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

a ^ b = u

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.

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 $$$O(\log{N})$$$.

Hello, But what would be the transition. by moving from i to i-1, what changes should be make in our dp states.

??