First One

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)

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

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define prt(k)  cout<<#k" = "<<k<<"  "
const int N = 100233;

int a[N];
int n;
int main()
{
    int re; read(re);
    while (re--) {
        read(n);
        ll ans = 0;
        for (ll i=1;i<=n;i++) {
            read(a[i]);
            ans += i * (n-i+1) + (n-i+1)*(n+i)/2;
        }
        for (int k=1;k<40;k++) {
            ll lim = 1LL<<k;
            ll s = 0;
            for (ll i=1, j=1; i<=n; i++) {
                while (j<=n && s<lim) s+=a[j++]; j--;
                if (s >= lim) {
                    ans += i * ll(n - j + 1) + ll(n + j) * ll(n - j + 1)/2;
                    j++;
                }
                else break;
                s -= a[i];
            }
        }
        printf("%I64d\n", ans);
    }
    return 0;
}

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