問題一覧 > 教育的問題

No.8052 Squaring

レベル : / 実行時間制限 : 1ケース 2.000秒 / メモリ制限 : 512 MB / スペシャルジャッジ問題 (複数の解が存在する可能性があります)
タグ : / 解いたユーザー数 4
作問者 : FF256grhy
0 ProblemId : 2865 / 出題時の順位表 / 自分の提出
問題文最終更新日: 2019-03-31 17:58:18

問題文

大きさが互いに相異なる正方形が N 個あり、i 番目 (1iN) に小さい正方形の一辺の長さは Ai です。この N 個の正方形すべてを 1 個ずつ並べて全体を正方形にすることが可能かどうかを判定し、可能な場合はその並べ方の一例を出力してください。なお、正方形同士が重なったり、隙間があったりしてはいけません。

入力

N
A1  AN

入力される値はすべて整数で、以下の制約を満たします。
1N26
1A1<<AN
A12++AN25002

出力

可能な場合:
L
c1,1c1,L

cL,1cL,L

・できあがった正方形の一辺の長さを L とする
・並べ方は、縦 L マス、横 L マスの文字配列 c として表現する
・各マスの文字は、全体の正方形のそのマスに相当する部分が 1 番目に小さい正方形である場合は 'A' 、2 番目に小さい正方形である場合は 'B' 、……、26 番目に小さい正方形である場合は 'Z' とする

不可能な場合:
-1

サンプル

サンプル1
入力
1
3
出力
3
AAA
AAA
AAA

一辺の長さが 3 である正方形を 1 個並べると、一辺の長さが 3 の正方形になります。

サンプル2
入力
2
1 3
出力
-1

2 個の正方形の面積の和は 10 なので、もし正方形にできるとしたらその一辺の長さは 10 にならなければいけませんが、そんなことは不可能です。

サンプル3
入力
24
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
出力
-1

面積の総和は 4900 なので、一辺の長さが 70 の正方形が作れそうな気もしますが、残念ながら実際にはこれらはどう並べても正方形にはなりません。

サンプル4
入力
23
1 2 3 4 5 7 8 10 12 13 14 15 16 19 21 28 29 31 32 37 38 41 44
出力例
110
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