Kruskal 模板

最小生成树指的是在图上面找到权值最小的一棵树，并且保证图上所有的点都在这棵树上。

解决办法：Kruskal 算法（贪心思想）

将边按权值从小到大排序，然后按这个顺序不断连边，直到所有点联通。

/**
 *  Fuck you.
 *  I love you too.
 */

#include<bits/stdc++.h>
#define lson i<<2
#define rson i<<2|1
#define LS l,mid,lson
#define RS mid+1,r,rson
#define mem(a,x) memset(a,x,sizeof(a))
#define gcd(a,b) __gcd(a,b)
#define ll long long
#define ull unsigned long long
#define lowbit(x) (x&-x)
#define enld endl
#define mian main
#define itn int
#define prinft printf

const double PI = acos (-1.0);
const int INF = 0x3f3f3f3f;
const int EXP = 1e-8;
const int N = 1e5 + 5;
const int MOD = 1e9 + 7;
const int MAXN = 1e5 + 5;

using namespace std;

int n;
int ans;
int par[N];

struct ed {
    int s, e, cost;
} edge[MAXN];

bool cmp (ed a, ed b) {
    return a.cost < b.cost;
}

int Find (int a) {
    return a == par[a] ? a : par[a] = Find (par[a]);
}

void join (int a, int b) {
    par[Find (a)] = Find (b);
}

int main() {
    while (~scanf ("%d", &n)) {
        ans = 0;
        for (int i = 0; i < n; ++i) {
            scanf ("%d%d%d", &edge[i].s, &edge[i].e, &edge[i].cost);
            par[edge[i].s] = edge[i].s;
            par[edge[i].e] = edge[i].e;
        }
        sort (edge, edge + n, cmp);
        for (int i = 0; i < n; ++i) {
            if (Find (edge[i].s) != Find (edge[i].e)) {
                cout << edge[i].s << ' ' << edge[i].e << endl;
                join (edge[i].s, edge[i].e);
                ans += edge[i].cost;
            }
        }
        cout << ans << endl;
    }
    return 0;
}

　　

Hdu - 1162 Eddy's picture （完全图）

 /**
  *  Fuck you.
  *  I love you too.
  */

 #include<bits/stdc++.h>
 #define lson i<<2
 #define rson i<<2|1
 #define LS l,mid,lson
 #define RS mid+1,r,rson
 #define mem(a,x) memset(a,x,sizeof(a))
 #define gcd(a,b) __gcd(a,b)
 #define ll long long
 #define ull unsigned long long
 #define lowbit(x) (x&-x)
 #define enld endl
 #define mian main
 #define itn int
 #define prinft printf

 const double PI = acos (-1.0);
 const int INF = 0x3f3f3f3f;
 ;
 ;
 ;
 ;

 using namespace std;

 int n;
 int ans;
 int par[N];

 struct ed {
     int s, e, cost;
 } edge[MAXN];

 bool cmp (ed a, ed b) {
     return a.cost < b.cost;
 }

 int Find (int a) {
     return a == par[a] ? a : par[a] = Find (par[a]);
 }

 void join (int a, int b) {
     par[Find (a)] = Find (b);
 }

 int main() {
     while (~scanf ("%d", &n)) {
         ans = ;
         ; i < n; ++i) {
             scanf ("%d%d%d", &edge[i].s, &edge[i].e, &edge[i].cost);
             par[edge[i].s] = edge[i].s;
             par[edge[i].e] = edge[i].e;
         }
         sort (edge, edge + n, cmp);
         ; i < n; ++i) {
             if (Find (edge[i].s) != Find (edge[i].e)) {
                 cout << edge[i].s << ' ' << edge[i].e << endl;
                 join (edge[i].s, edge[i].e);
                 ans += edge[i].cost;
             }
         }
         cout << ans << endl;
     }
     ;
 }

Hdu - 1233 还是畅通工程（将上面的模板添加一行即可AC）

 /**
  *  Fuck you.
  *  I love you too.
  */

 #include<bits/stdc++.h>
 #define lson i<<2
 #define rson i<<2|1
 #define LS l,mid,lson
 #define RS mid+1,r,rson
 #define mem(a,x) memset(a,x,sizeof(a))
 #define gcd(a,b) __gcd(a,b)
 #define ll long long
 #define ull unsigned long long
 #define lowbit(x) (x&-x)
 #define enld endl
 #define mian main
 #define itn int
 #define prinft printf

 const double PI = acos (-1.0);
 const int INF = 0x3f3f3f3f;
 ;
 ;
 ;
 ;

 using namespace std;

 int n;
 int ans;
 int par[N];

 struct ed {
     int s, e, cost;
 } edge[MAXN];

 bool cmp (ed a, ed b) {
     return a.cost < b.cost;
 }

 int Find (int a) {
     return a == par[a] ? a : par[a] = Find (par[a]);
 }

 void join (int a, int b) {
     par[Find (a)] = Find (b);
 }

 int main() {
     ) {
         ans = ;
         n = n * (n - ) / ;
         ; i < n; ++i) {
             scanf ("%d%d%d", &edge[i].s, &edge[i].e, &edge[i].cost);
             par[edge[i].s] = edge[i].s;
             par[edge[i].e] = edge[i].e;
         }
         sort (edge, edge + n, cmp);
         ; i < n; ++i) {
             if (Find (edge[i].s) != Find (edge[i].e)) {
                 //cout << edge[i].s << ' ' << edge[i].e << endl;
                 join (edge[i].s, edge[i].e);
                 ans += edge[i].cost;
             }
         }
         cout << ans << endl;
     }
     ;
 }

Hdu - 1598 find the most comfortable road

并查集 + 枚举

先排序（从大到小，从小到大都行），再枚举所有的边，记录其中的最大最小值，更新答案。

 /**
  *  Fuck you.
  *  I love you too.
  */

 #include<bits/stdc++.h>
 #define lson i<<2
 #define rson i<<2|1
 #define LS l,mid,lson
 #define RS mid+1,r,rson
 #define mem(a,x) memset(a,x,sizeof(a))
 #define gcd(a,b) __gcd(a,b)
 #define ll long long
 #define ull unsigned long long
 #define lowbit(x) (x&-x)
 #define enld endl
 #define mian main
 #define itn int
 #define prinft printf

 const double PI = acos (-1.0);
 const int INF = 0x3f3f3f3f;
 ;
 ;
 ;
 ;

 using namespace std;

 int n, m, q;
 int Max, Min, ans;
 int x, y;
 int par[N];

 struct ed {
     int s, e, cost;
 } edge[MAXN];

 bool cmp (ed a, ed b) {
     return a.cost < b.cost;
 }

 int Find (int a) {
     return a == par[a] ? a : par[a] = Find (par[a]);
 }

 void join (int a, int b) {
     par[Find (a)] = Find (b);
 }

 void init() {
     ; i < m+; ++i)
         par[i] = i;
 }

 int main() {
     while (~scanf ("%d%d", &n, &m)) {
         mem (par, );
         ; i < m; i++) {
             scanf ("%d%d%d", &edge[i].s, &edge[i].e, &edge[i].cost);
         }
         sort (edge, edge + m, cmp);
         scanf ("%d", &q);
         while (q--) {
             scanf ("%d%d", &x, &y);
             ans = INF;
             ; j < m; j++) {
                 init();
                 Min = INF, Max = ;
                 for (int i = j; i < m; i++) {
                     if (Find (edge[i].s) != Find (edge[i].e)) {
                         join (edge[i].s, edge[i].e);
                         Min = min (Min, edge[i].cost), Max = max (Max, edge[i].cost);
                     }
                     if (Find (x) == Find (y)) {
                         ans = min (ans, Max - Min);
                         break;
                     }
                 }
             }
             if (ans == INF)
                 cout << "-1" << endl;
             else {
                 cout << ans << endl;
             }
         }
     }
     ;
 }