P7168 [eJOI 2020] Triangulation (Day1)

[Instructions for use](https://www.luogu.com.cn/paste/1nsbzh41). --- In this problem, $(A,B)$ represents a diagonal from $A$ to $B$. Define the eJ distance from vertex $A$ to vertex $B$ in a regular polygon as the maximum of: the number of edges when going from $A$ to $B$ clockwise, and the number of edges when going from $A$ to $B$ counterclockwise. Based on this definition, we can also define the eJ distance from a vertex $A$ to a diagonal $B$ of the polygon: it is the maximum of the number of edges from $A$ to one endpoint of diagonal $B$ (the closer endpoint) when going clockwise, and the number of edges when going counterclockwise. For example, the eJ distance from point $0$ to diagonal $(0,5)$ is $5$. Going clockwise needs $5$ edges, going counterclockwise needs $2$ edges, so the answer is $\max\{5,2\}=5$.

Given an $N$-gon whose vertices are labeled clockwise as $0 \sim N-1$, A has drawn $n-3$ diagonals. It is guaranteed that these $n-3$ diagonals have no extra intersections except at vertices. Now A wants J to guess which diagonal has the smallest eJ distance to point $0$, and also report that distance. J cannot know the answer by mind reading, so he can only ask A for some clues. A tells J the value of $n$, and agrees that J may ask whether there is a diagonal between a pair of vertices, but J has a limit on the number of queries. J still wants to AK eJOI, so this problem is handed to you. #### Interaction rules You need to include the header file `triangulation.h`. ```cpp int solve(int n) ``` - This function can only be called once. - $n$: the number of vertices of the polygon. - Suppose the answer diagonal is $(a,b)$. This function should return $a \times n+b$. - If multiple diagonals are closest to point $0$, you may return any one of them. The `solve` function may call the following function multiple times: ```cpp int query(int x, int y) ``` - $x,y$: represent one query. - $0 \le x,y \le n-1$. - If $(x,y)$ exists, return $1$, otherwise return $0$.

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#### Sample 1 The sample input format only contains one integer $n$. |Function call|Return value| |:-:|:-:| |`solve(7)`|| |`query(0,3)`|$0$| |`query(0,5)`|$1$| |`query(1,5)`|$1$| ||The `solve` function returns $1 \times7+5=12$.| ||Correct.| #### Constraints For $100\%$ of the testdata, $5 \le n \le 100$. Assume $q$ is the number of queries you make for one test case. Let $w=\dfrac{n \times (n-3)}{2}$. Your score for one test case is: - If the queries are invalid, the answer is wrong, or $w