67 lines
1.5 KiB
Markdown
67 lines
1.5 KiB
Markdown
---
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id: 5900f54a1000cf542c51005c
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title: 'Problem 477: Number Sequence Game'
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challengeType: 5
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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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Two players alternate turns. At his turn, a player must select and remove either the first or the last number remaining in the sequence.
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The player score is the sum of all the numbers he has taken. Each player attempts to maximize his own sum.
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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 = {s1, s2, ..., sN} defined as:
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s1 = 0
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si+1 = (si2 + 45) modulo 1 000 000 007
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The sequence begins with S = {0, 45, 2070, 4284945, 753524550, 478107844, 894218625, ...}.
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You are given F(2) = 45, F(4) = 4284990, F(100) = 26365463243, F(104) = 2495838522951.
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Find F(108).
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# --hints--
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`euler477()` should return 25044905874565164.
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```js
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assert.strictEqual(euler477(), 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 euler477() {
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return true;
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}
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euler477();
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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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