2014 Multi-University Training Contest 2 1011 ZCC Loves Codefires 解题报告

暑期联训第二场。

高中被镇海虐了3年，大学继续被镇海虐，刚入ACM这条路不久，基础不够扎实，镇海还出这么变态的题目= =，就AC了最后一题。。

Problem Description

Though ZCC has many Fans, ZCC himself is a crazy Fan of a coder, called "Memset137".

It was on Codefires(CF), an online competitive programming site, that ZCC knew Memset137, and immediately became his fan.

But why?

Because Memset137 can solve all problem in rounds, without unsuccessful submissions; his estimation of time to solve certain problem is so accurate, that he can surely get an Accepted the second he has predicted. He soon became IGM, the best title of Codefires.
Besides, he is famous for his coding speed and the achievement in the field of Data Structures.

After become IGM, Memset137 has a new goal: He wants his score in CF rounds to be as large as possible.

What is score? In Codefires, every problem has 2 attributes, let's call them Ki and Bi(Ki, Bi＞0). if Memset137 solves the problem at Ti-th second, he gained Bi-Ki*Ti score. It's guaranteed Bi-Ki*Ti is always positive during the round time.

Now that Memset137 can solve every problem, in this problem, Bi is of no concern. Please write a program to calculate the minimal score he will lose.(that is, the sum of Ki*Ti).

 

Input

The first line contains an integer N(1≤N≤10^5), the number of problem in the round.

The second line contains N integers Ei(1≤Ei≤10^4), the time(second) to solve the i-th problem.

The last line contains N integers Ki(1≤Ki≤10^4), as was described.

 

Output

One integer L, the minimal score he will lose.

 

Sample Input

3
10 10 20
1 2 3

 

Sample Output

150

HintMemset137 takes the first 10 seconds to solve problem B, then solves problem C at the end of the 30th second. Memset137 gets AK at the end of the 40th second.
L = 10 * 2 + (10+20) * 3 + (10+20+10) * 1 = 150.

 

Problem Description

Though ZCC has many Fans, ZCC himself is a crazy Fan of a coder, called "Memset137".

It was on Codefires(CF), an online competitive programming site, that ZCC knew Memset137, and immediately became his fan.

But why?

Because Memset137 can solve all problem in rounds, without unsuccessful submissions; his estimation of time to solve certain problem is so accurate, that he can surely get an Accepted the second he has predicted. He soon became IGM, the best title of Codefires.
Besides, he is famous for his coding speed and the achievement in the field of Data Structures.

After become IGM, Memset137 has a new goal: He wants his score in CF rounds to be as large as possible.

What is score? In Codefires, every problem has 2 attributes, let's call them Ki and Bi(Ki, Bi＞0). if Memset137 solves the problem at Ti-th second, he gained Bi-Ki*Ti score. It's guaranteed Bi-Ki*Ti is always positive during the round time.

Now that Memset137 can solve every problem, in this problem, Bi is of no concern. Please write a program to calculate the minimal score he will lose.(that is, the sum of Ki*Ti).

 

Input

The first line contains an integer N(1≤N≤10^5), the number of problem in the round.

The second line contains N integers Ei(1≤Ei≤10^4), the time(second) to solve the i-th problem.

The last line contains N integers Ki(1≤Ki≤10^4), as was described.

 

Output

One integer L, the minimal score he will lose.

 

Sample Input

3
10 10 20
1 2 3

 

Sample Output

150

HintMemset137 takes the first 10 seconds to solve problem B, then solves problem C at the end of the 30th second. Memset137 gets AK at the end of the 40th second.
L = 10 * 2 + (10+20) * 3 + (10+20+10) * 1 = 150.

题目如上，总结就是类似分顺序取数，每个数大小不同，但是取出顺序会累加从而影响最后的结果，为了使最后结果最小，要找到最优解。

第一下看到这个题目，第一反应就是用动态规划去做，但是琢磨半天很难想出状态方程，因为它每个状态点无法比较状态对应的值大小（即使比较了也无意义）。

多次尝试之后，开始寻求其他方法，想了一种最朴素的方法，

定义结构体

point{
int E;
int K;
}
先用快速排序将按分值将point从大到小排序，然后依次从大到小进行冒泡，每次冒泡能保证前几次会使函数值减小，当再冒泡函数值增加时就停止该数的冒泡，换第二大的数进行冒泡。但是该算法每进行一次冒泡需要计算一次函数值，且n过大，最后导致TLE。

之后开始寻找变换的规律，

写出一组数据：

10 10 20 30

1     2   3   4

totEi	30	50	60	70
Ki	4	3	c276 2	1

交换3 和 4 后得到

totEi	20	50	60	70
Ki	3	4	2	1

可以看出，3和4的交换，对于其他项是不会有影响的，对值的影响来源于30*4+50*3与20*3+50*4的大小变换。
用常规变量表示的话就是，point(i)>point(i+1) 的充要条件是  Ei+1*Ki+1+(Ei+Ei+1)*Ki<Ei*Ki+(Ei+1+Ei)*Ki+1

化简得 Ei*Ki+1<Ei+1*Ki 即Ei/Ki > Ei+1/Ki+1

所以只要该条件满足，交换point(i)与point(i+1）就能得到最优解。

因而在point结构体中加入变量double s  // s=E/K;

根据s对 point进行快速排序，排序得到的就是最优解，求和就是要出的结果了。

代码#include<iostream>
#include<algorithm>
using namespace std;
struct point{
int E;
int K;
double s;
};
struct point p[100001];
int cmp(point p1,point p2)
{
return p1.s<p2.s;
}

int main()
{
freopen("in.txt","r",stdin);
int i,j,N;
int min;
__int64 sum=0;
__int64 totE=0;
cin>>N;
for(i=1;i<=N;i++)
cin>>p[i].E;
for(i=1;i<=N;i++)
cin>>p[i].K;
for(i=1;i<=N;i++)
p[i].s = p[i].E/(double)p[i].K;
sort(p+1,p+N+1,cmp);
for(i=1;i<=N;i++)
{
totE+=p[i].E;
sum+= totE*p[i].K;
}

cout<<sum<<endl;
}

Problem Description

Though ZCC has many Fans, ZCC himself is a crazy Fan of a coder, called "Memset137".

It was on Codefires(CF), an online competitive programming site, that ZCC knew Memset137, and immediately became his fan.

But why?

Because Memset137 can solve all problem in rounds, without unsuccessful submissions; his estimation of time to solve certain problem is so accurate, that he can surely get an Accepted the second he has predicted. He soon became IGM, the best title of Codefires.
Besides, he is famous for his coding speed and the achievement in the field of Data Structures.

After become IGM, Memset137 has a new goal: He wants his score in CF rounds to be as large as possible.

What is score? In Codefires, every problem has 2 attributes, let's call them Ki and Bi(Ki, Bi＞0). if Memset137 solves the problem at Ti-th second, he gained Bi-Ki*Ti score. It's guaranteed Bi-Ki*Ti is always positive during the round time.

Now that Memset137 can solve every problem, in this problem, Bi is of no concern. Please write a program to calculate the minimal score he will lose.(that is, the sum of Ki*Ti).

 

Input

The first line contains an integer N(1≤N≤10^5), the number of problem in the round.

The second line contains N integers Ei(1≤Ei≤10^4), the time(second) to solve the i-th problem.

The last line contains N integers Ki(1≤Ki≤10^4), as was described.

 

Output

One integer L, the minimal score he will lose.

 

Sample Input

3
10 10 20
1 2 3

 

Sample Output

150

HintMemset137 takes the first 10 seconds to solve problem B, then solves problem C at the end of the 30th second. Memset137 gets AK at the end of the 40th second.
L = 10 * 2 + (10+20) * 3 + (10+20+10) * 1 = 150.