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;
}
}
}
;
}