Change links from http to https
This commit is contained in:
Kris Koishigawa
mrugesh
@ -6,7 +6,7 @@ challengeType: 5
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## Description
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<section id='description'>
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The <a href="http://en.wikipedia.org/wiki/24_Game" target="_blank">24 Game</a> tests a person's mental arithmetic.
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The <a href="https://en.wikipedia.org/wiki/24_Game" target="_blank">24 Game</a> tests a person's mental arithmetic.
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The aim of the game is to arrange four numbers in a way that when evaluated, the result is 24
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</section>
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@ -11,7 +11,7 @@ This task is a variation of the <a href='https://en.wikipedia.org/wiki/The Nine
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In detail, to specify what is meant by a “name”:
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<ul>
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<li>The integer 1 has 1 name “1”.</li>
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<li>The integer 2 has 2 names “1+1”, and “2”.</li>
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<li>The integer 2 has 2 names “1+1” and “2”.</li>
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<li>The integer 3 has 3 names “1+1+1”, “2+1”, and “3”.</li>
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<li>The integer 4 has 5 names “1+1+1+1”, “2+1+1”, “2+2”, “3+1”, “4”.</li>
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<li>The integer 5 has 7 names “1+1+1+1+1”, “2+1+1+1”, “2+2+1”, “3+1+1”, “3+2”, “4+1”, “5”.</li>
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@ -26,7 +26,7 @@ This can be visualized in the following form:
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1 3 3 2 1 1
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</pre>
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Where row $n$ corresponds to integer $n$, and each column $C$ in row $m$ from left to right corresponds to the number of names beginning with $C$.
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Optionally note that the sum of the $n$-th row $P(n)$ is the <a href="http://mathworld.wolfram.com/PartitionFunctionP.html" title="link: http://mathworld.wolfram.com/PartitionFunctionP.html">integer partition function</a>.
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Optionally note that the sum of the $n$-th row $P(n)$ is the <a href="https://mathworld.wolfram.com/PartitionFunctionP.html" title="link: https://mathworld.wolfram.com/PartitionFunctionP.html">integer partition function</a>.
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</section>
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## Instructions
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@ -6,16 +6,18 @@ challengeType: 5
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## Description
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<section id='description'>
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These define three classifications of positive integers based on their <a href='http://rosettacode.org/wiki/Proper divisors' title='Proper divisors' target='_blank'>proper divisors</a>.
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These define three classifications of positive integers based on their <a href='https://rosettacode.org/wiki/Proper divisors' title='Proper divisors' target='_blank'>proper divisors</a>.
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Let $P(n)$ be the sum of the proper divisors of <b>n</b> where proper divisors are all positive integers <b>n</b> other than <b>n</b> itself.
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<pre>
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If <code style='border: 1px solid #ddd;'> P(n) < n </code> then <b>n</b> is classed as <b>deficient</b>
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If <code style='border: 1px solid #ddd;'> P(n) === n </code> then <b>n</b> is classed as <b>perfect</b>
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If <code style='border: 1px solid #ddd;'> P(n) > n </code> then <b>n</b> is classed as <b>abundant</b>
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</pre>
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Example:
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<b>6</b> has proper divisors of <b>1</b>, <b>2</b>, and <b>3</b>.
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<b>1 + 2 + 3 = 6</b>, so <b>6</b> is classed as a perfect number.
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If <code>P(n) < n</code> then <code>n</code> is classed as <code>deficient</code>
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If <code>P(n) === n</code> then <code>n</code> is classed as <code>perfect</code>
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If <code>P(n) > n</code> then <code>n</code> is classed as <code>abundant</code>
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<strong>Example</strong>:
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<strong>6</strong> has proper divisors of <strong>1</strong>, <strong>2</strong>, and <strong>3</strong>.
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<strong>1 + 2 + 3 = 6</strong>, so <strong>6</strong> is classed as a perfect number.
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</section>
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## Instructions
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@ -6,7 +6,7 @@ challengeType: 5
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## Description
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<section id='description'>
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A problem posed by <a href='http://en.wikipedia.org/wiki/Paul_Graham' target='_blank'>Paul Graham</a> is that of creating a function that takes a single (numeric) argument and which returns another function that is an accumulator. The returned accumulator function in turn also takes a single numeric argument, and returns the sum of all the numeric values passed in so far to that accumulator (including the initial value passed when the accumulator was created).
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A problem posed by <a href='https://en.wikipedia.org/wiki/Paul_Graham' target='_blank'>Paul Graham</a> is that of creating a function that takes a single (numeric) argument and which returns another function that is an accumulator. The returned accumulator function in turn also takes a single numeric argument, and returns the sum of all the numeric values passed in so far to that accumulator (including the initial value passed when the accumulator was created).
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</section>
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## Instructions
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@ -6,7 +6,7 @@ challengeType: 5
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## Description
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<section id='description'>
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Two integers $N$ and $M$ are said to be <a href='https://en.wikipedia.org/wiki/Amicable numbers' title='wp: Amicable numbers' target='_blank'>amicable pairs</a> if $N \neq M$ and the sum of the <a href="http://rosettacode.org/wiki/Proper divisors" title="Proper divisors">proper divisors</a> of $N$ ($\mathrm{sum}(\mathrm{propDivs}(N))$) $= M$ as well as $\mathrm{sum}(\mathrm{propDivs}(M)) = N$.
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Two integers $N$ and $M$ are said to be <a href='https://en.wikipedia.org/wiki/Amicable numbers' title='wp: Amicable numbers' target='_blank'>amicable pairs</a> if $N \neq M$ and the sum of the <a href="https://rosettacode.org/wiki/Proper divisors" title="Proper divisors">proper divisors</a> of $N$ ($\mathrm{sum}(\mathrm{propDivs}(N))$) $= M$ as well as $\mathrm{sum}(\mathrm{propDivs}(M)) = N$.
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<b>Example:</b>
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<b>1184</b> and <b>1210</b> are an amicable pair, with proper divisors:
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<ul>
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@ -9,7 +9,7 @@ challengeType: 5
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Compute all three of the <a class='rosetta__link--wiki' href='https://en.wikipedia.org/wiki/Pythagorean means' title='wp: Pythagorean means'>Pythagorean means</a> of the set of integers <big>1</big> through <big>10</big> (inclusive).
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Show that <big>$A(x_1,\ldots,x_n) \geq G(x_1,\ldots,x_n) \geq H(x_1,\ldots,x_n)$</big> for this set of positive integers.
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<ul>
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<li>The most common of the three means, the <a class='rosetta__link--rosetta' href='http://rosettacode.org/wiki/Averages/Arithmetic mean' title='Averages/Arithmetic mean' target='_blank'>arithmetic mean</a>, is the sum of the list divided by its length:<br>
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<li>The most common of the three means, the <a class='rosetta__link--rosetta' href='https://rosettacode.org/wiki/Averages/Arithmetic mean' title='Averages/Arithmetic mean' target='_blank'>arithmetic mean</a>, is the sum of the list divided by its length:<br>
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<big>$ A(x_1, \ldots, x_n) = \frac{x_1 + \cdots + x_n}{n}$</big></li>
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<li>The <a class='rosetta__link--wiki' href='https://en.wikipedia.org/wiki/Geometric mean' title='wp: Geometric mean' target='_blank'>geometric mean</a> is the $n$th root of the product of the list:<br>
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<big>$ G(x_1, \ldots, x_n) = \sqrt[n]{x_1 \cdots x_n} $</big></li>
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@ -35,7 +35,7 @@ Implement a function that takes two points and a radius and returns the two circ
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0.1234, 0.9876 0.1234, 0.9876 0.0
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</pre>
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<b>Ref:</b>
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<a href="http://mathforum.org/library/drmath/view/53027.html" title="link: http://mathforum.org/library/drmath/view/53027.html">Finding the Center of a Circle from 2 Points and Radius</a> from Math forum @ Drexel
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<a href="https://mathforum.org/library/drmath/view/53027.html" target="_blank">Finding the Center of a Circle from 2 Points and Radius</a> from Math forum @ Drexel
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</section>
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## Tests
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@ -64,10 +64,10 @@ For the input, expect the argument to be an array of objects (points) with <code
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<b>References and further readings:</b>
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<ul>
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<li><a href="https://en.wikipedia.org/wiki/Closest pair of points problem" title="wp: Closest pair of points problem">Closest pair of points problem</a></li>
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<li><a href="http://www.cs.mcgill.ca/~cs251/ClosestPair/ClosestPairDQ.html" title="link: http://www.cs.mcgill.ca/~cs251/ClosestPair/ClosestPairDQ.html">Closest Pair (McGill)</a></li>
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<li><a href="http://www.cs.ucsb.edu/~suri/cs235/ClosestPair.pdf" title="link: http://www.cs.ucsb.edu/~suri/cs235/ClosestPair.pdf">Closest Pair (UCSB)</a></li>
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<li><a href="http://classes.cec.wustl.edu/~cse241/handouts/closestpair.pdf" title="link: http://classes.cec.wustl.edu/~cse241/handouts/closestpair.pdf">Closest pair (WUStL)</a></li>
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<li><a href="http://www.cs.iupui.edu/~xkzou/teaching/CS580/Divide-and-conquer-closestPair.ppt" title="link: http://www.cs.iupui.edu/~xkzou/teaching/CS580/Divide-and-conquer-closestPair.ppt">Closest pair (IUPUI)</a></li>
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<li><a href="https://www.cs.mcgill.ca/~cs251/ClosestPair/ClosestPairDQ.html">Closest Pair (McGill)</a></li>
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<li><a href="https://www.cs.ucsb.edu/~suri/cs235/ClosestPair.pdf">Closest Pair (UCSB)</a></li>
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<li><a href="https://classes.cec.wustl.edu/~cse241/handouts/closestpair.pdf">Closest pair (WUStL)</a></li>
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<li><a href="https://www.cs.iupui.edu/~xkzou/teaching/CS580/Divide-and-conquer-closestPair.ppt">Closest pair (IUPUI)</a></li>
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</ul>
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</section>
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@ -6,7 +6,7 @@ challengeType: 5
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## Description
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<section id='description'>
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Given non-negative integers <big><b>m</b></big> and <big><b>n</b></big>, generate all size <big><b>m</b></big><a href="http://mathworld.wolfram.com/Combination.html" title="link: http://mathworld.wolfram.com/Combination.html"> combinations</a> of the integers from <big><b>0</b></big> (zero) to <big><b>n-1</b></big> in sorted order (each combination is sorted and the entire table is sorted).
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Given non-negative integers <big><b>m</b></big> and <big><b>n</b></big>, generate all size <big><b>m</b></big><a href="https://mathworld.wolfram.com/Combination.html"> combinations</a> of the integers from <big><b>0</b></big> (zero) to <big><b>n-1</b></big> in sorted order (each combination is sorted and the entire table is sorted).
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<b>Example:</b>
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<big><b>3</b></big> comb <big><b>5</b></big> is:
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<pre>
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@ -6,7 +6,7 @@ challengeType: 5
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## Description
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<section id='description'>
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Comma quibbling is a task originally set by Eric Lippert in his <a href="http://blogs.msdn.com/b/ericlippert/archive/2009/04/15/comma-quibbling.aspx" title="link: http://blogs.msdn.com/b/ericlippert/archive/2009/04/15/comma-quibbling.aspx" target="_blank">blog</a>.
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Comma quibbling is a task originally set by Eric Lippert in his <a href="https://blogs.msdn.com/b/ericlippert/archive/2009/04/15/comma-quibbling.aspx" target="_blank">blog</a>.
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</section>
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## Instructions
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@ -6,7 +6,7 @@ challengeType: 5
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## Description
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<section id='description'>
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There are four types of common coins in <a href="https://en.wikipedia.org/wiki/United_States" title="link: https://en.wikipedia.org/wiki/United_States">US</a> currency:
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There are four types of common coins in <a href="https://en.wikipedia.org/wiki/United_States" target="_blank">US</a> currency:
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<ul>
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<li>quarters (25 cents)</li>
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<li>dimes (10 cents)</li>
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@ -29,7 +29,7 @@ There are four types of common coins in <a href="https://en.wikipedia.org/wiki/U
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Implement a function to determine how many ways there are to make change for a dollar using these common coins (1 dollar = 100 cents)
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<b>Reference:</b>
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<ul>
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<li><a href="http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-11.html#%_sec_Temp_52" title="link: http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-11.html#%_sec_Temp_52">an algorithm from MIT Press</a>.</li>
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<li><a href="https://mitpress.mit.edu/sicp/full-text/book/book-Z-H-11.html#%_sec_Temp_52" target="_blank">an algorithm from MIT Press</a>.</li>
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</ul>
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</section>
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@ -6,9 +6,9 @@ challengeType: 5
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## Description
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<section id='description'>
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<i>FreeCell</i> is the solitaire card game that Paul Alfille introduced to the PLATO system in 1978. Jim Horne, at Microsoft, changed the name to FreeCell and reimplemented the game for <a href="http://rosettacode.org/wiki/DOS" title="DOS">DOS</a>, then <a href="http://rosettacode.org/wiki/Windows" title="Windows">Windows</a>. This version introduced 32000 numbered deals. (The <a href="http://www.solitairelaboratory.com/fcfaq.html" title="link: http://www.solitairelaboratory.com/fcfaq.html">FreeCell FAQ</a> tells this history.)
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As the game became popular, Jim Horne disclosed <a href="http://www.solitairelaboratory.com/mshuffle.txt" title="link: http://www.solitairelaboratory.com/mshuffle.txt">the algorithm</a>, and other implementations of FreeCell began to reproduce the Microsoft deals. These deals are numbered from 1 to 32000. Newer versions from Microsoft have 1 million deals, numbered from 1 to 1000000; some implementations allow numbers outside that range.
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The algorithm uses this <a href="http://rosettacode.org/wiki/linear congruential generator" title="linear congruential generator">linear congruential generator</a> from Microsoft C:
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<i>FreeCell</i> is the solitaire card game that Paul Alfille introduced to the PLATO system in 1978. Jim Horne, at Microsoft, changed the name to FreeCell and reimplemented the game for <a href="https://rosettacode.org/wiki/DOS" title="DOS">DOS</a>, then <a href="https://rosettacode.org/wiki/Windows" title="Windows">Windows</a>. This version introduced 32000 numbered deals. (The <a href="https://www.solitairelaboratory.com/fcfaq.html">FreeCell FAQ</a> tells this history.)
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As the game became popular, Jim Horne disclosed <a href="https://www.solitairelaboratory.com/mshuffle.txt">the algorithm</a>, and other implementations of FreeCell began to reproduce the Microsoft deals. These deals are numbered from 1 to 32000. Newer versions from Microsoft have 1 million deals, numbered from 1 to 1000000; some implementations allow numbers outside that range.
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The algorithm uses this <a href="https://rosettacode.org/wiki/linear congruential generator" title="linear congruential generator">linear congruential generator</a> from Microsoft C:
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<ul>
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<li>$state_{n + 1} \equiv 214013 \times state_n + 2531011 \pmod{2^{31}}$</li>
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<li>$rand_n = state_n \div 2^{16}$</li>
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@ -17,7 +17,7 @@ The algorithm uses this <a href="http://rosettacode.org/wiki/linear congruential
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The algorithm follows:
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<ol>
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<li>Seed the RNG with the number of the deal.
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<li>Create an <a href="http://rosettacode.org/wiki/array" title="array">array</a> of 52 cards: Ace of Clubs, Ace of Diamonds, Ace of Hearts, Ace of Spades, 2 of Clubs, 2 of Diamonds, and so on through the ranks: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. The array indexes are 0 to 51, with Ace of Clubs at 0, and King of Spades at 51.</li>
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<li>Create an <a href="https://rosettacode.org/wiki/array" title="array">array</a> of 52 cards: Ace of Clubs, Ace of Diamonds, Ace of Hearts, Ace of Spades, 2 of Clubs, 2 of Diamonds, and so on through the ranks: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. The array indexes are 0 to 51, with Ace of Clubs at 0, and King of Spades at 51.</li>
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<li>Until the array is empty:</li>
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<li>Choose a random card at index ≡ next random number (mod array length).</li>
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<ul>
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@ -61,7 +61,7 @@ The algorithm follows:
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## Instructions
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<section id='instructions'>
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Write a function to take a deal number and deal cards in the same order as this algorithm. The function must return a two dimensional array representing the FreeCell board.
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Deals can also be checked against <a href="http://freecellgamesolutions.com/" title="link: http://freecellgamesolutions.com/">FreeCell solutions to 1000000 games</a>. (Summon a video solution, and it displays the initial deal.)
|
||||
Deals can also be checked against <a href="https://freecellgamesolutions.com/">FreeCell solutions to 1000000 games</a>. (Summon a video solution, and it displays the initial deal.)
|
||||
</section>
|
||||
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||||
## Tests
|
||||
|
||||
@ -7,7 +7,7 @@ challengeType: 5
|
||||
## Description
|
||||
<section id='description'>
|
||||
Write a function to implement a Brain**** interpreter. The function will take a string as a parameter and should return a string as the output. More details are given below:
|
||||
RCBF is a set of <a href="http://rosettacode.org/wiki/Brainf***" title="Brainf***">Brainf***</a> compilers and interpreters written for Rosetta Code in a variety of languages.
|
||||
RCBF is a set of <a href="https://rosettacode.org/wiki/Brainf***" title="Brainf***">Brainf***</a> compilers and interpreters written for Rosetta Code in a variety of languages.
|
||||
Below are links to each of the versions of RCBF.
|
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An implementation need only properly implement the following instructions:
|
||||
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||||
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@ -9,7 +9,7 @@ challengeType: 5
|
||||
A Mersenne number is a number in the form of 2<sup>P</sup>-1.
|
||||
If P is prime, the Mersenne number may be a Mersenne prime
|
||||
(if P is not prime, the Mersenne number is also not prime).
|
||||
In the search for Mersenne prime numbers it is advantageous to eliminate exponents by finding a small factor before starting a, potentially lengthy, <a href="http://rosettacode.org/wiki/Lucas-Lehmer test" title="Lucas-Lehmer test" target="_blank">Lucas-Lehmer test</a>.
|
||||
In the search for Mersenne prime numbers it is advantageous to eliminate exponents by finding a small factor before starting a, potentially lengthy, <a href="https://rosettacode.org/wiki/Lucas-Lehmer test" title="Lucas-Lehmer test" target="_blank">Lucas-Lehmer test</a>.
|
||||
There are very efficient algorithms for determining if a number divides 2<sup>P</sup>-1 (or equivalently, if 2<sup>P</sup> mod (the number) = 1).
|
||||
Some languages already have built-in implementations of this exponent-and-mod operation (called modPow or similar).
|
||||
The following is how to implement this modPow yourself:
|
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@ -32,7 +32,7 @@ Since 2<sup>23</sup> mod 47 = 1, 47 is a factor of 2<sup>P</sup>-1.
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Since we've shown that 47 is a factor, 2<sup>23</sup>-1 is not prime.
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Further properties of Mersenne numbers allow us to refine the process even more.
|
||||
Any factor q of 2<sup>P</sup>-1 must be of the form 2kP+1, k being a positive integer or zero. Furthermore, q must be 1 or 7 mod 8.
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Finally any potential factor q must be <a href="http://rosettacode.org/wiki/Primality by Trial Division" title="Primality by Trial Division" target="_blank">prime</a>.
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||||
Finally any potential factor q must be <a href="https://rosettacode.org/wiki/Primality by Trial Division" title="Primality by Trial Division" target="_blank">prime</a>.
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As in other trial division algorithms, the algorithm stops when 2kP+1 > sqrt(N).These primality tests only work on Mersenne numbers where P is prime. For example, M<sub>4</sub>=15 yields no factors using these techniques, but factors into 3 and 5, neither of which fit 2kP+1.
|
||||
</section>
|
||||
|
||||
|
||||
@ -6,7 +6,7 @@ challengeType: 5
|
||||
|
||||
## Description
|
||||
<section id='description'>
|
||||
These number series are an expansion of the ordinary <a href="http://rosettacode.org/wiki/Fibonacci sequence" title="Fibonacci sequence" target="_blank">Fibonacci sequence</a> where:
|
||||
These number series are an expansion of the ordinary <a href="https://rosettacode.org/wiki/Fibonacci sequence" title="Fibonacci sequence" target="_blank">Fibonacci sequence</a> where:
|
||||
<ol>
|
||||
<li>For $n = 2$ we have the Fibonacci sequence; with initial values $[1, 1]$ and $F_k^2 = F_{k-1}^2 + F_{k-2}^2$</li>
|
||||
<li>For $n = 3$ we have the tribonacci sequence; with initial values $[1, 1, 2]$ and $F_k^3 = F_{k-1}^3 + F_{k-2}^3 + F_{k-3}^3$</li>
|
||||
|
||||
@ -6,7 +6,7 @@ challengeType: 5
|
||||
|
||||
## Description
|
||||
<section id='description'>
|
||||
The Fibonacci Word may be created in a manner analogous to the Fibonacci Sequence <a href="http://hal.archives-ouvertes.fr/docs/00/36/79/72/PDF/The_Fibonacci_word_fractal.pdf" title="link: http://hal.archives-ouvertes.fr/docs/00/36/79/72/PDF/The_Fibonacci_word_fractal.pdf" target="_blank">as described here</a>:
|
||||
The Fibonacci Word may be created in a manner analogous to the Fibonacci Sequence <a href="https://hal.archives-ouvertes.fr/docs/00/36/79/72/PDF/The_Fibonacci_word_fractal.pdf" target="_blank">as described here</a>:
|
||||
<pre>
|
||||
Define F_Word<sub>1</sub> as <b>1</b>
|
||||
Define F_Word<sub>2</sub> as <b>0</b>
|
||||
|
||||
@ -6,7 +6,7 @@ challengeType: 5
|
||||
|
||||
## Description
|
||||
<section id='description'>
|
||||
Write a generalized version of <a href="http://rosettacode.org/wiki/FizzBuzz">FizzBuzz</a> that works for any list of factors, along with their words.
|
||||
Write a generalized version of <a href="https://rosettacode.org/wiki/FizzBuzz">FizzBuzz</a> that works for any list of factors, along with their words.
|
||||
This is basically a "fizzbuzz" implementation where the rules of the game are supplied to the user. Create a function to implement this. The function should take two parameters.
|
||||
The first will be an array with the FizzBuzz rules. For example: <code>[ [3, "Fizz"] , [5, "Buzz"] ]</code>.
|
||||
This indcates that <code>Fizz</code> should be printed if the number is a multiple of 3 and <code>Buzz</code> if it is a multiple of 5. If it is a multiple of both then the strings should be concatenated in the order specified in the array. In this case, <code>FizzBuzz</code> if the number is a multiple of 3 and 5.
|
||||
|
||||
@ -25,7 +25,7 @@ The hailstone sequence is also known as hailstone numbers (because the values ar
|
||||
</ol>
|
||||
<b>See also:</b>
|
||||
<ul>
|
||||
<li><a href="http://xkcd.com/710" title="link: http://xkcd.com/710" target="_blank">xkcd</a> (humourous).</li>
|
||||
<li><a href="https://xkcd.com/710" target="_blank">xkcd</a> (humourous).</li>
|
||||
</ul>
|
||||
</section>
|
||||
|
||||
|
||||
@ -6,8 +6,8 @@ challengeType: 5
|
||||
|
||||
## Description
|
||||
<section id='description'>
|
||||
The <a href="http://mathworld.wolfram.com/HarshadNumber.html" title="link: http://mathworld.wolfram.com/HarshadNumber.html" target="_blank">Harshad</a> or Niven numbers are positive integers ≥ 1 that are divisible by the sum of their digits.
|
||||
For example, <b>42</b> is a <a href="http://rosettacode.org/wiki/oeis:A005349" title="oeis:A005349" target="_blank">Harshad number</a> as <b>42</b> is divisible by <b>(4 + 2)</b> without remainder.
|
||||
The <a href="https://mathworld.wolfram.com/HarshadNumber.html" target="_blank">Harshad</a> or Niven numbers are positive integers ≥ 1 that are divisible by the sum of their digits.
|
||||
For example, <b>42</b> is a <a href="https://rosettacode.org/wiki/oeis:A005349" title="oeis:A005349" target="_blank">Harshad number</a> as <b>42</b> is divisible by <b>(4 + 2)</b> without remainder.
|
||||
Assume that the series is defined as the numbers in increasing order.
|
||||
</section>
|
||||
|
||||
|
||||
@ -9,7 +9,7 @@ challengeType: 5
|
||||
Using two Arrays of equal length, create a Hash object where the elements from one array (the keys) are linked to the elements of the other (the values).
|
||||
<b>Related task:</b>
|
||||
<ul>
|
||||
<li><a href="http://rosettacode.org/wiki/Associative arrays/Creation" title="Associative arrays/Creation" target="_blank">Associative arrays/Creation</a></li>
|
||||
<li><a href="https://rosettacode.org/wiki/Associative arrays/Creation" title="Associative arrays/Creation" target="_blank">Associative arrays/Creation</a></li>
|
||||
</ul>
|
||||
</section>
|
||||
|
||||
|
||||
@ -10,7 +10,7 @@ challengeType: 5
|
||||
<span style="margin-left: 2em;"><big>$A = \sqrt{s(s-a)(s-b)(s-c)},$</big></span>
|
||||
where <big>s</big> is half the perimeter of the triangle; that is,
|
||||
<span style="margin-left: 2em;"><big>$s=\frac{a+b+c}{2}.$</big></span>
|
||||
<a href="http://www.had2know.com/academics/heronian-triangles-generator-calculator.html" title="link: http://www.had2know.com/academics/heronian-triangles-generator-calculator.html" target="_blank">Heronian triangles</a> are triangles whose sides and area are all integers.
|
||||
<a href="https://www.had2know.com/academics/heronian-triangles-generator-calculator.html" target="_blank">Heronian triangles</a> are triangles whose sides and area are all integers.
|
||||
An example is the triangle with sides <b>3, 4, 5</b> whose area is <b>6</b> (and whose perimeter is <b>12</b>).
|
||||
Note that any triangle whose sides are all an integer multiple of <b>3, 4, 5</b>; such as <b>6, 8, 10,</b> will also be a Heronian triangle.
|
||||
Define a Primitive Heronian triangle as a Heronian triangle where the greatest common divisor
|
||||
|
||||
@ -22,10 +22,10 @@ No maximum value for <b>n</b> should be assumed.
|
||||
<b>References</b>
|
||||
<ul>
|
||||
<li>
|
||||
Sloane's <a href="http://oeis.org/A005228" title="link: http://oeis.org/A005228" target="_blank">A005228</a> and <a href="http://oeis.org/A030124" title="link: http://oeis.org/A030124" target="_blank">A030124</a>.
|
||||
Sloane's <a href="https://oeis.org/A005228" target="_blank">A005228</a> and <a href="https://oeis.org/A030124" target="_blank">A030124</a>.
|
||||
</li>
|
||||
<li>
|
||||
<a href="http://mathworld.wolfram.com/HofstadterFigure-FigureSequence.html" title="link: http://mathworld.wolfram.com/HofstadterFigure-FigureSequence.html" target="_blank">Wolfram MathWorld</a>
|
||||
<a href="https://mathworld.wolfram.com/HofstadterFigure-FigureSequence.html" target="_blank">Wolfram MathWorld</a>
|
||||
</li>
|
||||
<li>
|
||||
Wikipedia: <a href="https://en.wikipedia.org/wiki/Hofstadter_sequence#Hofstadter_Figure-Figure_sequences" title="wp: Hofstadter_sequence#Hofstadter_Figure-Figure_sequences" target="_blank">Hofstadter Figure-Figure sequences</a>.
|
||||
|
||||
@ -8,7 +8,7 @@ challengeType: 5
|
||||
<section id='description'>
|
||||
The <a href="https://en.wikipedia.org/wiki/Hofstadter_sequence#Hofstadter_Q_sequence" title="wp: Hofstadter_sequence#Hofstadter_Q_sequence" target="_blank">Hofstadter Q sequence</a> is defined as:
|
||||
<span style="left-margin: 2em;">$Q(1)=Q(2)=1, \\ Q(n)=Q\big(n-Q(n-1)\big)+Q\big(n-Q(n-2)), \quad n>2.$</span>
|
||||
It is defined like the <a href="http://rosettacode.org/wiki/Fibonacci sequence" title="Fibonacci sequence" target="_blank">Fibonacci sequence</a>, but whereas the next term in the Fibonacci sequence is the sum of the previous two terms, in the Q sequence the previous two terms tell you how far to go back in the Q sequence to find the two numbers to sum to make the next term of the sequence.
|
||||
It is defined like the <a href="https://rosettacode.org/wiki/Fibonacci sequence" title="Fibonacci sequence" target="_blank">Fibonacci sequence</a>, but whereas the next term in the Fibonacci sequence is the sum of the previous two terms, in the Q sequence the previous two terms tell you how far to go back in the Q sequence to find the two numbers to sum to make the next term of the sequence.
|
||||
</section>
|
||||
|
||||
## Instructions
|
||||
|
||||
@ -14,7 +14,7 @@ Otherwise, when k-d trees are used with high-dimensional data, most of the point
|
||||
|
||||
## Instructions
|
||||
<section id='instructions'>
|
||||
Write a function to perform a nearest neighbour search using k-d tree. The function takes two parameters: an array of k-dimensional points, and a single k-dimensional point whose nearest neighbour should be returned by the function. A k-dimensional point will be given as an array of k elements.
|
||||
Write a function to perform a nearest neighbor search using k-d tree. The function takes two parameters: an array of k-dimensional points, and a single k-dimensional point whose nearest neighbor should be returned by the function. A k-dimensional point will be given as an array of k elements.
|
||||
</section>
|
||||
|
||||
## Tests
|
||||
|
||||
@ -15,7 +15,7 @@ Note that a split resulting in a part consisting purely of 0s is not valid, as 0
|
||||
Kaprekar numbers:
|
||||
<ul>
|
||||
<li> <code>2223</code> is a Kaprekar number, as <code>2223 * 2223 = 4941729</code>, <code>4941729</code> may be split to <code>494</code> and <code>1729</code>, and <code>494 + 1729 = 2223</code></li>
|
||||
<li>The series of Kaprekar numbers is known as <a href="http://rosettacode.org/wiki/oeis:A006886">A006886</a>, and begins as <code>1, 9, 45, 55, ...</code></li>
|
||||
<li>The series of Kaprekar numbers is known as <a href="https://rosettacode.org/wiki/oeis:A006886">A006886</a>, and begins as <code>1, 9, 45, 55, ...</code></li>
|
||||
</ul>
|
||||
</section>
|
||||
|
||||
|
||||
@ -8,7 +8,7 @@ challengeType: 5
|
||||
<section id='description'>
|
||||
The least common multiple of 12 and 18 is 36, because 12 is a factor (12 × 3 = 36), and 18 is a factor (18 × 2 = 36), and there is no positive integer less than 36 that has both factors. As a special case, if either <i>m</i> or <i>n</i> is zero, then the least common multiple is zero.
|
||||
One way to calculate the least common multiple is to iterate all the multiples of <i>m</i>, until you find one that is also a multiple of <i>n</i>.
|
||||
If you already have <i>gcd</i> for <a href="http://rosettacode.org/wiki/greatest common divisor">greatest common divisor</a>, then this formula calculates <i>lcm</i>.
|
||||
If you already have <i>gcd</i> for <a href="https://rosettacode.org/wiki/greatest common divisor">greatest common divisor</a>, then this formula calculates <i>lcm</i>.
|
||||
\( \operatorname{lcm}(m, n) = \frac{|m \times n|}{\operatorname{gcd}(m, n)} \)
|
||||
</section>
|
||||
|
||||
|
||||
@ -19,8 +19,8 @@ Create a function that returns the minimum possible size of the initial pile of
|
||||
Of course the tale is told in a world where the collection of any amount of coconuts in a day and multiple divisions of the pile, etc. can occur in time fitting the story line, so as not to affect the mathematics.
|
||||
<b>C.f:</b>
|
||||
<ul>
|
||||
<li><a href="https://www.youtube.com/watch?v=U9qU20VmvaU" title="link: https://www.youtube.com/watch?v=U9qU20VmvaU" target="_blank"> Monkeys and Coconuts - Numberphile</a> (Video) Analytical solution.</li>
|
||||
<li><a href="http://oeis.org/A002021" title="link: http://oeis.org/A002021" target="_blank">A002021 Pile of coconuts problem</a> The On-Line Encyclopedia of Integer Sequences. (Although some of its references may use the alternate form of the tale).</li>
|
||||
<li><a href="https://www.youtube.com/watch?v=U9qU20VmvaU" target="_blank"> Monkeys and Coconuts - Numberphile</a> (Video) Analytical solution.</li>
|
||||
<li><a href="https://oeis.org/A002021" target="_blank">A002021 Pile of coconuts problem</a> The On-Line Encyclopedia of Integer Sequences. (Although some of its references may use the alternate form of the tale).</li>
|
||||
</ul>
|
||||
</section>
|
||||
|
||||
|
||||
@ -6,7 +6,7 @@ challengeType: 5
|
||||
|
||||
## Description
|
||||
<section id='description'>
|
||||
The cocktail shaker sort is an improvement on the <a href="http://rosettacode.org/wiki/Bubble Sort" target="_blank">Bubble Sort</a>. The improvement is basically that values "bubble" both directions through the array, because on each iteration the cocktail shaker sort bubble sorts once forwards and once backwards. Pseudocode for the algorithm (from <a href="https://en.wikipedia.org/wiki/Cocktail sort" target="_blank">wikipedia</a>):</p>
|
||||
The cocktail shaker sort is an improvement on the <a href="https://rosettacode.org/wiki/Bubble Sort" target="_blank">Bubble Sort</a>. The improvement is basically that values "bubble" both directions through the array, because on each iteration the cocktail shaker sort bubble sorts once forwards and once backwards. Pseudocode for the algorithm (from <a href="https://en.wikipedia.org/wiki/Cocktail sort" target="_blank">wikipedia</a>):</p>
|
||||
<pre>
|
||||
<b>function</b> <i>cocktailSort</i>( A : list of sortable items )
|
||||
<b>do</b>
|
||||
|
||||
@ -7,8 +7,8 @@ challengeType: 5
|
||||
## Description
|
||||
<section id='description'>
|
||||
Implement a <i>comb sort</i>.
|
||||
The <b>Comb Sort</b> is a variant of the <a href="http://rosettacode.org/wiki/Bubble Sort" target="_blank">Bubble Sort</a>.
|
||||
Like the <a href="http://rosettacode.org/wiki/Shell sort" target="_blank">Shell sort</a>, the Comb Sort increases the gap used in comparisons and exchanges.
|
||||
The <b>Comb Sort</b> is a variant of the <a href="https://rosettacode.org/wiki/Bubble Sort" target="_blank">Bubble Sort</a>.
|
||||
Like the <a href="https://rosettacode.org/wiki/Shell sort" target="_blank">Shell sort</a>, the Comb Sort increases the gap used in comparisons and exchanges.
|
||||
Dividing the gap by $(1-e^{-\varphi})^{-1} \approx 1.247330950103979$ works best, but 1.3 may be more practical.
|
||||
Some implementations use the insertion sort once the gap is less than a certain amount.
|
||||
<b>Also see</b>
|
||||
@ -32,9 +32,9 @@ Pseudocode:
|
||||
gap := 1
|
||||
<b>end if</b>
|
||||
i := 0
|
||||
swaps := 0 <i>//see <a href="http://rosettacode.org/wiki/Bubble Sort">Bubble Sort</a> for an explanation</i>
|
||||
swaps := 0 <i>//see <a href="https://rosettacode.org/wiki/Bubble Sort">Bubble Sort</a> for an explanation</i>
|
||||
<i>//a single "comb" over the input list</i>
|
||||
<b>loop until</b> i + gap >= input<b>.size</b> <i>//see <a href="http://rosettacode.org/wiki/Shell sort">Shell sort</a> for similar idea</i>
|
||||
<b>loop until</b> i + gap >= input<b>.size</b> <i>//see <a href="https://rosettacode.org/wiki/Shell sort">Shell sort</a> for similar idea</i>
|
||||
<b>if</b> input[i] > input[i+gap]
|
||||
<b>swap</b>(input[i], input[i+gap])
|
||||
swaps := 1 <i>// Flag a swap has occurred, so the</i>
|
||||
|
||||
@ -6,7 +6,7 @@ challengeType: 5
|
||||
|
||||
## Description
|
||||
<section id='description'>
|
||||
Gnome sort is a sorting algorithm which is similar to <a href="http://rosettacode.org/wiki/Insertion sort" target="_blank">Insertion sort</a>, except that moving an element to its proper place is accomplished by a series of swaps, as in <a href="http://rosettacode.org/wiki/Bubble Sort" target="_blank">Bubble Sort</a>.
|
||||
Gnome sort is a sorting algorithm which is similar to <a href="https://rosettacode.org/wiki/Insertion sort" target="_blank">Insertion sort</a>, except that moving an element to its proper place is accomplished by a series of swaps, as in <a href="https://rosettacode.org/wiki/Bubble Sort" target="_blank">Bubble Sort</a>.
|
||||
The pseudocode for the algorithm is:
|
||||
<pre>
|
||||
<b>function</b> <i>gnomeSort</i>(a[0..size-1])
|
||||
|
||||
@ -8,7 +8,7 @@ challengeType: 5
|
||||
<section id='description'>
|
||||
Soundex is an algorithm for creating indices for words based on their pronunciation.
|
||||
The goal is for homophones to be encoded to the same representation so that they can be matched despite minor differences in spelling (from <a href="https://en.wikipedia.org/wiki/soundex" target="_blank">the WP article</a>).
|
||||
There is a major issue in many of the implementations concerning the separation of two consonants that have the same soundex code! According to the official Rules <a href="http://rosettacode.org/wiki/https://www.archives.gov/research/census/soundex.html" target="_blank">https://www.archives.gov/research/census/soundex.html</a>. So check for instance if <b>Ashcraft</b> is coded to <b>A-261</b>.
|
||||
There is a major issue in many of the implementations concerning the separation of two consonants that have the same soundex code! According to the <a href="https://www.archives.gov/research/census/soundex.html" target="_blank">official Rules</a>. So check for instance if <b>Ashcraft</b> is coded to <b>A-261</b>.
|
||||
<ul>
|
||||
<li>If a vowel (A, E, I, O, U) separates two consonants that have the same soundex code, the consonant to the right of the vowel is coded. Tymczak is coded as T-522 (T, 5 for the M, 2 for the C, Z ignored (see "Side-by-Side" rule above), 2 for the K). Since the vowel "A" separates the Z and K, the K is coded.</li>
|
||||
<li>If "H" or "W" separate two consonants that have the same soundex code, the consonant to the right of the vowel is not coded. Example: Ashcraft is coded A-261 (A, 2 for the S, C ignored, 6 for the R, 1 for the F). It is not coded A-226.</li>
|
||||
|
||||
@ -6,7 +6,7 @@ challengeType: 5
|
||||
|
||||
## Description
|
||||
<section id='description'>
|
||||
This task is inspired by <a href="http://drdobbs.com/windows/198701685" target="_blank">Mark Nelson's DDJ Column "Wordplay"</a> and one of the weekly puzzle challenges from Will Shortz on NPR Weekend Edition <a href="http://www.npr.org/templates/story/story.php?storyId=9264290"target="_blank">[1]</a> and originally attributed to David Edelheit.
|
||||
This task is inspired by <a href="https://drdobbs.com/windows/198701685" target="_blank">Mark Nelson's DDJ Column "Wordplay"</a> and one of the weekly puzzle challenges from Will Shortz on NPR Weekend Edition <a href="https://www.npr.org/templates/story/story.php?storyId=9264290"target="_blank">[1]</a> and originally attributed to David Edelheit.
|
||||
The challenge was to take the names of two U.S. States, mix them all together, then rearrange the letters to form the names of two <i>different</i> U.S. States (so that all four state names differ from one another).
|
||||
What states are these?
|
||||
The problem was reissued on <a href="https://tapestry.tucson.az.us/twiki/bin/view/Main/StateNamesPuzzle" target="_blank">the Unicon Discussion Web</a> which includes several solutions with analysis. Several techniques may be helpful and you may wish to refer to <a href="https://en.wikipedia.org/wiki/Goedel_numbering">Gödel numbering</a>, <a href="https://en.wikipedia.org/wiki/Equivalence_relation" target="_blank">equivalence relations</a>, and <a href="https://en.wikipedia.org/wiki/Equivalence_classes" target="_blank">equivalence classes</a>. The basic merits of these were discussed in the Unicon Discussion Web.
|
||||
|
||||
@ -6,7 +6,7 @@ challengeType: 5
|
||||
|
||||
## Description
|
||||
<section id='description'>
|
||||
For this task, the Stern-Brocot sequence is to be generated by an algorithm similar to that employed in generating the <a href="http://rosettacode.org/wiki/Fibonacci sequence" target="_blank">Fibonacci sequence</a>.
|
||||
For this task, the Stern-Brocot sequence is to be generated by an algorithm similar to that employed in generating the <a href="https://rosettacode.org/wiki/Fibonacci sequence" target="_blank">Fibonacci sequence</a>.
|
||||
<ol>
|
||||
<li>The first and second members of the sequence are both 1:</li>
|
||||
<ul><li>1, 1</li></ul>
|
||||
|
||||
@ -6,7 +6,7 @@ challengeType: 5
|
||||
|
||||
## Description
|
||||
<section id='description'>
|
||||
<a href="http://rosettacode.org/wiki/eso:Subleq" target="_blank">Subleq</a> is an example of a <a href="https://en.wikipedia.org/wiki/One_instruction_set_computer" target="_blank">One-Instruction Set Computer (OISC)</a>.
|
||||
<a href="https://rosettacode.org/wiki/eso:Subleq" target="_blank">Subleq</a> is an example of a <a href="https://en.wikipedia.org/wiki/One_instruction_set_computer" target="_blank">One-Instruction Set Computer (OISC)</a>.
|
||||
It is named after its only instruction, which is <b>SU</b>btract and <b>B</b>ranch if <b>L</b>ess than or <b>EQ</b>ual
|
||||
to zero.
|
||||
Your task is to create an interpreter which emulates such a machine.
|
||||
|
||||
@ -6,7 +6,7 @@ challengeType: 5
|
||||
|
||||
## Description
|
||||
<section id='description'>
|
||||
Given two <a href="http://rosettacode.org/wiki/set" target="_blank">set</a>s <i>A</i> and <i>B</i>, compute $(A \setminus B) \cup (B \setminus A).$
|
||||
Given two <a href="https://rosettacode.org/wiki/set" target="_blank">set</a>s <i>A</i> and <i>B</i>, compute $(A \setminus B) \cup (B \setminus A).$
|
||||
That is, enumerate the items that are in <i>A</i> or <i>B</i> but not both. This set is called the <a href="https://en.wikipedia.org/wiki/Symmetric difference" target="_blank">symmetric difference</a> of <i>A</i> and <i>B</i>.
|
||||
In other words: $(A \cup B) \setminus (A \cap B)$ (the set of items that are in at least one of <i>A</i> or <i>B</i> minus the set of items that are in both <i>A</i> and <i>B</i>).
|
||||
</section>
|
||||
|
||||
@ -24,9 +24,9 @@ Taxicab numbers are also known as:
|
||||
Write a function that returns the lowest <code>n</code> taxicab numbers. For each of the taxicab numbers, show the number as well as its constituent cubes.
|
||||
<b>See also:</b>
|
||||
<ul>
|
||||
<li><a href="http://oeis.org/A001235" target="_blank">A001235 taxicab numbers</a> on The On-Line Encyclopedia of Integer Sequences.</li>
|
||||
<li><a href="http://mathworld.wolfram.com/Hardy-RamanujanNumber.html" target="_blank">Hardy-Ramanujan Number</a> on MathWorld.</li>
|
||||
<li><a href="http://mathworld.wolfram.com/TaxicabNumber.html" target="_blank">taxicab number</a> on MathWorld.</li>
|
||||
<li><a href="https://oeis.org/A001235" target="_blank">A001235 taxicab numbers</a> on The On-Line Encyclopedia of Integer Sequences.</li>
|
||||
<li><a href="https://mathworld.wolfram.com/Hardy-RamanujanNumber.html" target="_blank">Hardy-Ramanujan Number</a> on MathWorld.</li>
|
||||
<li><a href="https://mathworld.wolfram.com/TaxicabNumber.html" target="_blank">taxicab number</a> on MathWorld.</li>
|
||||
<li><a href="https://en.wikipedia.org/wiki/Taxicab_number" target="_blank">taxicab number</a> on Wikipedia.</li>
|
||||
</ul>
|
||||
</section>
|
||||
|
||||
@ -40,12 +40,12 @@ synopsys
|
||||
<small>Note: the above data would be un-orderable if, for example, <code>dw04</code> is added to the list of dependencies of <code>dw01</code>.</small>
|
||||
<b>C.f.:</b>
|
||||
<ul>
|
||||
<li><a href="http://rosettacode.org/wiki/Topological sort/Extracted top item" title="Topological sort/Extracted top item" target="_blank">Topological sort/Extracted top item</a>.</li>
|
||||
<li><a href="https://rosettacode.org/wiki/Topological sort/Extracted top item" title="Topological sort/Extracted top item" target="_blank">Topological sort/Extracted top item</a>.</li>
|
||||
</ul>
|
||||
There are two popular algorithms for topological sorting:
|
||||
<ul>
|
||||
<li><a href="https://en.wikipedia.org/wiki/Topological sorting" title="wp: Topological sorting" target="_blank">Kahn's 1962 topological sort</a></li>
|
||||
<li><a href="http://www.embeddedrelated.com/showarticle/799.php" title="link: http://www.embeddedrelated.com/showarticle/799.php" target="_blank">depth-first search</a></li>
|
||||
<li><a href="https://www.embeddedrelated.com/showarticle/799.php" target="_blank">depth-first search</a></li>
|
||||
</ul>
|
||||
</section>
|
||||
|
||||
|
||||
@ -7,7 +7,7 @@ challengeType: 5
|
||||
## Description
|
||||
<section id='description'>
|
||||
In strict <a href="https://en.wikipedia.org/wiki/Functional programming" title="wp: functional programming" target="_blank">functional programming</a> and the <a href="https://en.wikipedia.org/wiki/lambda calculus" title="wp: lambda calculus" target="_blank">lambda calculus</a>, functions (lambda expressions) don't have state and are only allowed to refer to arguments of enclosing functions. This rules out the usual definition of a recursive function wherein a function is associated with the state of a variable and this variable's state is used in the body of the function.
|
||||
The <a href="http://mvanier.livejournal.com/2897.html" target="_blank">Y combinator</a> is itself a stateless function that, when applied to another stateless function, returns a recursive version of the function. The Y combinator is the simplest of the class of such functions, called <a href="https://en.wikipedia.org/wiki/Fixed-point combinator" title="wp: fixed-point combinator" target="_blank">fixed-point combinators</a>.
|
||||
The <a href="https://mvanier.livejournal.com/2897.html" target="_blank">Y combinator</a> is itself a stateless function that, when applied to another stateless function, returns a recursive version of the function. The Y combinator is the simplest of the class of such functions, called <a href="https://en.wikipedia.org/wiki/Fixed-point combinator" title="wp: fixed-point combinator" target="_blank">fixed-point combinators</a>.
|
||||
</section>
|
||||
|
||||
## Instructions
|
||||
@ -15,7 +15,7 @@ The <a href="http://mvanier.livejournal.com/2897.html" target="_blank">Y combina
|
||||
Define the stateless Y combinator function and use it to compute <a href="https://en.wikipedia.org/wiki/Factorial" title="wp: factorial">factorial</a>. The <code>factorial(N)</code> function is already given to you.
|
||||
<b>See also:</b>
|
||||
<ul>
|
||||
<li><a href="http://vimeo.com/45140590" target="_blank">Jim Weirich: Adventures in Functional Programming</a>.</li>
|
||||
<li><a href="https://vimeo.com/45140590" target="_blank">Jim Weirich: Adventures in Functional Programming</a>.</li>
|
||||
</ul>
|
||||
</section>
|
||||
|
||||
|
||||
Reference in New Issue
Block a user