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* fix: clean-up Project Euler 141-160 * fix: corrections from review Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> * fix: use different notation for consistency * Update curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-144-investigating-multiple-reflections-of-a-laser-beam.md Co-authored-by: gikf <60067306+gikf@users.noreply.github.com> Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
61 lines
1.6 KiB
Markdown
61 lines
1.6 KiB
Markdown
---
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id: 5900f4021000cf542c50ff13
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title: 'Problem 149: Searching for a maximum-sum subsequence'
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challengeType: 5
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forumTopicId: 301778
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dashedName: problem-149-searching-for-a-maximum-sum-subsequence
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---
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# --description--
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Looking at the table below, it is easy to verify that the maximum possible sum of adjacent numbers in any direction (horizontal, vertical, diagonal or anti-diagonal) is $16 (= 8 + 7 + 1)$.
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$$\begin{array}{|r|r|r|r|}
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\hline
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−2 & 5 & 3 & 2 \\\\ \hline
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9 & −6 & 5 & 1 \\\\ \hline
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3 & 2 & 7 & 3 \\\\ \hline
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−1 & 8 & −4 & 8 \\\\ \hline
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\end{array}$$
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Now, let us repeat the search, but on a much larger scale:
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First, generate four million pseudo-random numbers using a specific form of what is known as a "Lagged Fibonacci Generator":
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For $1 ≤ k ≤ 55$, $s_k = (100003 − 200003k + 300007{k}^3) \\ (modulo\\ 1000000) − 500000$.
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For $56 ≤ k ≤ 4000000$, $s_k = (s_{k − 24} + s_{k − 55} + 1000000) \\ (modulo\\ 1000000) − 500000$.
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Thus, $s_{10} = −393027$ and $s_{100} = 86613$.
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The terms of $s$ are then arranged in a 2000×2000 table, using the first 2000 numbers to fill the first row (sequentially), the next 2000 numbers to fill the second row, and so on.
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Finally, find the greatest sum of (any number of) adjacent entries in any direction (horizontal, vertical, diagonal or anti-diagonal).
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# --hints--
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`maximumSubSequence()` should return `52852124`.
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```js
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assert.strictEqual(maximumSubSequence(), 52852124);
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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 maximumSubSequence() {
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return true;
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}
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maximumSubSequence();
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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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