hdu 5358 First One 2015多校联合训练赛#6 枚举

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。中间j的累加和

推公式即可。

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
#include
#include
#include
#include
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;
}