Code Festival B Union Find

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Problem

This is an entry for Code Festival. See below for some English.

この問題は Code Festival 「短縮王」のための問題です。この問題のテストケースは本番より制限がゆるいため、ゴルフ場で通ったアルゴリズムが本番で通らない可能性があります。 CODE FESTIVAL本戦参加者の方は、会場で配布されている、ルールブック記載のURLにてご解答ください。

以下問題の原文です


B - Union Find

N 人の人をいくつかのグループにします。 はじめは全員別々のグループです。

以下の 2 つのクエリを処理してください。

Bi 番目の人を含むグループと Ci 番目の人を含むグループを 1 つのグループに統合する。
Bi 番目の人と Ci 番目の人が同じグループかを判定する。
入力
入力は以下の形式で標準入力から与えられる。

N Q
A1 B1 C1
A2 B2 C2
:
AQ BQ CQ
1 行目には、2 つの整数 N(1≦N≦10^5), Q(1≦Q≦10^5) が空白区切りで与えられる。
2 行目からの Q 行では、クエリを表す 3 個の整数 Ai(Ai=0,1), Bi(1≦Bi≦N), Ci(1≦Ci≦N) が空白区切りで与えられる。Ai=0 は統合クエリを表し、Bi 番目の人を含むグループと Ci 番目の人を含むグループを 1 つのグループに統合する。Ai=1 は判定クエリを表し、Bi 番目の人と Ci 番目の人が同じグループかを判定する。
出力
Ai=1 である i について、Bi と Ci が同じグループならば YES を、違うグループならば NO を出力せよ。出力の末尾に改行を入れること。


これは非公式な本来の問題のコピーです。ゴルフ場と AtCoder の仕様が違うため、ゴルフ場で良い成績が出たから本番でもそのまま通るとは限りません。表彰されるためには本来のサイトで投稿する必要があります。投稿サイトは後日ここからリンクをはる予定です。

普段からこのサイトに参加している人へ: 普通に解答を投稿してくれて良いです。ただし状況に応じて問題の更新や解答のリセットなどをするかもしれません。11月16日以降は普通の問題になるはずです。また、この問題では普段ではありえない量の入出力を伴います。使っている言語で timeout して、 performance checker で常識的な時間で終了する場合、レポートしていただければタイムリミットをこの問題のみゆるめる場合があります。

There are N people and they'll be categorized into some groups. All people in different groups at first. The first line consists of N and Q where N (1 <= N <= 100000) is the number of people and Q (1 <= Q <= 100000) is the number of commands. Q lines follow. Each line consists of Ai, Bi, and Ci. If Ai is 0, you should combine two groups which have people Bi and Ci. If Ai is 1, you should output YES when the people Bi and Ci are in the same group. Otherwise you should output NO.

For golfers in this site: feel free to submit solutions as usual. Please just understand the problem may be updated and your solutions may be rejudged. No update will be done after Nov. 16.

Personal note: unlike usual, I may examine submitted solutions even before the deadline (I've never done this, trust me :), potentially to introduce interesting techniques in the event. As usual, I can promise I don't abuse the knowledge got in this way.

Options

exec is denied

now post-mortem time, all source codes will be revealed

Sample input:_

5 8
0 1 2
1 1 5
0 2 3
1 1 5
0 3 4
1 1 5
0 4 5
1 1 5

Sample output:

NO
NO
NO
YES

Sample input:_

100000 99999
0 1 2
0 2 3
1 76970 34222
0 3 4
1 13491 12441
0 4 5
0 5 6
0 6 7
0 7 8
0 43998 45159
1 12697 91106
0 8 9
1 38822 18633
0 79066 53263
0 9 10
0 75003 33013
0 10 11
1 72558 63520
1 43548 49820
0 11 12
0 12 13
0 65256 45628
0 13 14
0 14 15
0 15 16
0 16 17
1 38725 44358
1 27376 45601
1 1643 22983
0 17 18
0 18 19
0 19 20
1 89266 59041
0 20 21
1 27061 44201
1 42704 73204
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0 40743 25088
0 23 24
0 24 25
1 94908 78768
0 25 26
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0 27 28
1 98779 91344
0 28 29
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0 30 31
1 28788 49364
0 31 32
1 87655 93829
1 7948 35736
1 94789 87506
0 32 33
1 56003 31028
1 5382 50667
1 68443 13846
1 80126 96138
0 64022 39371
0 33 34
1 48311 1480
0 34 35
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0 36 37
0 37 38
1 60798 5289
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0 95204 51581
1 44072 44086
1 31555 32964
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1 61875 2682
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1 68896 77896
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1 80700 31227
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1 77788 16635
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1 23405 88152
1 95886 47380
1 60660 48793
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1 20697 2424
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1 81048 2331
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