MST Unification【Codeforces Round #535 (Div. 3).F】【最小生成树性质】

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题目链接http://codeforces.com/contest/1108/problem/F


  昨夜比赛的时候,想法就是在Kruskal生成树上跑dfs()上的DP,然后WA在了26组,后来赛后想了下,就是在取DP关系的时候出现了漏洞,可能会让新加入的边以及等值的替换边进行替换之后形成两棵树(一个是树、另一棵成环)这样的情况,然后距离结束还只剩下十分钟……来不及了,睡了……QAQ,今早起来的时候再这么一想,为什么不求出所有的可以链接两棵树的方案数,再求出有效的方案数(有效方案数就是Kruskal的求法),然后不断这样加上它们的差值……这不就是最优解了吗!?

  然后就开始敲了……1A,我的天…… 哎,懵逼态……嘤!


#include <iostream>
#include <cstdio>
#include <cmath>
#include <string>
#include <cstring>
#include <algorithm>
#include <limits>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <cstdlib>
#include <ctime>
#define lowbit(x) ( x&(-x) )
#define pi 3.141592653589793
#define e 2.718281828459045
#define INF 0x3f3f3f3f3f3f3f3f
#define HalF (l + r)>>1
#define lsn rt<<1
#define rsn rt<<1|1
#define Lson lsn, l, mid
#define Rson rsn, mid+1, r
#define QL Lson, ql, qr
#define QR Rson, ql, qr
#define myself rt, l, r
using namespace std;
typedef unsigned long long ull;
typedef long long ll;
const int maxN = 2e5 + 7;
int N, M, ans, root[maxN];
struct Eddge
{
    int u, v;
    ll val;
    Eddge(int a=-1, int b=0, ll c=0):u(a), v(b), val(c) {}
}edge[maxN];
bool cmp(Eddge e1, Eddge e2) { return e1.val < e2.val; }
int fid(int x) { return x == root[x]?x:(root[x] = fid(root[x])); }
inline void init() { for(int i=1; i<=N; i++) root[i] = i; }
int main()
{
    scanf("%d%d", &N, &M);
    init();
    int e1, e2; ll e3;
    for(int i=1; i<=M; i++)
    {
        scanf("%d%d%lld", &e1, &e2, &e3);
        edge[i] = Eddge(e1, e2, e3);
    }
    sort(edge + 1, edge + M + 1, cmp);
    ans = 0;
    int i = 1, j = 1;
    while(i < M)
    {
        j = i;
        int cnt = 0, all_way = 0;
        while(j <= M && edge[j].val == edge[i].val)
        {
            int x = edge[j].u, y = edge[j].v;
            int u = fid(x), v = fid(y);
            if(u != v) all_way++;
            j++;
        }
        j = i;
        while(j <= M && edge[j].val == edge[i].val)
        {
            int x = edge[j].u, y = edge[j].v;
            int u = fid(x), v = fid(y);
            if(u != v)
            {
                cnt++;
                root[u] = v;
            }
            j++;
        }
        i = j;
        ans += all_way - cnt;
    }
    printf("%d\n", ans);
    return 0;
}

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