Editorial for PIB '20 P2 - 2 + 2 = 5 - Olympiads Online Judge

Editorial for PIB '20 P2 - 2 + 2 = 5

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Author: ChrisT

Note that the function $f(x) = \left\lfloor \frac{x}{2} \right\rfloor - \left\lfloor \frac{x}{7} \right\rfloor$ $f (x) = ⌊ \frac{x}{2} ⌋ - ⌊ \frac{x}{7} ⌋$ increases by one every multiple of 2 it hits, and decreases by 1 every multiple of 7 it hits. Since there are $\ge 3$ $\geq 3$ multiples of 2 in between any two multiples of 7, the function is strictly increasing upon multiples of 7. We also note that for this same reason, the multiples of 7 are the local minima of this function. With this knowledge, we can binary search for the last multiple of 7 such that $f(x) \le T$ $f (x) \leq T$ , and then just check the 6 numbers after it.

Time Complexity: $\mathcal{O}(\log T)$ $O (\log T)$

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