A806.Bracelet Crossings--Gold

普及+/提高

USACO

通过率:0%

时间限制:1.00s

内存限制:128MB

题目描述

Bessie the cow enjoys arts and crafts. In her free time, she has made NN
(1N501\le N\le 50) bracelets, conveniently numbered 1N1 \ldots N. The iith
bracelet is painted color ii out of a set of NN different colors. After
constructing the bracelets, Bessie placed them on a table for display (which
we can think of as the 2D plane). She was careful to arrange the bracelets to
satisfy the following three conditions:

  1. Every bracelet was a single closed polygonal chain -- a series of vertices (points) connected sequentially by line segments, where the first and last points are the same (Feel welcome to consult the wikipedia page for more detail: polygonal chain),
  2. No bracelet intersected itself (this corresponds to a "simple" polygonal chain); and
  3. No two bracelets intersected.
    Unfortunately, right after Bessie arranged the bracelets in such a careful
    manner, Farmer John drove by in his tractor, shaking the table and causing the
    bracelets to shift around and possibly break into multiple (not necessarily
    closed or simple) polygonal chains! Afterward, Bessie wanted to check whether
    the three conditions above still held. However, it was dark, so she couldn't
    see the bracelets anymore.
    Fortunately, Bessie had a flashlight. She chose MM (1M501\le M\le 50) vertical
    lines x=1,x=2,,x=Mx=1, x=2, \ldots, x=M and for each line, she swept the beam of the
    flashlight along that line from y=y=-\infty to y=y=\infty, recording the
    colors of all bracelets she saw in the order they appeared. Luckily, no beam
    crossed over any vertex of any polygonal chain or two line segments at the
    same time. Furthermore, for each beam, every color that appeared appeared
    exactly twice.
    Can you help Bessie use this information to determine whether it is possible
    that the bracelets still satisfy all three of the conditions above?

输入格式

Each input case contains TT sub-cases (1T501 \leq T \leq 50) that must all
solved independently to solve the full input case. Consecutive test cases are
separated by newlines.
The first line of the input contains TT. Each of the TT sub-test cases then
follow.
The first line of each sub-test case contains two integers NN and MM. Each
sub-test case then contains MM additional lines. For each ii from 11 to
MM, the ii-th additional line contains an integer kik_i (0ki2N0\le k_i\le 2N,
kik_i even), followed by kik_i integers ci1,ci2,,cikic_{i1}, c_{i2},\ldots, c_{ik_i}
(cij[1,N]c_{ij}\in [1,N], every cijc_{ij} appears zero or two times). This means that
when Bessie swept her flashlight from (i,)(i,-\infty) to (i,)(i,\infty), she
encountered the colors ci1,ci2,,cikic_{i1}, c_{i2},\ldots, c_{ik_i} in that order.

输出格式

For each sub-test case, print YES if it is possible for the three conditions
above to be satisfied. Otherwise, print NO.

输入输出样例

  • 输入#1

    5
    1 2
    2 1 1
    2 1 1
    1 3
    2 1 1
    0
    2 1 1
    2 1
    4 1 2 1 2
    4 2
    6 1 2 2 3 3 1
    6 1 2 4 4 2 1
    2 2
    4 1 1 2 2
    4 2 2 1 1
    

    输出#1

    YES
    NO
    NO
    YES
    NO
    

说明/提示

An example of a feasible bracelet configuration for the first sub-case is:

For the fourth sub-case, a feasible arrangement is the following:

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