View source for Cycles of a permutation

=={{header|Phix}}==
{{trans|Wren}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
 <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
 <span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.2"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (tagstart)</span>
 <span style="color: #008080;">function</span> <span style="color: #000000;">smallest_first</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">cycle</span><span style="color: #0000FF;">)</span>
     <span style="color: #000080;font-style:italic;">-- Rearrange a cycle so the lowest element is first.</span>
     <span style="color: #004080;">integer</span> <span style="color: #000000;">mdx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">smallest</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cycle</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
     <span style="color: #008080;">return</span> <span style="color: #000000;">cycle</span><span style="color: #0000FF;">[</span><span style="color: #000000;">mdx</span><span style="color: #0000FF;">..$]</span> <span style="color: #0000FF;">&</span> <span style="color: #000000;">cycle</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">mdx</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
  
 <span style="color: #008080;">function</span> <span style="color: #000000;">one_line_to_string</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">one_line</span><span style="color: #0000FF;">)</span>
     <span style="color: #000080;font-style:italic;">-- Converts a list in one line notation to a space separated string.</span>
     <span style="color: #008080;">return</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">one_line</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">)</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
 <span style="color: #008080;">function</span> <span style="color: #000000;">cycles_to_string</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">cycles</span><span style="color: #0000FF;">)</span>
     <span style="color: #000080;font-style:italic;">-- Converts a list in cycle notation to a string where each cycle 
     -- is space separated and enclosed in parentheses.</span>
     <span style="color: #008080;">return</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">cycles</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">},{</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">},{</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">}}),</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"(%s)"</span><span style="color: #0000FF;">)</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
 <span style="color: #008080;">function</span> <span style="color: #000000;">one_line_notation</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
     <span style="color: #000080;font-style:italic;">-- Returns a list in one line notation derived from two strings s and t.</span>
     <span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
     <span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">)</span>
     <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
     <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">l</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
         <span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">i</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
         <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span>
     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
     <span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
  
 <span style="color: #008080;">function</span> <span style="color: #000000;">cycle_notation</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
     <span style="color: #000080;font-style:italic;">-- Returns a list in cycle notation derived from two strings s and t.</span>
     <span style="color: #004080;">sequence</span> <span style="color: #000000;">used</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #004600;">false</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)),</span>
            <span style="color: #000000;">cycles</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
     <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">used</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
         <span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">used</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
             <span style="color: #000000;">used</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
             <span style="color: #004080;">integer</span> <span style="color: #000000;">ix</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
             <span style="color: #008080;">if</span> <span style="color: #000000;">ix</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">i</span> <span style="color: #008080;">then</span>
                 <span style="color: #004080;">sequence</span> <span style="color: #000000;">cycle</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">}</span>
                 <span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
                    <span style="color: #000000;">cycle</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">ix</span>
                    <span style="color: #000000;">used</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ix</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
                    <span style="color: #000000;">ix</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ix</span><span style="color: #0000FF;">],</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
                    <span style="color: #008080;">if</span> <span style="color: #000000;">ix</span><span style="color: #0000FF;">=</span><span style="color: #000000;">i</span> <span style="color: #008080;">then</span>
                        <span style="color: #000000;">cycle</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">smallest_first</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cycle</span><span style="color: #0000FF;">)</span>
                        <span style="color: #000000;">cycles</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cycles</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cycle</span><span style="color: #0000FF;">)</span>
                        <span style="color: #008080;">exit</span>
                    <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
                 <span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
             <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
         <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
     <span style="color: #008080;">return</span> <span style="color: #000000;">cycles</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
  
 <span style="color: #008080;">function</span> <span style="color: #000000;">one_line_inverse</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">one_line</span><span style="color: #0000FF;">)</span>
     <span style="color: #000080;font-style:italic;">-- Converts a list in one line notation to its inverse.</span>
     <span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">one_line</span><span style="color: #0000FF;">)</span>
     <span style="color: #004080;">string</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">),</span> 
            <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagstart</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'A'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">)</span>
     <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
         <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">one_line</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]+</span><span style="color: #008000;">'A'</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span>
     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
     <span style="color: #008080;">return</span> <span style="color: #000000;">one_line_notation</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
 <span style="color: #008080;">function</span> <span style="color: #000000;">cycle_inverse</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">cycles</span><span style="color: #0000FF;">)</span>
     <span style="color: #000080;font-style:italic;">-- Converts a list of cycles to its inverse.</span>
     <span style="color: #004080;">sequence</span> <span style="color: #000000;">cycles2</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cycles</span><span style="color: #0000FF;">))</span>
     <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cycles</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
         <span style="color: #004080;">sequence</span> <span style="color: #000000;">cycle</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cycles</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
         <span style="color: #000000;">cycles2</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cycle</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">&</span> <span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cycle</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$])</span>
     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
     <span style="color: #008080;">return</span> <span style="color: #000000;">cycles2</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
  
 <span style="color: #008080;">function</span> <span style="color: #000000;">one_line_permute</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">perm</span><span style="color: #0000FF;">)</span>
     <span style="color: #000080;font-style:italic;">-- Permutes a string using perm in one line notation.</span>
     <span style="color: #004080;">string</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span>
     <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">perm</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">perm</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]]</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
     <span style="color: #008080;">return</span> <span style="color: #000000;">t</span>
 <span style="color: #000080;font-style:italic;">--alternative one-liner:
 --  return reinstate(s,tagset(length(perm)),extract(s,perm))</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
 <span style="color: #008080;">function</span> <span style="color: #000000;">cycle_permute</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">cycles</span><span style="color: #0000FF;">)</span>
     <span style="color: #000080;font-style:italic;">-- Permutes a string using perm in cycle notation.</span>
     <span style="color: #004080;">sequence</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span>
     <span style="color: #008080;">for</span> <span style="color: #000000;">cycle</span> <span style="color: #008080;">in</span> <span style="color: #000000;">cycles</span> <span style="color: #008080;">do</span>
         <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cycle</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
             <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">cycle</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">cycle</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]]</span>
         <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
         <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">cycle</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">cycle</span><span style="color: #0000FF;">[$]]</span>              
     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
     <span style="color: #008080;">return</span> <span style="color: #000000;">t</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
  
 <span style="color: #008080;">function</span> <span style="color: #000000;">cycle_combine</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">cycles1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cycles2</span><span style="color: #0000FF;">)</span>
     <span style="color: #000080;font-style:italic;">// Returns a single perm in cycle notation resulting 
     // from applying cycles1 first and then cycles2.</span>
     <span style="color: #004080;">integer</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">flatten</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cycles1</span><span style="color: #0000FF;">)),</span>
                     <span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">flatten</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cycles1</span><span style="color: #0000FF;">)))</span>
     <span style="color: #004080;">string</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagstart</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'A'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m</span><span style="color: #0000FF;">),</span>
            <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cycle_permute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cycles1</span><span style="color: #0000FF;">)</span>
     <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cycle_permute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cycles2</span><span style="color: #0000FF;">)</span>
     <span style="color: #008080;">return</span> <span style="color: #000000;">cycle_notation</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
  
 <span style="color: #008080;">function</span> <span style="color: #000000;">one_line_to_cycle</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">one_line</span><span style="color: #0000FF;">)</span>
     <span style="color: #000080;font-style:italic;">// Converts a list in one line notation to cycle notation.</span>
     <span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">one_line</span><span style="color: #0000FF;">)</span>
     <span style="color: #004080;">string</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagstart</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'A'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">),</span>
            <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">)</span>
     <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
         <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">one_line</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]+</span><span style="color: #008000;">'A'</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span>
     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
     <span style="color: #008080;">return</span> <span style="color: #000000;">cycle_notation</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
 <span style="color: #008080;">function</span> <span style="color: #000000;">cycle_to_one_line</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">cycles</span><span style="color: #0000FF;">)</span>
     <span style="color: #000080;font-style:italic;">-- Converts a list in cycle notation to one line notation.</span>
     <span style="color: #004080;">string</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagstart</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'A'</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">flatten</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cycles</span><span style="color: #0000FF;">))),</span>
            <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cycle_permute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cycles</span><span style="color: #0000FF;">)</span>
     <span style="color: #008080;">return</span> <span style="color: #000000;">one_line_notation</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
  
 <span style="color: #008080;">function</span> <span style="color: #000000;">cycle_order</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">cycles</span><span style="color: #0000FF;">)</span>
     <span style="color: #000080;font-style:italic;">-- Returns the order of a permutation.</span>
     <span style="color: #008080;">return</span> <span style="color: #7060A8;">lcm</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cycles</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">))</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
  
 <span style="color: #008080;">function</span> <span style="color: #000000;">cycle_signature</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">cycles</span><span style="color: #0000FF;">)</span>
     <span style="color: #000080;font-style:italic;">-- Returns the signature of a permutation.</span>
     <span style="color: #008080;">return</span> <span style="color: #7060A8;">even</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cycles</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">even</span><span style="color: #0000FF;">)))*</span><span style="color: #000000;">2</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
 <span style="color: #008080;">constant</span> <span style="color: #000000;">DAYS</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span>
                   <span style="color: #000000;">MON</span> <span style="color: #0000FF;">:=</span> <span style="color: #008000;">"HANDYCOILSERUPT"</span><span style="color: #0000FF;">,</span>
                   <span style="color: #000000;">TUE</span> <span style="color: #0000FF;">:=</span> <span style="color: #008000;">"SPOILUNDERYACHT"</span><span style="color: #0000FF;">,</span>
                   <span style="color: #000000;">WED</span> <span style="color: #0000FF;">:=</span> <span style="color: #008000;">"DRAINSTYLEPOUCH"</span><span style="color: #0000FF;">,</span>
                   <span style="color: #000000;">THU</span> <span style="color: #0000FF;">:=</span> <span style="color: #008000;">"DITCHSYRUPALONE"</span><span style="color: #0000FF;">,</span>
                   <span style="color: #000000;">FRI</span> <span style="color: #0000FF;">:=</span> <span style="color: #008000;">"SOAPYTHIRDUNCLE"</span><span style="color: #0000FF;">,</span>
                   <span style="color: #000000;">SAT</span> <span style="color: #0000FF;">:=</span> <span style="color: #008000;">"SHINEPARTYCLOUD"</span><span style="color: #0000FF;">,</span>
                   <span style="color: #000000;">SUN</span> <span style="color: #0000FF;">:=</span> <span style="color: #008000;">"RADIOLUNCHTYPES"</span>
                 <span style="color: #0000FF;">}</span>
  
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"On Thursdays Alf and Betty should rearrange their letters using these cycles:\n"</span><span style="color: #0000FF;">)</span>
 <span style="color: #004080;">sequence</span> <span style="color: #000000;">cycle_wt</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cycle_notation</span><span style="color: #0000FF;">(</span><span style="color: #000000;">WED</span><span style="color: #0000FF;">,</span><span style="color: #000000;">THU</span><span style="color: #0000FF;">)</span>
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">cycles_to_string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cycle_wt</span><span style="color: #0000FF;">)})</span>
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"So that %s becomes %s\n\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">WED</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cycle_permute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">WED</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cycle_wt</span><span style="color: #0000FF;">)})</span>
  
 <span style="color: #004080;">sequence</span> <span style="color: #000000;">one_line</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cycle_to_one_line</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cycle_wt</span><span style="color: #0000FF;">)</span>
 <span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #000000;">one_line_to_cycle</span><span style="color: #0000FF;">(</span><span style="color: #000000;">one_line</span><span style="color: #0000FF;">)==</span><span style="color: #000000;">cycle_wt</span><span style="color: #0000FF;">)</span>
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Or they could use the one line notation:\n%s\n\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">one_line_to_string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">one_line</span><span style="color: #0000FF;">)})</span>
  
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"To revert to the Wednesday arrangement they should use these cycles:\n"</span><span style="color: #0000FF;">)</span>
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s\n\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">cycles_to_string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cycle_inverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cycle_wt</span><span style="color: #0000FF;">))})</span>
 
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Or with the one line notation:\n"</span><span style="color: #0000FF;">)</span>
 <span style="color: #004080;">sequence</span> <span style="color: #000000;">one_line2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">one_line_inverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">one_line</span><span style="color: #0000FF;">)</span>
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">one_line_to_string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">one_line2</span><span style="color: #0000FF;">))</span>
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"So that %s becomes %s\n\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">THU</span><span style="color: #0000FF;">,</span><span style="color: #000000;">one_line_permute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">THU</span><span style="color: #0000FF;">,</span><span style="color: #000000;">one_line2</span><span style="color: #0000FF;">)})</span>
  
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Starting with the Sunday arrangement and applying each of the daily arrangements\n"</span><span style="color: #0000FF;">)</span>
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"consecutively, the arrangements will be:\n\n"</span><span style="color: #0000FF;">)</span>
  
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"     %s\n\n"</span><span style="color: #0000FF;">,{(</span><span style="color: #000000;">SUN</span><span style="color: #0000FF;">)})</span>
 <span style="color: #004080;">sequence</span> <span style="color: #000000;">signatures</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span> <span style="color: #000000;">orders</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
 <span style="color: #004080;">integer</span> <span style="color: #000000;">yesterday</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">DAYS</span><span style="color: #0000FF;">)</span>
 <span style="color: #008080;">for</span> <span style="color: #000000;">today</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">DAYS</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
     <span style="color: #004080;">string</span> <span style="color: #000000;">td</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">DAYS</span><span style="color: #0000FF;">[</span><span style="color: #000000;">today</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">yd</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">DAYS</span><span style="color: #0000FF;">[</span><span style="color: #000000;">yesterday</span><span style="color: #0000FF;">]</span>
     <span style="color: #004080;">sequence</span> <span style="color: #000000;">ol</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">one_line_notation</span><span style="color: #0000FF;">(</span><span style="color: #000000;">yd</span><span style="color: #0000FF;">,</span><span style="color: #000000;">td</span><span style="color: #0000FF;">),</span>
              <span style="color: #000000;">cy</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cycle_notation</span><span style="color: #0000FF;">(</span><span style="color: #000000;">yd</span><span style="color: #0000FF;">,</span><span style="color: #000000;">td</span><span style="color: #0000FF;">)</span>
     <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">td</span><span style="color: #0000FF;">,</span><span style="color: #000000;">one_line_permute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">yd</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ol</span><span style="color: #0000FF;">)})</span>
     <span style="color: #008080;">if</span> <span style="color: #000000;">today</span><span style="color: #0000FF;">>=</span><span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">SAT</span><span style="color: #0000FF;">,</span><span style="color: #000000;">DAYS</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
     <span style="color: #000000;">signatures</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">cycle_signature</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cy</span><span style="color: #0000FF;">)</span>
     <span style="color: #000000;">orders</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">cycle_order</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cy</span><span style="color: #0000FF;">)</span>
     <span style="color: #000000;">yesterday</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">today</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
 
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"To go from Wednesday to Friday in a single step they should use these cycles:\n"</span><span style="color: #0000FF;">)</span>
 <span style="color: #004080;">sequence</span> <span style="color: #000000;">cycles_tf</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cycle_notation</span><span style="color: #0000FF;">(</span><span style="color: #000000;">THU</span><span style="color: #0000FF;">,</span><span style="color: #000000;">FRI</span><span style="color: #0000FF;">),</span>
          <span style="color: #000000;">cycles_wf</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cycle_combine</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cycle_wt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cycles_tf</span><span style="color: #0000FF;">)</span>
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">cycles_to_string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cycles_wf</span><span style="color: #0000FF;">)})</span>
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"So that %s becomes %s\n\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">WED</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cycle_permute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">WED</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cycles_wf</span><span style="color: #0000FF;">)})</span>
  
 <span style="color: #008080;">constant</span> <span style="color: #000000;">FMT</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"""
 These are the %s of the permutations:
   Mon Tue Wed Thu Fri Sat Sun
   %s
 
 """</span>
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">FMT</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">"signatures"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">signatures</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%2d "</span><span style="color: #0000FF;">)})</span>
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">FMT</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">"orders"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">orders</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%3d"</span><span style="color: #0000FF;">)})</span>
 
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Applying the Friday cycle to a string 10 times:\n\n"</span><span style="color: #0000FF;">)</span>
 <span style="color: #004080;">string</span> <span style="color: #000000;">prev</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"STOREDAILYPUNCH"</span>
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"   %s\n\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">prev</span><span style="color: #0000FF;">})</span>
 <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</span>
     <span style="color: #000000;">prev</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cycle_permute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">prev</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cycles_tf</span><span style="color: #0000FF;">)</span>
     <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">prev</span><span style="color: #0000FF;">})</span>
     <span style="color: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">9</span> <span style="color: #008080;">then</span> <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</syntaxhighlight>-->
Output identical to Julia/Wren