
3 0 1
0 2 3
1 3 5

Sample Output 1

3

Sample Input 2

6 9
0 1 1
0 2 3
1 2 1
1 3 7
2 4 1
1 4 3
3 4 1
3 5 1
4 5 6

Sample Output 2

5

Solution in Rust (judge verdict: Accepted)

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($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)*}
    };
}
 
#[allow(unused_macros)]
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)*}
    };
 
    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}
 
#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };
 
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
 
    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };
 
    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };
 
    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };
 
    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

fn main() {
    input! {
        _v: usize,
        e: usize,
        p: [(usize, usize, usize); e],
    }

    let mut h = Vec::<HeapElement>::new();
    for a in p.iter() {
        let t = HeapElement {
            from: a.0,
            into: a.1,
            val: a.2,
        };
        h.push(t);
    }
    let mut k = Kruskal::new(&mut h);
    k.sort();
    let ans = k.kruskal();

    println!("{}", ans);
}


struct HeapElement {
    from: usize,
    into: usize,
    val: usize,
}

struct Kruskal<'a> {
    heap: &'a mut Vec<HeapElement>,
    uf: Uf,
}

impl<'a> Kruskal<'a> {

    fn new(h: &'a mut Vec<HeapElement>) -> Self {
        Kruskal {
            heap: h,
            uf: Uf::new(100010),
        }
    }

    fn sort(&mut self) {
        self.heap.sort_by_key(|h| h.val);
    }

// heapはsortされていることを仮定
    fn kruskal(&mut self) -> usize {
        let mut count = 0;
        for h in self.heap.iter() {
            if !self.uf.same(h.from, h.into) {
                count = count + h.val;
                self.uf.unite(h.from, h.into);
            }
        }
        count
    }
}

struct Uf {
    par: Vec<usize>,
    rank: Vec<usize>,
}

impl Uf {
    fn new(n: usize) -> Uf {
        Uf {
            par: (0..n).collect(),
            rank: vec![0; n],
        }
    }

    fn root(&mut self, x: usize) -> usize {
        if self.par[x] == x { 
            return x; 
        } else { 
            let tmp = self.par[x];
            self.par[x] = self.root(tmp);
            return self.par[x];
        };
    }

    fn same(&mut self, x: usize, y: usize) -> bool {
        self.root(x) == self.root(y)
    }

    fn unite(&mut self, x: usize, y: usize) {
        let a = self.root(x);
        let b= self.root(y);

        if a == b {
            return;
        }

        if self.rank[a] < self.rank[b] {
            self.par[a] = b;
        } else {
            self.par[b] = a;
            if self.rank[a] == self.rank[b] {
                self.rank[x] = self.rank[x] + 1;
            }
        }
    }

}