[区间合并，优化] hdu5358多校联合 第六场 First one

First One
Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 142 Accepted Submission(s): 37

Problem Description
soda has an integer array a1,a2,…,an. Let S(i,j) be the sum of ai,ai+1,…,aj. Now soda wants to know the value below:
∑i=1n∑j=in(⌊log2S(i,j)⌋+1)×(i+j)

Note: In this problem, you can consider log20 as 0.

Input
There are multiple test cases. The first line of input contains an integer T, indicating the number of test cases. For each test case:

The first line contains an integer n (1≤n≤105), the number of integers in the array.
The next line contains n integers a1,a2,…,an (0≤ai≤105).

Output
For each test case, output the value.

Sample Input
1
2
1 1

Sample Output
12

Source
2015 Multi-University Training Contest 6

由于下取整log（sum）的值是很小的。可以枚举每个位置为开始位置，然后枚举每个log（sum）只需36*n的。后面的i+j累加和也可以推公式推出来。

但是找log值相同的区间，需要用log(sum)*n的复杂度预处理出来，如果每次二分位置会超时。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<vector>
using namespace std;
#define ll long long
#define maxn 100007
ll num[maxn];
ll pos[maxn][36];

int main(){
    int t;
    scanf("%d",&t);
    while(t--){
        int n;
        scanf("%d",&n);
        for(int i = 0;i < n; i++){
            scanf("%I64d",&num[i]);
        }

        num[n] = 0;
        for(ll i = 0;i < 36; i++){
            ll di = 1LL<<(i+1);
            ll su = num[0];
            int p = 0;
            for(int j = 0;j < n; j++){
                if(j) su -= num[j-1];
                while(su < di && p < n){
                    su += num[++p];
                }
                pos[j][i] = p;
            }
        }

        ll ans = 0,res;
        for(int i = 0;i < n; i++){
            ll p = i,q;
            for(int j = 0;j < 36 ;j ++){
                q = pos[i][j];
                res = (j+1)*((i+1)*(q-p)+(p+q+1)*(q-p)/2);
                ans += res;
                p = q;
            }
        }
        printf("%I64d\n",ans);
    }
    return 0;
}