pku 2231 Moo Volume 线性方法求sig(sig|a[i]-a[j]|)

Moo Volume

Time Limit: 1000MS	Memory Limit: 65536K
Total Submissions: 12801	Accepted: 3690

Description

Farmer John has received a noise complaint from his neighbor, Farmer Bob, stating that his cows are making too much noise. 

FJ's N cows (1 <= N <= 10,000) all graze at various locations on a long one-dimensional pasture. The cows are very chatty animals. Every pair of cows simultaneously carries on a conversation (so every cow is simultaneously MOOing at all of the N-1 other cows). When cow i MOOs at cow j, the volume of this MOO must be equal to the distance between i and j, in order for j to be able to hear the MOO at all. Please help FJ compute the total volume of sound being generated by all N*(N-1) simultaneous MOOing sessions.

Input

* Line 1: N 

* Lines 2..N+1: The location of each cow (in the range 0..1,000,000,000).

Output

There are five cows at locations 1, 5, 3, 2, and 4.

Sample Input

5
1
5
3
2
4      

Sample Output

40      

Hint

INPUT DETAILS: 

There are five cows at locations 1, 5, 3, 2, and 4. 

OUTPUT DETAILS: 

Cow at 1 contributes 1+2+3+4=10, cow at 5 contributes 4+3+2+1=10, cow at 3 contributes 2+1+1+2=6, cow at 2 contributes 1+1+2+3=7, and cow at 4 contributes 3+2+1+1=7. The total volume is (10+10+6+7+7) = 40. #include<iostream> #include<cstdio> #include<algorithm> using namespace std; long long a[11000]; int main() {     int n;     while(scanf("%d",&n)==1)     {         for(int i=1;i<=n;i++) cin>>a[i];         sort(a+1,a+1+n);         long long sum=0;         for(int i=1;i<n;i++)         {             int j=i+1;             sum+=i*(n-i)*(a[j]-a[i]);         }         sum*=2;         cout<<sum<<endl;     }     return 0; }