1679: [Usaco2005 Jan]Moo Volume 牛的呼声
Time Limit: 1 Sec Memory Limit: 64 MB Submit: 1097 Solved: 571 [Submit][Status][Discuss]
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.
约翰的邻居鲍勃控告约翰家的牛们太会叫．
约翰的N(1≤N≤10000)只牛在一维的草场上的不同地点吃着草．她们都是些爱说闲话的奶牛，每一只同时与其他N-1只牛聊着天．一个对话的进行，需要两只牛都按照和她们间距离等大的音量吼叫，因此草场上存在着N（N-1）/2个声音． 请计算这些音量的和．
Input
* Line 1: N * Lines 2..N+1: The location of each cow (in the range 0..1,000,000,000).
第1行输入N，接下来输入N个整数，表示一只牛所在的位置．
Output
* Line 1: A single integer, the total volume of all the MOOs.
一个整数，表示总音量．
Sample Input
5
1
5
3
2
4
INPUT DETAILS:
There are five cows at locations 1, 5, 3, 2, and 4.
Sample Output
40
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.
排序后发现每一个区间的贡献为左边点数*右边点数*2
#include <cstdio>
#include <algorithm>
using namespace std;
int n;
long long x[10000 + 10];
int main(){
scanf("%d", &n);
for(int i = 1; i <= n; i++) scanf("%d", x + i);
sort(x + 1, x + n + 1);
long long ans = 0;
for(int i = 2; i <= n; i++)
ans += (x[i] - x[i - 1]) * (i - 1) * (n - i + 1);
printf("%lld\n", ans * 2);
return 0;
}