67de105117
* fix: clean-up Project Euler 241-260 * fix: typo * Update curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-255-rounded-square-roots.md Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
69 lines
2.4 KiB
Markdown
69 lines
2.4 KiB
Markdown
---
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id: 5900f4601000cf542c50ff72
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title: 'Problem 244: Sliders'
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challengeType: 5
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forumTopicId: 301891
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dashedName: problem-244-sliders
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---
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# --description--
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You probably know the game Fifteen Puzzle. Here, instead of numbered tiles, we have seven red tiles and eight blue tiles.
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A move is denoted by the uppercase initial of the direction (Left, Right, Up, Down) in which the tile is slid, e.g. starting from configuration ($S$), by the sequence $LULUR$ we reach the configuration ($E$):
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($S$) <img class="img-responsive" alt="configuration S" src="https://cdn.freecodecamp.org/curriculum/project-euler/sliders-1.gif" style="display: inline-block; background-color: white; padding: 10px;">, ($E$) <img class="img-responsive" alt="configuration E" src="https://cdn.freecodecamp.org/curriculum/project-euler/sliders-2.gif" style="display: inline-block; background-color: white; padding: 10px;">
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For each path, its checksum is calculated by (pseudocode):
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$$\begin{align}
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& \text{checksum} = 0 \\\\
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& \text{checksum} = (\text{checksum} × 243 + m_1) \\; \text{mod} \\; 100\\,000\\,007 \\\\
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& \text{checksum} = (\text{checksum} × 243 + m_2) \\; \text{mod} \\; 100\\,000\\,007 \\\\
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& \ldots \\\\
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& \text{checksum} = (\text{checksum} × 243 + m_n) \\; \text{mod} \\; 100\\,000\\,007
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\end{align}$$
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where $m_k$ is the ASCII value of the $k^{\text{th}}$ letter in the move sequence and the ASCII values for the moves are:
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$$\begin{array}{|c|c|}
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\hline
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L & 76 \\\\ \hline
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R & 82 \\\\ \hline
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U & 85 \\\\ \hline
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D & 68 \\\\ \hline
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\end{array}$$
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For the sequence $LULUR$ given above, the checksum would be 19761398. Now, starting from configuration ($S$), find all shortest ways to reach configuration ($T$).
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($S$) <img class="img-responsive center-block" alt="configuration S" src="https://cdn.freecodecamp.org/curriculum/project-euler/sliders-3.gif" style="display: inline-block; background-color: white; padding: 10px;">, ($T$) <img class="img-responsive center-block" alt="configuration T" src="https://cdn.freecodecamp.org/curriculum/project-euler/sliders-4.gif" style="display: inline-block; background-color: white; padding: 10px;">
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What is the sum of all checksums for the paths having the minimal length?
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# --hints--
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`sliders()` should return `96356848`.
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```js
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assert.strictEqual(sliders(), 96356848);
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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 sliders() {
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return true;
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}
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sliders();
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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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