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 C (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#define INF 1010001000
#define MAX_V 10001
#define MAX_E 100000
#define min(a, b) a<b?a:b

typedef struct edge {
    int from, to, cost;
}edge;

int par[MAX_V], rank[MAX_V];

void init(int n);
int find(int x);
void unite(int x, int y);
int same(int x, int y);
int cmp(const void *a, const void *b);
int kruskal(void);

edge input[MAX_E];
int V, E;


int main(void)
{
    int i, j, s, t, d;
    scanf("%d %d", &V, &E);
    for (i = 0; i < E; i++) {
        scanf("%d %d %d", &input[i].from, &input[i].to, &input[i].cost);
    }
    printf("%d\n", kruskal());
    return 0;
}


int kruskal(void)
{
    edge e;
    int i, res = 0;
    init(V);
    qsort(input, E, sizeof(edge), cmp);
    for (i = 0; i < E; i++) {
        e = input[i];
        if (same(e.from, e.to)) {
            unite(e.from, e.to);
            res += e.cost;
        }
    }
    return res;
}

int cmp(const void *a, const void *b)
{
    edge temp1 = *(edge *) a;
    edge temp2 = *(edge *) b;
    return temp1.cost - temp2.cost;
}

void init(int n)
{
    int i;
    for (i = 0; i < n; i++) {
        par[i] = i;
        rank[i] = 0;
    }
}

int find(int x)
{
    if (par[x] == x) {
        return x;
    } else {
        return par[x] = find(par[x]);
    }
}

void unite(int x, int y)
{
    x = find(x);
    y = find(y);
    if (x == y) {
        return ;
    }
    if (rank[x] < rank[y]) {
        par[x] = y;
    } else {
        par[y] = x;
        if (rank[x] == rank[y]) {
            rank[x]++;
        }
    }
}

int same(int x, int y)
{
    //同じなら0, 違うならそれ以外
    return find(x) - find(y);
}