MooFest
Time Limit: 1000MS | Memory Limit: 30000K | |
Total Submissions: 9189 | Accepted: 4158 |
Description
Every year, Farmer John's N (1 <= N <= 20,000) cows attend "MooFest",a social gathering of cows from around the world. MooFest involves a variety of events including haybale stacking, fence jumping, pin the tail on the farmer, and of course, mooing. When the cows all stand in line for a particular event, they moo so loudly that the roar is practically deafening. After participating in this event year after year, some of the cows have in fact lost a bit of their hearing.
Each cow i has an associated "hearing" threshold v(i) (in the range 1..20,000). If a cow moos to cow i, she must use a volume of at least v(i) times the distance between the two cows in order to be heard by cow i. If two cows i and j wish to converse, they must speak at a volume level equal to the distance between them times max(v(i),v(j)).
Suppose each of the N cows is standing in a straight line (each cow at some unique x coordinate in the range 1..20,000), and every pair of cows is carrying on a conversation using the smallest possible volume.
Compute the sum of all the volumes produced by all N(N-1)/2 pairs of mooing cows.
Each cow i has an associated "hearing" threshold v(i) (in the range 1..20,000). If a cow moos to cow i, she must use a volume of at least v(i) times the distance between the two cows in order to be heard by cow i. If two cows i and j wish to converse, they must speak at a volume level equal to the distance between them times max(v(i),v(j)).
Suppose each of the N cows is standing in a straight line (each cow at some unique x coordinate in the range 1..20,000), and every pair of cows is carrying on a conversation using the smallest possible volume.
Compute the sum of all the volumes produced by all N(N-1)/2 pairs of mooing cows.
Input
* Line 1: A single integer, N
* Lines 2..N+1: Two integers: the volume threshold and x coordinate for a cow. Line 2 represents the first cow; line 3 represents the second cow; and so on. No two cows will stand at the same location.
* Lines 2..N+1: Two integers: the volume threshold and x coordinate for a cow. Line 2 represents the first cow; line 3 represents the second cow; and so on. No two cows will stand at the same location.
Output
* Line 1: A single line with a single integer that is the sum of all the volumes of the conversing cows.
Sample Input
4 3 1 2 5 2 6 4 3
Sample Output
57
Source
题意 给你若干牛的声贝值和他们的x坐标 叫你求每两个牛之间的距离乘上他们两个的最大声贝值
我们怎么分析呢?我们这样考虑
大声贝的牛出现 会影响乘法的声贝值
那么我们按照声贝排序 按小到大的顺序 这样每次我乘法的声贝值都是取新加的这个牛
这个牛x坐标前面有几个牛呢? 维护一个lsum 左边的牛 那么右边的牛数目自然为i-1-lsum
那么左边的牛的距离和是多少呢?是lsum * x - lsumdisx(左边牛的距离和) 那么右边牛的距离自然为sumdisx(总距离和)-lsumdisx-(i-1-lsum)*x
那么我们这样树状数组 维护一个 数量前缀数组a
距离前缀和数组b 就可以实现了
#include <cstdio> #include <cstring> #include <iostream> #include <cmath> #include <algorithm> using namespace std; const int MAX_N = 20024; long long a[MAX_N],b[MAX_N],xsum[MAX_N]; struct node { int x; int v; bool operator < ( const node &t) const { return v<t.v; } }col[MAX_N]; long long getsum(int x,long long *arr){ long long ans = 0; for(int i = x;i;i-=i&(-i)) ans+=arr[i]; return ans; } void change(int x,long long dis,long long *arr,long long v){ for(;x<=dis;x+=x&(-x)) arr[x]+=v; } int main(){ int n; scanf("%d",&n); long long dis = -1; for(int i=1;i<=n;++i){ scanf("%d%d",&col[i].v,&col[i].x); if(col[i].x>=dis) dis= col[i].x; } sort(col+1,col+1+n); long long ans = 0; for(int i=1;i<=n;++i) xsum[i] = xsum[i-1]+col[i].x; for(int i=1;i<=n;++i){ long long dl = getsum(col[i].x,a); long long dr = i-1-dl; long long lsum = getsum(col[i].x,b); long long rsum = xsum[i-1]-lsum; ans+=col[i].v*(dl*col[i].x-lsum); ans+=col[i].v*(rsum-dr*col[i].x); change(col[i].x,dis,a,1); change(col[i].x,dis,b,col[i].x); } printf("%lld\n",ans); return 0; }