Hatena::Grouptopcoder

hirosegolf@競技プログラミング

2018-07-14

AGC026

| 00:42

成績:ABEを解いて100位

コンテストページ:https://beta.atcoder.jp/contests/agc026

とりあえず、Fから考え始めた。

Nが偶数の場合は、どちらかの端から取っていくのが最善であることがすぐ分かる。

Nが奇数の場合は、すぐには思いつかなかった。

Fは、配点的にも難しい可能性があるので、放置して次に進むことに。(ここで消費時間10分ほど)



Eを考え始める。

Eは、ある条件を満たす部分列であって、辞書式で最大のものを作る問題。

N=3000なので、O(N^2)解法まで許されるということを念頭において考察を開始した。

辞書式順序を考えているので、まず最初にbが幾つ並ぶかが重要。

そこで、その部分から考え始めることにした。

最初に選ぶbの場所の座標をxとして、またそれに対応するaの場所をyとする。

x>yは、aから始まるという酷いシチュエーションなので、とりあえず、x<yの場合を考えることにした。</ppp>

すると、xとyの中間の位置にあるbは全て回収していくのが最善となる。

よってスタート場所を指定すれば、最初にbが幾つ並ぶかが分かることになる。この個数が単独一位になっている箇所が1箇所だけであれば、それで開始箇所が分かるが、そんなに甘くないことはすぐに分かる。

よってb...baとなってから以降の箇所についても、ちゃんと考えないといけない。

このあたり、じっくり考えないとすぐに混乱するので、時間がかなり消費される。

ここを考えてると、aの個数とbの個数が一致するような切れ目(i番目までに含まれるaとbが一致するようなi)が重要になってくることに気づいた。

これに気づいた理由は正確には覚えてないが、丁寧に考えれば、どんな道筋を辿っても必然的に思いつくことで、非自明な箇所ではない。しかし、反射的に思いつく内容でもないので、少しは時間を消費した。


abが同数となる切れ目で分割しておくアイデアに気づいいてからは次の通り。

最初の文字がaとbで場合分けをする必要がありそうだと思う。

bから始まる場合はさっきの発想を延長させればいい。

aから始まる場合は、少し考えてabab交互に並べるのがよいと分かる。


実装については次のようになった。


string s;
vector<string> ss;
char a = 'a';
char b = 'b';

vector<int> make_jump(string s){
	int n = s.size()/2;
	vi jump(s.size(), -1);
	int ia = -1, ib=-1;
	rep(k,n){
		ia++;
		ib++;
		while(s[ia]==b)ia++;
		while(s[ib]==a)ib++;
		jump[ia] = ib;
		jump[ib] = ia;
	}
	return jump;

}

vector<string> find_kouho(string s){
	vector<string> ret;
	vi jump = make_jump(s);
	if(s[0]==a){
		int n = s.size()/2;
		int i=0;
		int cnt = 0;
		while(i<s.size()){
			assert(s[i]==a);
			cnt++;
			i = jump[i]+1;
			while(i<s.size() && s[i]==b )i++;
		}
		string ret_s;
		rep(j,cnt){
			ret_s.push_back(a);
			ret_s.push_back(b);
		}
		ret.push_back(ret_s);
	}
	if(s[0]==b){
		rep(start,s.size()) if(s[start]==b){
			string ret_s;
			FOR(i,start, s.size()){
				if(s[i]==b || (s[i]==a && i>=jump[start])  )ret_s.push_back(s[i]);
			}
			ret.push_back(ret_s);
		}
	}
	return ret;
}

void _main(istream &inp){

	int si;
	inp >> si >> s;
	assert(s.size()==2*si);
	int start = 0;
	int cnt = 0;
	for(int i=0; i<=s.size(); i++){
		if(i>0 && cnt==0){
			ss.push_back(string(s.begin()+start, s.begin()+i));
			start = i;
		}
		if(i<s.size()){
			if(s[i]==b)cnt++;
			else cnt--;
		}
	}
	//debug(ss);
	string cur;
	for(int k=ss.size()-1; k>=0; k--){
		string best = cur;
		for(string u:find_kouho(ss[k]) ){
			if(u+cur >= best){
				best = u+cur;
			}
		}
		cur = best;
	}
	cout << cur << endl;
}

実装自体は綺麗にできたと思うが、そもそも量が多いので、実装にもそれなりに時間がかかってしまった。バグには殆どハマっていない。慎重にやりすぎた可能性はある。


結局Eの消費時間は80分ほど。(合計で90分)

ここは、時間を使いすぎてる感があるが、今の所、改善方法は思いつかず。




残り時間やばいなと思いつつDを開く。

とりあえず、左から順に埋めてくdpを考える。

全ての数え上げと、右側部分が交互に並んでいる場合の数え上げと、2つ用意してdpすれば良さそうだと思って、漸化式を作り始める。

しかし、それだと駄目なことに気づく。

Dの配点は1100点でBCを解いたほうが配点が高い。それを思ってDをやめてBCに移ったが、結果的にCは解けなかったので、Dに時間を掛けたほうが良かったかもしれない。

何はともあれ、BをDを諦めた時点で残り時間は40分ほどだったように思う。


Cの問題を見る。

数え上げの問題。全ての場合の数は、C(2N,N)。また、Nは最大で18にもなる。だから、全探索じゃ間に合わない。全て同じ文字の場合はC(2N,N)になるので、枝刈りしても駄目で、適当にまとめ上げて数える必要がある。

これもすぐには思いつかなかったので、とりあえずBに移ることに。


Bの問題を見る。

これは、さっくり解けた。しかし、実装が多少面倒なので、おそらく15分ぐらい消費した?


この時点で実は残り時間が7分ぐらい。もう、Dを解くのは絶対に無理なのでAを開く。


Aは、すごく簡単。4分ほどで解く。



全体の反省点:

パフォーマンス2634でレートは微増した。すごく駄目な成績というわけではないが、よい成績でもない。Eは時間を掛けすぎたが、それなりに考察の重さがあったので、ちょっと厳しい。最速正解者は25分だが、それはちょっと手の届く領域という感じではない。

CDはそれなりに時間を使って解けなかったのはちょっと勿体なかった。一つの問題に時間を集中させた方が得策だったか?



追記:

CDの解説を読んだ。

Cは真ん中で切るという発想は、ちょっと非凡である。

なぜなら問題自体には、中心部分という要素がないので。

結果論としては具体例を調べるのに時間を掛けるべきだったかもしれない。

Dについては下から埋めていくdpだった。思いつくのは十分可能だと思うが、左から埋めてくdpでも何とかなりそうだという気分の時に、このような方針転換をするのは勇気がいる。

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