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 $$$O(\log{N})$$$.
http://codeforces.net/blog/entry/71647#comment-559893
Hope it helps a bit.