hdu 3874（树状数组）题解

Problem Description

Mery has a beautiful necklace. The necklace is made up of N magic balls. Each ball has a beautiful value. The balls with the same beautiful value look the same, so if two or more balls have the same beautiful value, we just count it once. We define the beautiful value of some interval [x,y] as F(x,y). F(x,y) is calculated as the sum of the beautiful value from the xth ball to the yth ball and the same value is ONLY COUNTED ONCE. For example, if the necklace is 1 1 1 2 3 1, we have F(1,3)=1, F(2,4)=3, F(2,6)=6.

Now Mery thinks the necklace is too long. She plans to take some continuous part of the necklace to build a new one. She wants to know each of the beautiful value of M continuous parts of the necklace. She will give you M intervals [L,R] (1<=L<=R<=N) and you must tell her F(L,R) of them.

 

Input

The first line is T(T<=10), representing the number of test cases.
  For each case, the first line is a number N,1 <=N <=50000, indicating the number of the magic balls. The second line contains N non-negative integer numbers not greater 1000000, representing the beautiful value of the N balls. The third line has a number M, 1 <=M <=200000, meaning the nunber of the queries. Each of the next M lines contains L and R, the query.

 

Output

For each query, output a line contains an integer number, representing the result of the query.

 

Sample Input

261 2 3 4 3 531 23 52 661 1 1 2 3 531 12 43 5

 

Sample Output

3714136

思路：

树状数组对于维护数组有很大优势，复杂度O(M*lgN)。树状数组讲解

我们用树状数组维护题中的数组，但是他要求不能计算重复的点，这里用了一个很巧妙的方法：先将问题按照最右边界从小到大排序，然后对这个数组去重，最后我们记录当前问题的答案，再做下一个问题，这样我们就能保证每个问题都去重并且没有删去元素。

代码：

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<cctype>
#include<queue>
#include<cmath>
#include<string>
#include<stack>
#include<set>
#include<map>
#include<vector>
#include<iostream>
#include<algorithm>
#include<sstream>
#define ll long long
const int N=50005;
const int MAX=200005;
const int INF=1e9;
using namespace std;
map<int,int> mp;
int num[N],n;
ll ans[MAX],tree[N];
struct node{
	int l,r,no;
}que[MAX];
int cmp(node a,node b){
	if(a.r<b.r) return 1;
	return 0;
}

//树状数组操作-start
int lowbit(int x){
	return x&(-x);
}
void update(int x,int val){	//更新
	for(int i=x;i<=n;i+=lowbit(i)){
		tree[i]+=val;
	}
}
ll sum(int x){	//计算1~x的和
	ll count=0;
	for(int i=x;i>=1;i-=lowbit(i)){
		count+=tree[i];
	}
	return count;
}
//树状数组操作-end 

int main(){
	int T,m;
	cin>>T;
	while(T--){
		memset(tree,0,sizeof(tree));
		cin>>n;
		for(int i=1;i<=n;i++){
			scanf("%d",&num[i]);
		}
		cin>>m;
		for(int i=1;i<=m;i++){
			scanf("%d%d",&que[i].l,&que[i].r);
			que[i].no=i;	//表示这是第几个问题
		}
		sort(que+1,que+m+1,cmp);
		mp.clear();	//map存储num[i]的最新位置
		int pos=1;
		for(int i=1;i<=m;i++){
			while(pos<=que[i].r){
				if(mp[num[pos]]!=0){	//如果重复出现
					update(mp[num[pos]],-num[pos]);	//删掉之前那个
				}
				mp[num[pos]]=pos;
				update(pos,num[pos]);
				pos++;
			}
			ans[que[i].no]=sum(que[i].r)-sum(que[i].l-1);
		}
		for(int i=1;i<=m;i++){
			printf("%lld\n",ans[i]);
		}
	}
    return 0;
}