No.3052 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 3
作問者 :
FF256grhy
タグ : / 解いたユーザー数 3
作問者 :
FF256grhy
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 ($1 \leq i \leq N$) に小さい正方形の一辺の長さは $A_i$ 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
$N$ $A_1$ $\cdots$ $A_N$
入力される値はすべて整数で、以下の制約を満たします。
・$1 \leq N \leq 26$
・$1 \leq A_1 < \cdots < A_N$
・$A_1 ^ 2 + \cdots + A_N ^ 2 \leq 500 ^ 2$
出力
可能な場合：
$L$
$c_{1, 1} \cdots c_{1, L}$
$\vdots$
$c_{L, 1} \cdots c_{L, L}$
・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 $\sqrt{10}$ 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
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