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![解法2 : 動的計画法
?? 現在のマスへは、一つ?三つ前のマスからしか到達できない
?? 位置 p まで最適に移動してくれば、
その先の最適な移動方法はこれまでの移動方法によらない。
?? なので、位置だけを状態に持てばよく、次の漸化式が成立
?? X[0] = 0
?? X[p] = min(X[p-1], X[p-2], X[p-3]) + R[p]
?? R[p] : 位置 p が水たまりなら 1 、そうでないなら 0](https://image.slidesharecdn.com/brain-121230212537-phpapp01/85/WUPC2nd-B-5-320.jpg)
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WUPC2nd B問題
- 1. 第2回 早稲田大学プログラミングコンテスト B: 雨上がり keyword: 貪欲法、動的計画法
- 2. 問題概要 ?? 一本に続いた道と、途中に水たまりがいくつかあります。 ?? 主人公は「一歩」or「二歩」or「三歩」前に進めます。 ?? なるだけ水たまりを踏まないようにゴールまで行きたいです。 ?? 最適な方法で移動した時、水たまりを踏む数の最小数は？ スタート ゴール : 普通の道路 : 水たまり
- 3. 制約 ?? 3 <= 道路長 <= 100 ?? スタートとゴールは水たまりではない
- 4. 解法1 : 貪欲法 ?? 「一歩先」「二歩先」「三歩先」のうちどれかが水たまりでない ?? そこに進めばOK ?? 次が全て水たまりなら ?? 後続の水たまりを回避したいため、必ず三歩進む ?? なるべく前に進んだほうがお得だから。
- 5. 解法2 : 動的計画法 ?? 現在のマスへは、一つ?三つ前のマスからしか到達できない ?? 位置 p まで最適に移動してくれば、 その先の最適な移動方法はこれまでの移動方法によらない。 ?? なので、位置だけを状態に持てばよく、次の漸化式が成立 ?? X[0] = 0 ?? X[p] = min(X[p-1], X[p-2], X[p-3]) + R[p] ?? R[p] : 位置 p が水たまりなら 1 、そうでないなら 0
- 6. 統計 ?? First AC : uwi (03:08) ?? 正解数 : 177 ?? 通した人(/205) : 86% ?? ACだった解答(/378) : 47%