hdu3015 Disharmony Trees

Posted 2020-09-10 zsychanpin

Problem Description

One day Sophia finds a very big square. There are n trees in the square. They are all so tall. Sophia is very interesting in them.

She finds that trees maybe disharmony and the Disharmony Value between two trees is associated with two value called FAR and SHORT.

The FAR is defined as the following:If we rank all these trees according to their X Coordinates in ascending order.The tree with smallest X Coordinate is ranked 1th.The trees with the same X Coordinates are ranked the same. For example,if there are 5 tree with X Coordinates 3,3,1,3,4. Then their ranks may be 2,2,1,2,5. The FAR of two trees with X Coordinate ranks D1 and D2 is defined as F = abs(D1-D2).

The SHORT is defined similar to the FAR. If we rank all these trees according to their heights in ascending order，the tree with shortest height is ranked 1th.The trees with the same heights are ranked the same. For example, if there are 5 tree with heights 4,1,9,7,4. Then their ranks may be 2,1,5,4,2. The SHORT of two trees with height ranks H1 and H2 is defined as S=min(H1,H2).

Two tree’s Disharmony Value is defined as F*S. So from the definition above we can see that, if two trees’s FAR is larger , the Disharmony Value is bigger. And the Disharmony value is also associated with the shorter one of the two trees. 

Now give you every tree’s X Coordinate and their height , Please tell Sophia the sum of every two trees’s Disharmony value among all trees.

 

Input

There are several test cases in the input

For each test case, the first line contain one integer N (2 <= N <= 100,000) N represents the number of trees.

Then following N lines, each line contain two integers : X, H (0 < X,H <=1,000,000,000 ), indicating the tree is located in Coordinates X and its height is H.

 

Output

For each test case output the sum of every two trees’s Disharmony value among all trees. The answer is within signed 64-bit integer.

 

Sample Input

2
10 100
20 200
4
10 100
50 500
20 200
20 100

 

Sample Output

1
13
这道题和之前那题几乎相同。开两个一维树状数组b1,b2。分别维护x的位置和小于等于x位置的个数。
先对x，h进行离散化，用r1,r2储存他们的名次。然后按h大小从大到小的顺序依次枚举即可了。
#include<iostream>
#include<stdio.h>
#include<string.h>
#include<math.h>
#include<vector>
#include<map>
#include<queue>
#include<stack>
#include<string>
#include<algorithm>
using namespace std;
struct node{
	int x,h,r1,r2;
}a[100006];
int b1[100006],b2[100006],n;

bool cmp1(node a,node b){
	return a.x<b.x;
}
bool cmp2(node a,node b){
	return a.h<b.h;
}

int lowbit(int x){
	return x&(-x);
}
void update1(int pos,int num)
{
	while(pos<=n){
		b1[pos]+=num;pos+=lowbit(pos);
	}
}
int getsum1(int pos)
{
	int num=0;
	while(pos>0){
		num+=b1[pos];pos-=lowbit(pos);
	}
	return num;
}

void update2(int pos,int num)
{
	while(pos<=n){
		b2[pos]+=num;pos+=lowbit(pos);
	}
}
int getsum2(int pos)
{
	int num=0;
	while(pos>0){
		num+=b2[pos];pos-=lowbit(pos);
	}
	return num;
}


int main()
{
	int m,i,j,p,t1,t2;
	__int64 sum,sum1;
	while(scanf("%d",&n)!=EOF)
	{
		for(i=1;i<=n;i++){
			scanf("%d%d",&a[i].x,&a[i].h);
			b1[i]=b2[i]=0;
		}
		sort(a+1,a+1+n,cmp1);
		a[1].r1=1;p=1;
		for(i=2;i<=n;i++){
			if(a[i].x==a[p].x){
				a[i].r1=a[p].r1;
			}
			else{
				a[i].r1=i;p=i;
			}
		}
		sort(a+1,a+1+n,cmp2);
		a[1].r2=1;p=1;
		for(i=2;i<=n;i++){
			if(a[i].h==a[p].h){
				a[i].r2=a[p].r2;
			}
			else{
				a[i].r2=i;p=i;
			}
		}
		
		sum=0;sum1=0;
		for(i=n;i>=1;i--){
			t1=getsum1(a[i].r1);
			t2=getsum2(a[i].r1);
			sum+=a[i].r2*( t2*a[i].r1-t1 + sum1-t1-(n-i-t2)*a[i].r1 );
			sum1+=a[i].r1;
			update1(a[i].r1,a[i].r1);
			update2(a[i].r1,1);
			//printf("%I64d\n",sum);
		}
		printf("%I64d\n",sum);
	}
}