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63 lines
1.6 KiB
Markdown
63 lines
1.6 KiB
Markdown
---
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id: 5900f54a1000cf542c51005c
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title: '问题 477：数字序列游戏'
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challengeType: 1
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forumTopicId: 302154
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dashedName: problem-477-number-sequence-game
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---
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# --description--
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The number sequence game starts with a sequence $S$ of $N$ numbers written on a line.
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两名玩家交替轮流。 在轮到他时，玩家必须选择并删除序列中剩余的第一个或最后一个数字。
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玩家得分是他所取所有数字的总和。 每个玩家都试图最大化自己的总和。
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If $N = 4$ and $S = \\{1, 2, 10, 3\\}$, then each player maximizes his score as follows:
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- Player 1: removes the first number (1)
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- Player 2: removes the last number from the remaining sequence (3)
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- Player 1: removes the last number from the remaining sequence (10)
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- Player 2: removes the remaining number (2)
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Player 1 score is $1 + 10 = 11$.
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Let $F(N)$ be the score of player 1 if both players follow the optimal strategy for the sequence $S = \\{s_1, s_2, \ldots, s_N\\}$ defined as:
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- $s_1 = 0$
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- $s_{i + 1} = ({s_i}^2 + 45)$ modulo $1\\,000\\,000\\,007$
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The sequence begins with $S = \\{0, 45, 2\\,070, 4\\,284\\,945, 753\\,524\\,550, 478\\,107\\,844, 894\\,218\\,625, \ldots\\}$.
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You are given $F(2) = 45$, $F(4) = 4\\,284\\,990$, $F(100) = 26\\,365\\,463\\,243$, $F(104) = 2\\,495\\,838\\,522\\,951$.
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Find $F({10}^8)$.
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# --hints--
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`numberSequenceGame()` should return `25044905874565164`.
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```js
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assert.strictEqual(numberSequenceGame(), 25044905874565164);
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```
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# --seed--
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## --seed-contents--
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```js
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function numberSequenceGame() {
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return true;
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}
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numberSequenceGame();
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```
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# --solutions--
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```js
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// solution required
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```
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