動的計画法(ダイナミック・プログラミング)をやろうぜ☆(^~^)?

はっべーーーーーーっ☆(^~^)! どぶっ☆(^~^) 公開下書き

KITASHIRAKAWA_Chiyuri_80x100x8_01_Futu.gif
「 ↓ 動的計画法を効率的かつ高速に習得したかったら、 Educational DP Contest の例題をやれだぜ☆」

Educational DP Contest / DP まとめコンテスト - 問題

KIFUWARABE_80x100x8_01_Futu.gif
「 じゃあ お父んのブログなんか読まなくてもいいじゃないか☆?」

OKAZAKI_Yumemi_80x80x8_02_Syaberu.gif
「 でも AtCoder の参加者のソースは ライセンス が不明だから パクれないのよ」

KITASHIRAKAWA_Chiyuri_80x100x8_01_Futu.gif
「 ソースコードの著作権は参加者に帰属するみたいな感じの 1ミリも同意できない文 が書いてたので
わたしが 一から MITライセンス で書き直すことにするぜ☆」

KIFUWARABE_80x100x8_01_Futu.gif
「 再車輪か☆」

KITASHIRAKAWA_Chiyuri_80x100x8_01_Futu.gif
「 再……、車輪の再発明な☆ どうせ 再 なら 素早くやろう☆」

problem

 1-- 4-- 8-- 5-- 3-- %
 |   |   |   |   |   |
 |   |   |   |   |   |
 0-- 2-- 3-- 4-- 2-- 2
 |   |   |   |   |   |
 |   |   |   |   |   |
 7-- 1-- 1-- 2-- 3-- 1
 |   |   |   |   |   |
 |   |   |   |   |   |
 3-- 1-- 9-- 3-- 1-- 2
 |   |   |   |   |   |
 |   |   |   |   |   |
 5-- 2-- 6-- 5-- 2-- 5
 |   |   |   |   |   |
 |   |   |   |   |   |
 @-- 3-- 4-- 0-- 8-- 6

KITASHIRAKAWA_Chiyuri_80x100x8_01_Futu.gif
「 ↑ これが問題で、時計回りに45°回転させるぜ☆」

high-score 0

pos
[Next 1 column(s)]

                +-- 1
                |   |
            +-- 0   +-- 4
            |   |   |   |
        +-- 7   +-- 2   +-- 8
        |   |   |   |   |   |
    +-- 3   +-- 1   +-- 3   +-- 5
    |   |   |   |   |   |   |   |
+-- 5   +-- 1   +-- 1   +-- 4   +-- 3
|   |   |   |   |   |   |   |   |   |
@   +-- 2   +-- 9   +-- 2   +-- 2   +-- %
|   |   |   |   |   |   |   |   |   |
+-- 3   +-- 6   +-- 3   +-- 3   +-- 2
    |   |   |   |   |   |   |   |
    +-- 4   +-- 5   +-- 1   +-- 1
        |   |   |   |   |   |
        +-- 0   +-- 2   +-- 2
            |   |   |   |
            +-- 8   +-- 5
                |   |
                +-- 6

KITASHIRAKAWA_Chiyuri_80x100x8_01_Futu.gif
「 ↑ これがゲーム画面だぜ☆
@ が君だぜ☆ 階段 % を目指せだぜ☆」

KIFUWARABE_80x100x8_01_Futu.gif
「  がなんで階段なんだぜ☆!」

KITASHIRAKAWA_Chiyuri_80x100x8_01_Futu.gif
「 操作は 上に行くか、下に行くか 選ぶのみ☆ 強制右スクロールだぜ☆
途中に落ちている数を足していって、ハイスコアを目指せだぜ☆」

OKAZAKI_Yumemi_80x80x8_02_Syaberu.gif
「 そんなん簡単よ」

KITASHIRAKAWA_Chiyuri_80x100x8_01_Futu.gif
「 やってみろだぜ☆
上に行くのは do u、 下に行くのは do d だぜ☆」

do u
pos
[Next 2 column(s)]

                +-- 1
                |   |
            +-- 0   +-- 4
            |   |   |   |
        +-- 7   +-- 2   +-- 8
        |   |   |   |   |   |
    +-- 3   +-- 1   +-- 3   +-- 5
    |   |   |   |   |   |   |   |
+-- @   +-- 1   +-- 1   +-- 4   +-- 3
|   |   |   |   |   |   |   |   |   |
    +-- 2   +-- 9   +-- 2   +-- 2   +--
|   |   |   |   |   |   |   |   |   |
+-- 3   +-- 6   +-- 3   +-- 3   +-- 2
    |   |   |   |   |   |   |   |
    +-- 4   +-- 5   +-- 1   +-- 1
        |   |   |   |   |   |
        +-- 0   +-- 2   +-- 2
            |   |   |   |
            +-- 8   +-- 5
                |   |
                +-- 6

score 5

KITASHIRAKAWA_Chiyuri_80x100x8_01_Futu.gif
「 下じゃなくていいのかだぜ☆?」

OKAZAKI_Yumemi_80x80x8_02_Syaberu.gif
「 ど真ん中の 9 と、45°上の端っこの 8 を狙えばしまいよ!」

do d
pos
[Next 3 column(s)]

                +-- 1
                |   |
            +-- 0   +-- 4
            |   |   |   |
        +-- 7   +-- 2   +-- 8
        |   |   |   |   |   |
    +-- 3   +-- 1   +-- 3   +-- 5
    |   |   |   |   |   |   |   |
+--     +-- 1   +-- 1   +-- 4   +-- 3
|   |   |   |   |   |   |   |   |   |
    +-- @   +-- 9   +-- 2   +-- 2   +--
|   |   |   |   |   |   |   |   |   |
+-- 3   +-- 6   +-- 3   +-- 3   +-- 2
    |   |   |   |   |   |   |   |
    +-- 4   +-- 5   +-- 1   +-- 1
        |   |   |   |   |   |
        +-- 0   +-- 2   +-- 2
            |   |   |   |
            +-- 8   +-- 5
                |   |
                +-- 6

score 7

KIFUWARABE_80x100x8_01_Futu.gif
「 他にもあるかも知れないのに……☆」

OKAZAKI_Yumemi_80x80x8_02_Syaberu.gif
「 ぱっと見た感じ こんなでかい数、落ちてないわよ!」

do d
pos
[Next 4 column(s)]

                +-- 1
                |   |
            +-- 0   +-- 4
            |   |   |   |
        +-- 7   +-- 2   +-- 8
        |   |   |   |   |   |
    +-- 3   +-- 1   +-- 3   +-- 5
    |   |   |   |   |   |   |   |
+--     +-- 1   +-- 1   +-- 4   +-- 3
|   |   |   |   |   |   |   |   |   |
    +--     +-- 9   +-- 2   +-- 2   +--
|   |   |   |   |   |   |   |   |   |
+-- 3   +-- @   +-- 3   +-- 3   +-- 2
    |   |   |   |   |   |   |   |
    +-- 4   +-- 5   +-- 1   +-- 1
        |   |   |   |   |   |
        +-- 0   +-- 2   +-- 2
            |   |   |   |
            +-- 8   +-- 5
                |   |
                +-- 6

score 13

KIFUWARABE_80x100x8_01_Futu.gif
「 目先の利益ばかり 追いかけていくな……☆」

OKAZAKI_Yumemi_80x80x8_02_Syaberu.gif
「 一番いいところに行く途中に 良いもんが落ちてんのよ!」

do u
pos
[Next 5 column(s)]

                +-- 1
                |   |
            +-- 0   +-- 4
            |   |   |   |
        +-- 7   +-- 2   +-- 8
        |   |   |   |   |   |
    +-- 3   +-- 1   +-- 3   +-- 5
    |   |   |   |   |   |   |   |
+--     +-- 1   +-- 1   +-- 4   +-- 3
|   |   |   |   |   |   |   |   |   |
    +--     +-- @   +-- 2   +-- 2   +--
|   |   |   |   |   |   |   |   |   |
+-- 3   +--     +-- 3   +-- 3   +-- 2
    |   |   |   |   |   |   |   |
    +-- 4   +-- 5   +-- 1   +-- 1
        |   |   |   |   |   |
        +-- 0   +-- 2   +-- 2
            |   |   |   |
            +-- 8   +-- 5
                |   |
                +-- 6

score 22

OKAZAKI_Yumemi_80x80x8_02_Syaberu.gif
「 ↑ 9 取った!」

KITASHIRAKAWA_Chiyuri_80x100x8_01_Futu.gif
「 こんなゲームで ダイナミック・プログラミング やるまでもないよな☆」

do u
pos
[Next 6 column(s)]

                +-- 1
                |   |
            +-- 0   +-- 4
            |   |   |   |
        +-- 7   +-- 2   +-- 8
        |   |   |   |   |   |
    +-- 3   +-- 1   +-- 3   +-- 5
    |   |   |   |   |   |   |   |
+--     +-- 1   +-- @   +-- 4   +-- 3
|   |   |   |   |   |   |   |   |   |
    +--     +--     +-- 2   +-- 2   +--
|   |   |   |   |   |   |   |   |   |
+-- 3   +--     +-- 3   +-- 3   +-- 2
    |   |   |   |   |   |   |   |
    +-- 4   +-- 5   +-- 1   +-- 1
        |   |   |   |   |   |
        +-- 0   +-- 2   +-- 2
            |   |   |   |
            +-- 8   +-- 5
                |   |
                +-- 6

score 23

OKAZAKI_Yumemi_80x80x8_02_Syaberu.gif
「 ↑ 次は 8 行くわよ!」

KIFUWARABE_80x100x8_01_Futu.gif
「 迷いがないぜ☆」

do u
pos
[Next 7 column(s)]

                +-- 1
                |   |
            +-- 0   +-- 4
            |   |   |   |
        +-- 7   +-- 2   +-- 8
        |   |   |   |   |   |
    +-- 3   +-- 1   +-- @   +-- 5
    |   |   |   |   |   |   |   |
+--     +-- 1   +--     +-- 4   +-- 3
|   |   |   |   |   |   |   |   |   |
    +--     +--     +-- 2   +-- 2   +--
|   |   |   |   |   |   |   |   |   |
+-- 3   +--     +-- 3   +-- 3   +-- 2
    |   |   |   |   |   |   |   |
    +-- 4   +-- 5   +-- 1   +-- 1
        |   |   |   |   |   |
        +-- 0   +-- 2   +-- 2
            |   |   |   |
            +-- 8   +-- 5
                |   |
                +-- 6

score 26

KIFUWARABE_80x100x8_01_Futu.gif
「 夢美は ちゃんと 探索したのか☆?」

OKAZAKI_Yumemi_80x80x8_02_Syaberu.gif
「 でかい数を取りゃ いいのよーっ!」

do u
pos
[Next 8 column(s)]

                +-- 1
                |   |
            +-- 0   +-- 4
            |   |   |   |
        +-- 7   +-- 2   +-- @
        |   |   |   |   |   |
    +-- 3   +-- 1   +--     +-- 5
    |   |   |   |   |   |   |   |
+--     +-- 1   +--     +-- 4   +-- 3
|   |   |   |   |   |   |   |   |   |
    +--     +--     +-- 2   +-- 2   +--
|   |   |   |   |   |   |   |   |   |
+-- 3   +--     +-- 3   +-- 3   +-- 2
    |   |   |   |   |   |   |   |
    +-- 4   +-- 5   +-- 1   +-- 1
        |   |   |   |   |   |
        +-- 0   +-- 2   +-- 2
            |   |   |   |
            +-- 8   +-- 5
                |   |
                +-- 6

score 34

OKAZAKI_Yumemi_80x80x8_02_Syaberu.gif
「 8 取った!」

KIFUWARABE_80x100x8_01_Futu.gif
「 もう後は 下に行くだけだな☆」

do d
pos
[Next 9 column(s)]

                +-- 1
                |   |
            +-- 0   +-- 4
            |   |   |   |
        +-- 7   +-- 2   +--  
        |   |   |   |   |   |
    +-- 3   +-- 1   +--     +-- @
    |   |   |   |   |   |   |   |
+--     +-- 1   +--     +-- 4   +-- 3
|   |   |   |   |   |   |   |   |   |
    +--     +--     +-- 2   +-- 2   +--
|   |   |   |   |   |   |   |   |   |
+-- 3   +--     +-- 3   +-- 3   +-- 2
    |   |   |   |   |   |   |   |
    +-- 4   +-- 5   +-- 1   +-- 1
        |   |   |   |   |   |
        +-- 0   +-- 2   +-- 2
            |   |   |   |
            +-- 8   +-- 5
                |   |
                +-- 6

score 39

OKAZAKI_Yumemi_80x80x8_02_Syaberu.gif
「 これより 良い経路があるんなら 選んでみなさいよ!」

KITASHIRAKAWA_Chiyuri_80x100x8_01_Futu.gif
「 オッカムのカミソリは無いんで、最後まで続けてくれだぜ☆」

pos
[Next 10 column(s)]

                +-- 1
                |   |
            +-- 0   +-- 4
            |   |   |   |
        +-- 7   +-- 2   +--  
        |   |   |   |   |   |
    +-- 3   +-- 1   +--     +--  
    |   |   |   |   |   |   |   |
+--     +-- 1   +--     +-- 4   +-- @
|   |   |   |   |   |   |   |   |   |
    +--     +--     +-- 2   +-- 2   +--
|   |   |   |   |   |   |   |   |   |
+-- 3   +--     +-- 3   +-- 3   +-- 2
    |   |   |   |   |   |   |   |
    +-- 4   +-- 5   +-- 1   +-- 1
        |   |   |   |   |   |
        +-- 0   +-- 2   +-- 2
            |   |   |   |
            +-- 8   +-- 5
                |   |
                +-- 6

score 42

OKAZAKI_Yumemi_80x80x8_02_Syaberu.gif
「 つら……」

do d
pos
[Finished]

                +-- 1
                |   |
            +-- 0   +-- 4
            |   |   |   |
        +-- 7   +-- 2   +--  
        |   |   |   |   |   |
    +-- 3   +-- 1   +--     +--  
    |   |   |   |   |   |   |   |
+--     +-- 1   +--     +-- 4   +--  
|   |   |   |   |   |   |   |   |   |
    +--     +--     +-- 2   +-- 2   [email protected]
|   |   |   |   |   |   |   |   |   |
+-- 3   +--     +-- 3   +-- 3   +-- 2
    |   |   |   |   |   |   |   |
    +-- 4   +-- 5   +-- 1   +-- 1
        |   |   |   |   |   |
        +-- 0   +-- 2   +-- 2
            |   |   |   |
            +-- 8   +-- 5
                |   |
                +-- 6

score 42
update
high-score 42

OKAZAKI_Yumemi_80x80x8_02_Syaberu.gif
「 終わった!」

KIFUWARABE_80x100x8_01_Futu.gif
「 42点より 良い点は 取れないのでは?」

OKAZAKI_Yumemi_80x80x8_02_Syaberu.gif
「 ほら見ろ!」

KITASHIRAKAWA_Chiyuri_80x100x8_01_Futu.gif
「 本当に無いか 調べてみようぜ☆?」

```plain
resolve
[Resolve / Next 1 column(s)]

                +-- 1
                |   |
            +-- 0   +-- 4
            |   |   |   |
        +-- 7   +-- 2   +-- 8
        |   |   |   |   |   |
    +-- 3   +-- 1   +-- 3   +-- 5
    |   |   |   |   |   |   |   |
+-- 5   +-- 1   +-- 1   +-- 4   +-- 3
|   |   |   |   |   |   |   |   |   |
@   +-- 2   +-- 9   +-- 2   +-- 2   +--
|   |   |   |   |   |   |   |   |   |
+-- 3   +-- 6   +-- 3   +-- 3   +-- 2
    |   |   |   |   |   |   |   |
    +-- 4   +-- 5   +-- 1   +-- 1
        |   |   |   |   |   |
        +-- 0   +-- 2   +-- 2
            |   |   |   |
            +-- 8   +-- 5
                |   |
                +-- 6

cur = [0]
cur = add_max(cur, [5,3])
    = [5,3]

[Resolve / Next 2 column(s)]

                +-- 1
                |   |
            +-- 0   +-- 4
            |   |   |   |
        +-- 7   +-- 2   +-- 8
        |   |   |   |   |   |
    +-- 3   +-- 1   +-- 3   +-- 5
    |   |   |   |   |   |   |   |
+-- 5   +-- 1   +-- 1   +-- 4   +-- 3
|   |   |   |   |   |   |   |   |   |
+   +-- 2   +-- 9   +-- 2   +-- 2   +--
|   |   |   |   |   |   |   |   |   |
+-- 3   +-- 6   +-- 3   +-- 3   +-- 2
    |   |   |   |   |   |   |   |
    +-- 4   +-- 5   +-- 1   +-- 1
        |   |   |   |   |   |
        +-- 0   +-- 2   +-- 2
            |   |   |   |
            +-- 8   +-- 5
                |   |
                +-- 6

cur = [5,3]
cur = add_max(cur, [3,2,4])
    = [8,7,7]

[Resolve / Next 3 column(s)]

                +-- 1
                |   |
            +-- 0   +-- 4
            |   |   |   |
        +-- 7   +-- 2   +-- 8
        |   |   |   |   |   |
    +-- 8   +-- 1   +-- 3   +-- 5
    |   |   |   |   |   |   |   |
+---+   +-- 1   +-- 1   +-- 4   +-- 3
|   |   |   |   |   |   |   |   |   |
+   +-- 7   +-- 9   +-- 2   +-- 2   +--
|       |   |   |   |   |   |   |   |
+---+   +-- 6   +-- 3   +-- 3   +-- 2
    |   |   |   |   |   |   |   |
    +-- 7   +-- 5   +-- 1   +-- 1
        |   |   |   |   |   |
        +-- 0   +-- 2   +-- 2
            |   |   |   |
            +-- 8   +-- 5
                |   |
                +-- 6

cur = [8,7,7]
cur = add_max(cur, [7,1,6,0])
    = [15,9,13,7]

[Resolve / Next 4 column(s)]

                +-- 1
                |   |
            +-- 0   +-- 4
            |   |   |   |
        +--15   +-- 2   +-- 8
        |   |   |   |   |   |
    +---+   +-- 1   +-- 3   +-- 5
    |   |   |   |   |   |   |   |
+---+   +-- 9   +-- 1   +-- 4   +-- 3
|   |       |   |   |   |   |   |   |
+   +---+   +-- 9   +-- 2   +-- 2   +--
|       |   |   |   |   |   |   |   |
+---+   +--13   +-- 3   +-- 3   +-- 2
    |   |   |   |   |   |   |   |
    +---+   +-- 5   +-- 1   +-- 1
        |   |   |   |   |   |
        +-- 7   +-- 2   +-- 2
            |   |   |   |
            +-- 8   +-- 5
                |   |
                +-- 6

cur = [15,9,13,7]
cur = add_max(cur, [0,1,9,5,8])
    = [15,16,22,18,15]

[Resolve / Next 5 column(s)]

                +-- 1
                |   |
            +--15   +-- 4
            |   |   |   |
        +---+   +-- 2   +-- 8
        |   |   |   |   |   |
    +---+   +--16   +-- 3   +-- 5
    |   |       |   |   |   |   |
+---+   +--     +-- 1   +-- 4   +-- 3
|   |           |   |   |   |   |   |
+   +---+   +--22   +-- 2   +-- 2   +--
|       |   |   |   |   |   |   |   |
+---+   +---+   +-- 3   +-- 3   +-- 2
    |   |   |   |   |   |   |   |
    +---+   +--18   +-- 1   +-- 1
        |       |   |   |   |
        +---+   +-- 2   +-- 2
            |   |   |   |
            +--15   +-- 5
                |   |
                +-- 6

cur = [15,16,22,18,15]
cur = add_max(cur, [1,2,1,3,2,6])
    = [16,18,23,25,20,21]

[Resolve / Next 6 column(s)]

                +--16
                |   |
            +---+   +-- 4
            |   |   |   |
        +---+   +--18   +-- 8
        |   |   |   |   |   |
    +---+   +---+   +-- 3   +-- 5
    |   |           |   |   |   |
+---+   +--     +--23   +-- 4   +-- 3
|   |           |   |   |   |   |   |
+   +---+   +---+   +-- 2   +-- 2   +--
|       |   |   |   |   |   |   |   |
+---+   +---+   +--25   +-- 3   +-- 2
    |   |   |       |   |   |   |
    +---+   +---+   +-- 1   +-- 1
        |       |   |   |   |
        +---+   +--20   +-- 2
            |       |   |
            +---+   +-- 5
                |   |
                +--21

cur = [16,18,23,25,20,21]
cur = add_max(cur, [4,3,2,1,5])
    = [22,26,27,26,26]

[Resolve / Next 7 column(s)]

                +--  
                |    
            +---+   +--22
            |   |   |   |
        +---+   +---+   +-- 8
        |   |   |       |   |
    +---+   +---+   +--26   +-- 5
    |   |           |   |   |   |
+---+   +--     +---+   +-- 4   +-- 3
|   |           |       |   |   |   |
+   +---+   +---+   +--27   +-- 2   +--
|       |   |   |   |   |   |   |   |
+---+   +---+   +---+   +-- 3   +-- 2
    |   |   |       |   |   |   |
    +---+   +---+   +--26   +-- 1
        |       |       |   |
        +---+   +--     +-- 2
            |           |
            +---+   +--26
                |   |
                +---+

cur = [22,26,27,26,26]
cur = add_max(cur, [8,4,3,2])
    = [34,31,29,28]

[Resolve / Next 8 column(s)]

                +--  
                |    
            +---+   +--  
            |   |   |    
        +---+   +---+   +--34
        |   |   |       |   |
    +---+   +---+   +---+   +-- 5
    |   |           |   |   |   |
+---+   +--     +---+   +--31   +-- 3
|   |           |       |   |   |   |
+   +---+   +---+   +---+   +-- 2   +--
|       |   |   |   |       |   |   |
+---+   +---+   +---+   +--29   +-- 2
    |   |   |       |   |   |   |
    +---+   +---+   +---+   +-- 1
        |       |       |   |
        +---+   +--     +--28
            |           |
            +---+   +---+
                |   |
                +---+

cur = [34,31,29,28]
cur = add_max(cur, [5,2,1])
    = [39,33,30]

[Resolve / Next 9 column(s)]

                +--  
                |    
            +---+   +--  
            |   |   |    
        +---+   +---+   +---+
        |   |   |       |   |
    +---+   +---+   +---+   +--39
    |   |           |   |       |
+---+   +--     +---+   +---+   +-- 3
|   |           |       |   |   |   |
+   +---+   +---+   +---+   +--33   +--
|       |   |   |   |           |   |
+---+   +---+   +---+   +---+   +-- 2
    |   |   |       |   |   |   |
    +---+   +---+   +---+   +--30
        |       |       |    
        +---+   +--     +--  
            |           |
            +---+   +---+
                |   |
                +---+

cur = [39,33,30]
cur = add_max(cur, [3,2])
    = [42,35]

[Resolve / Next 10 column(s)]

                +--  
                |    
            +---+   +--  
            |   |   |    
        +---+   +---+   +---+
        |   |   |       |   |
    +---+   +---+   +---+   +---+
    |   |           |   |       |
+---+   +--     +---+   +---+   +--42
|   |           |       |   |       |
+   +---+   +---+   +---+   +---+   +--
|       |   |   |   |           |   |
+---+   +---+   +---+   +---+   +--35
    |   |   |       |   |   |    
    +---+   +---+   +---+   +--  
        |       |       |    
        +---+   +--     +--  
            |           |
            +---+   +---+
                |   |
                +---+

cur = [42,35]
cur = add_max(cur, [0])
    = [42]

[Finished]

                +--  
                |    
            +---+   +--  
            |   |   |    
        +---+   +---+   +---+
        |   |   |       |   |
    +---+   +---+   +---+   +---+
    |   |           |   |       |
+---+   +--     +---+   +---+   +---+
|   |           |       |   |       |
+   +---+   +---+   +---+   +---+   +--42
|       |   |   |   |           |    
+---+   +---+   +---+   +---+   +--  
    |   |   |       |   |   |    
    +---+   +---+   +---+   +--  
        |       |       |    
        +---+   +--     +--  
            |           |
            +---+   +---+
                |   |
                +---+

cur = [42]
max-score 42

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