Flowers
Problem's Link: http://acm.hnu.cn/online/?action=problem&type=show&id=13409&courseid=0
Mean:
有N颗种子，每颗种子初始时营养值为0。当一颗种子营养值达到th后就会开花。
有两种操作：
1.给所有的种子浇w升水；
2.给某个种子施f升肥；
对于第i颗种子，每浇1升水会增加vw点营养值，每施1升肥可以增加vf点营养值，该种种子的肥料单价为pf，当营养值达到th后开花。
浇水必须一起浇，而且水的单价是一样的，都是pw。花的th可能为负，而且有的花浇水营养值会减少。
analyse:
很明显的凸函数。
由于浇水的量所有种子都相同，所以三分水量即可。
Time complexity: O(N)
Source code:
/*
* this code is made by crazyacking
* Verdict: Accepted
* Submission Date: 2015-08-16-19.52
* Time: 0MS
* Memory: 137KB
*/
#include <queue>
#include <cstdio>
#include <set>
#include <string>
#include <stack>
#include <cmath>
#include <climits>
#include <map>
#include <cstdlib>
#include <iostream>
#include <vector>
#include <algorithm>
#include <cstring>
#define eps 1e-14
#define LL __int64
#define ULL unsigned __int64
using namespace std;
const int MAXN = 10 +( int) 1e5;
LL n , pw , vw [ MAXN ], pf [ MAXN ], vf [ MAXN ], th [ MAXN ];
double tmp , t;
double cal( double & w)
{
tmp = w * pw;
for( int i = 0; i <n; ++ i)
{
t = th [ i ] - w * vw [ i ];
if( t <= 0) continue;
tmp +=( t) * pf [ i ] * 1. / vf [ i ];
}
return tmp;
}
double work( double l , double r)
{
double mid , mmid;
int st = 100;
while( st --)
{
mid =( l + r) / 2;
mmid =( mid + r) / 2;
if( cal( mid) - cal( mmid) > eps)
l = mid;
else r = mmid;
}
return l;
}
int main()
{
ios_base :: sync_with_stdio( false);
cin . tie( 0);
while( scanf( "%I64d" , &n ),n)
{
scanf( "%I64d" , & pw);
for( int i = 0; i <n; ++ i)
{
scanf( "%I64d %I64d %I64d %I64d" , & vw [ i ], & pf [ i ], & vf [ i ], & th [ i ]);
}
double val = work( 0 , 200);
printf( "%.6lf \n " , cal( val));
}
return 0;
}
/*
*/
* this code is made by crazyacking
* Verdict: Accepted
* Submission Date: 2015-08-16-19.52
* Time: 0MS
* Memory: 137KB
*/
#include <queue>
#include <cstdio>
#include <set>
#include <string>
#include <stack>
#include <cmath>
#include <climits>
#include <map>
#include <cstdlib>
#include <iostream>
#include <vector>
#include <algorithm>
#include <cstring>
#define eps 1e-14
#define LL __int64
#define ULL unsigned __int64
using namespace std;
const int MAXN = 10 +( int) 1e5;
LL n , pw , vw [ MAXN ], pf [ MAXN ], vf [ MAXN ], th [ MAXN ];
double tmp , t;
double cal( double & w)
{
tmp = w * pw;
for( int i = 0; i <n; ++ i)
{
t = th [ i ] - w * vw [ i ];
if( t <= 0) continue;
tmp +=( t) * pf [ i ] * 1. / vf [ i ];
}
return tmp;
}
double work( double l , double r)
{
double mid , mmid;
int st = 100;
while( st --)
{
mid =( l + r) / 2;
mmid =( mid + r) / 2;
if( cal( mid) - cal( mmid) > eps)
l = mid;
else r = mmid;
}
return l;
}
int main()
{
ios_base :: sync_with_stdio( false);
cin . tie( 0);
while( scanf( "%I64d" , &n ),n)
{
scanf( "%I64d" , & pw);
for( int i = 0; i <n; ++ i)
{
scanf( "%I64d %I64d %I64d %I64d" , & vw [ i ], & pf [ i ], & vf [ i ], & th [ i ]);
}
double val = work( 0 , 200);
printf( "%.6lf \n " , cal( val));
}
return 0;
}
/*
*/
