BZOJ 3442 学习小组 费用流

题目大意：给出学生的数目和学习小组的数目，学生参加小组需要交纳费用，每个小组会支出C[i]*cnt[i]^2。每个学生可以参加k个小组，问最多的学生参加时，最小支出费用。

思路：如果不算后面那个什么鬼的条件的话，见图十分显然。

S->每个学生 f:k,c:0

每个学生->每个学习小组 f:1,c:-F[i]

每个学习小组->T f:1,c:1 * C[i],3 * C[i],5 * C[i],7 * C[i],......

后面的条件其实是说，每个学生的k次机会不一定全用光，但是所有人都要参加至少一个小组。于是我们可以每个人->T f:k - 1,c:0

然后跑费用流

CODE：

#define _CRT_SECURE_NO_DEPRECATE

#include <queue>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define MAX 510
#define MAXE 200010
#define INF 0x3f3f3f3f
#define S 0
#define T (MAX - 1)
using namespace std;

 struct MinCostMaxFlow{
	int head[MAX],total;
	int next[MAXE],aim[MAXE],flow[MAXE],cost[MAXE];
	int from[MAX],p[MAX];

	int f[MAX];
	bool v[MAX];

	MinCostMaxFlow() {
		total = 1;
	}
	void Add(int x,int y,int f,int c) {
		next[++total] = head[x];
		aim[total] = y;
		flow[total] = f;
		cost[total] = c;
		head[x] = total;
	}
	void Insert(int x,int y,int f,int c) {
		Add(x,y,f,c);
		Add(y,x,0,-c);
	}
	bool SPFA() {
		static queue<int> q;
		while(!q.empty())	q.pop();
		memset(f,0x3f,sizeof(f));
		memset(v,false,sizeof(v));
		f[S] = 0;
		q.push(S);
		while(!q.empty()) {
			int x = q.front(); q.pop();
			v[x] = false;
			for(int i = head[x]; i; i = next[i])
				if(flow[i] && f[aim[i]] > f[x] + cost[i]) {
					f[aim[i]] = f[x] + cost[i];
					if(!v[aim[i]])
						v[aim[i]] = true,q.push(aim[i]);
					from[aim[i]] = x;
					p[aim[i]] = i;
				}
		}
		return f[T] != INF;
	}
	int EdmondsKarp() {
		int re = 0;
		while(SPFA()) {
			int max_flow = INF;
			for(int i = T; i != S; i = from[i])
				max_flow = min(max_flow,flow[p[i]]);
			for(int i = T; i != S; i = from[i]) {
				flow[p[i]] -= max_flow;
				flow[p[i]^1] += max_flow;
			}
			re += f[T] * max_flow;
		}
		return re;
	}
}solver;

int points,groups,k;
int C[MAX],F[MAX];
bool map[MAX][MAX];

int main()
{
	cin >> points >> groups >> k;
	for(int i = 1; i <= groups; ++i)	scanf("%d",&C[i]);
	for(int i = 1; i <= groups; ++i)	scanf("%d",&F[i]);
	for(int i = 1; i <= points; ++i)
		for(int j = 1;j <= groups; ++j)
			scanf("%1d",&map[i][j]);
	for(int i = 1; i <= points; ++i) {
		solver.Insert(S,i,k,0);
		for(int j = 1; j <= groups; ++j)
			if(map[i][j])
				solver.Insert(i,points + j,1,-F[j]);
	}
	if(k - 1)
		for(int i = 1; i <= points; ++i)
			solver.Insert(i,T,k - 1,0);
	for(int i = 1; i <= groups; ++i)
		for(int j = 1; j <= points; ++j)
			solver.Insert(i + points,T,1,((j << 1) - 1) * C[i]);
	cout << solver.EdmondsKarp() << endl;
	return 0;
}