Watering Hole

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题目背景

John的农场缺水了！！！

题目描述

Farmer John has decided to bring water to his N (1 <= N <= 300) pastures which are conveniently numbered 1..N. He may bring water to a pasture either by building a well in that pasture or connecting the pasture via a pipe to another pasture which already has water.
Digging a well in pasture i costs W_i (1 <= W_i <= 100,000).
Connecting pastures i and j with a pipe costs P_ij (1 <= P_ij <= 100,000; P_ij = P_ji; P_ii=0).
Determine the minimum amount Farmer John will have to pay to water all of his pastures.

翻译

农民John 决定将水引入到他的边长为n(1<=n<=300)的牧场。他准备通过挖若干井，并在各块田中修筑水道来连通各块田地以供水。在第i 号田中挖一口井需要花W_i(1<=W_i<=100,000)元。连接i 号田与j 号田需要P_ij (1 <= P_ij <= 100,000 , P_ji=P_ij)元。
请求出农民John 需要为连通整个牧场的每一块田地所需要的钱数。

输入输出格式

输入格式：

第1 行为一个整数n。
第2 到n+1 行每行一个整数，从上到下分别为W_1 到W_n。
第n+2 到2n+1 行为一个矩阵，表示需要的经费（P_ij）。

输出格式：

只有一行，为一个整数，表示所需要的钱数。

输入输出样例

输入样例#1：

454430 2 2 22 0 3 32 3 0 42 3 4 0

输出样例#1：

说明

John等着用水，你只有1s时间！！！
用最少的花费把所有点都连起来，最小生成树……井的话就看做一个超级源点0号点，这就成了求 0 - n 这 n + 1 个点的最小生成树。
代码如下

#include<iostream>#include<cstdio>#include<cstring>#include<algorithm>#include<queue>using namespace std;const int size = 200010;int n;int num[size];struct dc{    int f,t,d;}l[size];int tot = 1;void build(int f,int t,int d){    l[tot].f = f;    l[tot].t = t;    l[tot].d = d;    tot ++;}int f[size];int find(int x){    if(f[x] == x)        return x;    return f[x] = find(f[x]);}bool cmp(dc a,dc b){    return a.d < b.d;}int main(){    scanf("%d",&n);    for(int i = 1 ; i <= n ; i ++)        scanf("%d",&num[i]) , f[i] = i;    for(int i = 1 ; i <= n ; i ++)        for(int j = 1 ; j <= n ; j ++)        {            int d;            scanf("%d",&d);            build(i,j,d);        }    for(int i = 1 ; i <= n ; i ++)        build(0,i,num[i]);    sort(l+1,l+tot,cmp);    int ans = 0;    for(int i = 1 ; i < tot ; i ++)    {        int ff = l[i].f , ft = l[i].t;        if(find(ff) != find(ft))        {            f[find(ff)] = find(ft);            ans += l[i].d;        }    }    printf("%d\n",ans);    return 0;}

传送门：https://www.luogu.org/problem/show?pid=1550

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