freeCodeCamp/curriculum/challenges/chinese/10-coding-interview-prep/project-euler/problem-477-number-sequence-game.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f54a1000cf542c51005c	问题 477：数字序列游戏	1	302154	problem-477-number-sequence-game

--description--

The number sequence game starts with a sequence S of N numbers written on a line.

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。

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。

If N = 4 and S = \\{1, 2, 10, 3\\}, then each player maximizes his score as follows:

• Player 1: removes the first number (1)
• Player 2: removes the last number from the remaining sequence (3)
• Player 1: removes the last number from the remaining sequence (10)
• Player 2: removes the remaining number (2)

Player 1 score is 1 + 10 = 11.

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:

• s_1 = 0
• s_{i + 1} = ({s_i}^2 + 45) modulo 1\\,000\\,000\\,007

The sequence begins with S = \\{0, 45, 2\\,070, 4\\,284\\,945, 753\\,524\\,550, 478\\,107\\,844, 894\\,218\\,625, \ldots\\}.

You are given F(2) = 45, F(4) = 4\\,284\\,990, F(100) = 26\\,365\\,463\\,243, F(104) = 2\\,495\\,838\\,522\\,951.

Find F({10}^8).

--hints--

numberSequenceGame() should return 25044905874565164.

assert.strictEqual(numberSequenceGame(), 25044905874565164);

--seed--

--seed-contents--

function numberSequenceGame() {

  return true;
}

numberSequenceGame();

--solutions--

// solution required