spirited_away_'s blog

By spirited_away_, history, 5 weeks ago, In English,

Given a number N, The problem asks you to find all such pairs u,v such that there exists another set of pairs a,b such that

  1. a ^ b = u

  2. a + b = v

where u , v <= N.

I finally concluded that basically we have to find a+b<=N, but how to proceed from here. Can we use counting principle to solve this problem, i mean count all a+b == N and a+b < N and to avoid repeatation we will considere a >= b.

Can anyone tell me the approach and intutition to solve it. Editorial is in japanese.

 
 
 
 
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5 weeks ago, # |
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Apply dynamic programming on digits. First change $$$v$$$ into binary representation and then doing dynamic programming from the most significant bit to the least significant bit, maintaining the last two remaining digits of $$$v-a-b$$$ would be enough. Time complexity is $$$O(\log{N})$$$.