INCXOR - Editorial

Author: Lewin Gan
Testers: Kamil Dębowski
Editorialist: Lewin Gan

Medium-Hard

PROBLEM:

Find the number of increasing sequences that are also increasing when XOR-ed by another sequence.

QUICK EXPLANATION:

First, it’s helpful to be familiar with digit dp. The state we need to keep is whether or not b_i is strictly less than b_{i+1} and a_i XOR b_i is strictly less than a_{i+1} XOR b_{i+1}. This is a total of 2^(2(N-1)) states per digit.

EXPLANATION:

Using the logic above, we can solve f(bit, mask1, mask2) denoting number of ways given we can fill in the bits 0 to bit. The i-th bit in mask1 (resp mask2) is 1 if and only if b_i (resp a_i XOR b_i) is strictly less than b_{i+1} (resp a_{i+1} XOR b_{i+1}).

Using this logic, we can brute force over all 2^n ways to fill in the current bit for b, make sure they satisfy the constraints in mask, and recurse to smaller cases.

To see more details, see the setter’s solution.

AUTHOR’S AND TESTER’S SOLUTIONS:

Setter
Tester Solution will be added soon.

2 Likes

Hi, Could someone please explain this line

The i-th bit in mask1 (resp mask2) is 1 if and only if b_i (resp a_i XOR b_i) is strictly less than b_{i+1} (resp a_{i+1} XOR b_{i+1}).

in a little more detail.

Thanks a lot for the editorial!

The problem setters code is in Java. Can u add the testers or the editorialists code if it is in c++.

2 Likes

I am getting the following error. When i am trying to view setter solution.
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