BZOJ 1449: [JSOI2009]球队收益( 最小费用最大流)

先考虑假如全部输了的收益. 再考虑每场比赛球队赢了所得收益的增加量,用这个来建图..

--------------------------------------------------------------------------------------------------

#include<cstdio>

#include<cstring>

#include<algorithm>

#include<queue>

#include<iostream>

 

#define rep( i , n ) for( int i = 0 ; i < n ; ++i )

#define clr( x , c ) memset( x , c , sizeof( x ) )

#define Rep( i , n ) for( int i = 1 ; i <= n ; ++i )

 

using namespace std;

 

const int maxn = 6000 + 5;

const int INF = 0x3f3f3f3f;

 

struct edge {

int to , cap , cost;

edge *next , *rev;

};

 

edge* pt;

edge* head[ maxn ];

edge EDGE[ 20000 ];

 

void init() { 

pt = EDGE;

clr( head , 0 );

}

 

inline void add( int u , int v , int d , int w ) {

pt -> to = v;

pt -> cap = d;

pt -> cost = w;

pt ->next = head[ u ];

head[ u ] = pt++;

}

 

inline void add_edge( int u , int v , int d , int w ) {

add( u , v , d , w );

add( v , u , 0 , -w );

head[ u ] -> rev = head[ v ];

head[ v ] -> rev = head[ u ];

}

 

edge* p[ maxn ];

int d[ maxn ] , a[ maxn ] , inQ[ maxn ];

 

int min_cost( int S , int T ) {

int cost = 0;

for( ; ; ) {

clr( d , INF );

d[ S ] = 0;

clr( inQ , 0 );

queue< int > Q;

a[ S ] = INF , Q.push( S );

while( ! Q.empty() ) {

int x = Q.front();

Q.pop();

inQ[ x ] = false;

   for( edge* e = head[ x ] ; e ; e =  e -> next )

       if( e -> cap > 0 && d[ e -> to ] > d[ x ] + e -> cost ) {

       

        int to = e -> to;

       

        d[ to ] = d[ x ] + e -> cost;

        a[ to ] = min( a[ x ] , e -> cap );

        p[ to ] = e;

       

        if( ! inQ[ to ] ) 

           Q.push( to ) , inQ[ to ] = true;

           

       }

       

}

if( d [ T ] == INF ) break;

cost += d[ T ] * a[ T ];

int x = T;

while( x != S ) {

p[ x ] -> cap -= a[ T ];

p[ x ] -> rev -> cap += a[ T ];

x = p[ x ] -> rev -> to;

}

}

return cost; 

}

 

int win[ maxn ] , lose[ maxn ];

int C[ maxn ] , D[ maxn ];

int cnt[ maxn ];

 

int main() {

  

init();

int n , m;

cin >> n >> m;

int s = 0 , t = n + m + 1;

Rep( i , n ) {

   scanf( "%d%d%d%d" , &win[ i ] , &lose[ i ] , &C[ i ] , &D[ i ] );

   cnt[ i ] = 0;

}

Rep( i , m ) {

int u , v;

scanf( "%d%d" , &u , &v );

cnt[ u ]++ , cnt[ v ]++;

add_edge( s , i , 1 , 0 );

add_edge( i , u + m , 1 , 0 );

add_edge( i , v + m , 1 , 0 );

}

int ans = 0;

Rep( i , n ) {

int x = i + m;

lose[ i ] += cnt[ i ];

ans += C[ i ] * win[ i ] * win[ i ] + D[ i ] * lose[ i ] * lose[ i ];

while( cnt[ i ]-- ) {

add_edge( x , t , 1 , 2 * ( C[ i ] * win[ i ] - D[ i ] * lose[ i ] ) + C[ i ] + D[ i ] );

win[ i ]++;

lose[ i ]--;

}

}

cout << min_cost( s , t ) + ans << "\n";

return 0;

}

  

-------------------------------------------------------------------------------------------------- 

1449: [JSOI2009]球队收益

Time Limit: 5 Sec   Memory Limit: 64 MB
Submit: 500   Solved: 272
[ Submit][ Status][ Discuss]

Description

Input

Output

一个整数表示联盟里所有球队收益之和的最小值。

Sample Input

3 3
1 0 2 1
1 1 10 1
0 1 3 3
1 2
2 3
3 1

Sample Output

43

HINT

Source