AtCoder Beginner Contest 207
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Problem Statement
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You are given two sets $S=\{(a_1,b_1),(a_2,b_2),\ldots,(a_N,b_N)\}$ and $T=\{(c_1,d_1),(c_2,d_2),\ldots,(c_N,d_N)\}$ of $N$ points each on a two-dimensional plane.
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Determine whether it is possible to do the following operations on $S$ any number of times (possibly zero) in any order so that $S$ matches $T$.
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- Choose a real number
$p\ (0 \lt p \lt 360)$and rotate every point in$S$$p$degrees clockwise about the origin. - Choose real numbers
$q$and$r$and move every point in$S$by$q$in the$x$-direction and by$r$in the$y$-direction. Here,$q$and$r$can be any real numbers, be it positive, negative, or zero.
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Constraints
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$1 \leq N \leq 100$$-10 \leq a_i,b_i,c_i,d_i \leq 10$$(a_i,b_i) \neq (a_j,b_j)$if$i \neq j$.$(c_i,d_i) \neq (c_j,d_j)$if$i \neq j$.- All values in input are integers.
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Input
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Input is given from Standard Input in the following format:
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N
a_1 b_1
a_2 b_2
\hspace{0.6cm}\vdots
a_N b_N
c_1 d_1
c_2 d_2
\hspace{0.6cm}\vdots
c_N d_N翻译中…
Output
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If we can match $S$ with $T$, print Yes; otherwise, print No.
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样例
Input #1
3
0 0
0 1
1 0
2 0
3 0
3 1
Output #1
Yes
The figure below shows the given sets of points, where the points in $S$ and $T$ are painted red and green, respectively:
In this case, we can match $S$ with $T$ as follows:
1. Rotate every point in $S$ $270$ degrees clockwise about the origin.
2. Move every point in $S$ by $3$ in the $x$-direction and by $0$ in the $y$-direction.
Input #2
3
1 0
1 1
3 0
-1 0
-1 1
-3 0
Output #2
No
The figure below shows the given sets of points:
Although $S$ and $T$ are symmetric about the $y$-axis, we cannot match $S$ with $T$ by rotations and translations as stated in Problem Statement.
Input #3
4
0 0
2 9
10 -2
-6 -7
0 0
2 9
10 -2
-6 -7
Output #3
Yes
Input #4
6
10 5
-9 3
1 -5
-6 -5
6 9
-9 0
-7 -10
-10 -5
5 4
9 0
0 -10
-10 -2
Output #4
Yes
题目信息
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