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How to count the number of subsequence in an array with 'and' operator sum equal to 0?
By xuanquang1999, history, 7 years ago, In English

I have recently encountered this problem:

"Given an array a1, a2, ..., an, (1 ≤ n ≤ 105, 1 ≤ ai ≤ 106), count the number of subsequence ap1, ap2, ..., apk that ap1&ap2&...&apk = 0 (print the remain of division of that number by 109 + 7"

The best solution that I can come up is a dynamic programming solution that is not fast enough to solve this problem. How to solve this problem?

Thanks in advance.

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7 years ago, # |
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Auto comment: topic has been updated by xuanquang1999 (previous revision, new revision, compare).

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7 years ago, # |
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I'm not sure about this soultion.

Let's count all subsequences — 2^n. Now let count all subsequences with their and greater than 0. For all masks save count of numbers, that the mask is their submask. So using inclusion-exclusion principle we can calculate the answer.

UPD: OK

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7 years ago, # |
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Ignore.

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7 years ago, # |
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Here is the same task on codeforces : 449D - Jzzhu and Numbers. Maybe it will be helpful.

We were doing it on extra classes before a few days, but I do not know part with calculating function f from editorial.

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7 years ago, # |
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That was wrong, ignore it

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