Data update
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Ingy döt Net
parent
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157b70a810
604 changed files with 14253 additions and 2100 deletions
5
Task/Pascals-triangle/Haskell/pascals-triangle-10.hs
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5
Task/Pascals-triangle/Haskell/pascals-triangle-10.hs
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@ -0,0 +1,5 @@
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fac = product . enumFromTo 1
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binCoef n k = fac n `div` (fac k * fac (n - k))
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pascal = ((fmap . binCoef) <*> enumFromTo 0) . pred
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11
Task/Pascals-triangle/Haskell/pascals-triangle-11.hs
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Task/Pascals-triangle/Haskell/pascals-triangle-11.hs
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@ -0,0 +1,11 @@
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*Main> putStr $ unlines $ map unwords $ map (map show) $ pascal 10
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1
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1 1
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1 2 1
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1 3 3 1
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1 4 6 4 1
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1 5 10 10 5 1
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1 6 15 20 15 6 1
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1 7 21 35 35 21 7 1
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1 8 28 56 70 56 28 8 1
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1 9 36 84 126 126 84 36 9 1
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@ -1,4 +1 @@
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pascal :: [[Integer]]
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pascal =
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(1 : [ 0 | _ <- head pascal])
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: [zipWith (+) (0:row) row | row <- pascal]
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nextRow = (zipWith (+) . (0 :)) <*> (<> [0])
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@ -1,2 +1 @@
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*Pascal> take 5 <$> (take 5 $ triangle)
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[[1,0,0,0,0],[1,1,0,0,0],[1,2,1,0,0],[1,3,3,1,0],[1,4,6,4,1]]
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nextRow = (zipWith (+) <*> reverse) . (0 :)
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@ -1,5 +1,4 @@
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fac = product . enumFromTo 1
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binCoef n k = fac n `div` (fac k * fac (n - k))
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pascal = ((fmap . binCoef) <*> enumFromTo 0) . pred
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pascal :: [[Integer]]
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pascal =
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(1 : [ 0 | _ <- head pascal])
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: [zipWith (+) (0:row) row | row <- pascal]
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@ -1,11 +1,2 @@
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*Main> putStr $ unlines $ map unwords $ map (map show) $ pascal 10
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1
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1 1
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1 2 1
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1 3 3 1
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1 4 6 4 1
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1 5 10 10 5 1
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1 6 15 20 15 6 1
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1 7 21 35 35 21 7 1
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1 8 28 56 70 56 28 8 1
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1 9 36 84 126 126 84 36 9 1
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*Pascal> take 5 <$> (take 5 $ triangle)
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[[1,0,0,0,0],[1,1,0,0,0],[1,2,1,0,0],[1,3,3,1,0],[1,4,6,4,1]]
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@ -1,14 +1,75 @@
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(phixonline)-->
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">row</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">13</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">row</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">row</span> <span style="color: #0000FF;">&</span> <span style="color: #000000;">1</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">row</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">2</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">row</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">row</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">row</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rows</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
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<span style="color: #008080;">function</span> <span style="color: #000000;">check</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">string</span> <span style="color: #000000;">name</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- helper routine</span>
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<span style="color: #004080;">string</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">row</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>
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<span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">rows</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: #008080;">then</span>
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<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: goes wrong on line %d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">name</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>
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<span style="color: #008080;">return</span> <span style="color: #004600;">false</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">return</span> <span style="color: #004600;">true</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">sum_prior</span><span style="color: #0000FF;">()</span> <span style="color: #000080;font-style:italic;">-- First method</span>
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<span style="color: #000000;">row</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span> <span style="color: #000080;font-style:italic;">-- (using just one row)</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">119</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">row</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">1</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">row</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">2</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">row</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">row</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">check</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"sum_prior"</span><span style="color: #0000FF;">)</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>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<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: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,(</span><span style="color: #000000;">13</span><span style="color: #0000FF;">-</span><span style="color: #000000;">m</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">2</span><span style="color: #0000FF;">))</span>
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<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;">row</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
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<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;">" %3d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">row</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">algebraic</span><span style="color: #0000FF;">()</span> <span style="color: #000080;font-style:italic;">-- Second method</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">119</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
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<span style="color: #000000;">row</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
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<span style="color: #000080;font-style:italic;">-- c *= (i-j)/(j+1) -- NO: precedence differs, and eg 5*(1/5) inexact</span>
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<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">j</span><span style="color: #0000FF;">)/(</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- ..whereas (5*1)/5 is exact</span>
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<span style="color: #000000;">row</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">c</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">check</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"algebraic"</span><span style="color: #0000FF;">)</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>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #7060A8;">puts</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>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
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<span style="color: #000080;font-style:italic;">-- Aside: error with c was self-evident and more relevant when it was an integer,
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--- but I made it an atom to get past the 33/63 limits that imposed.</span>
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">builtin</span><span style="color: #0000FF;">()</span> <span style="color: #000080;font-style:italic;">-- Third method</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">119</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">row</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">i</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">row</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">choose</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">j</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">check</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"builtin"</span><span style="color: #0000FF;">)</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>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
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<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">arbitrary_precision</span><span style="color: #0000FF;">()</span> <span style="color: #000080;font-style:italic;">-- Fourth method, but run first
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-- perfectly accurate until you
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-- run out of memory or patience.</span>
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<span style="color: #004080;">mpz</span> <span style="color: #000000;">z</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">119</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">row</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">i</span> <span style="color: #008080;">do</span>
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<span style="color: #7060A8;">mpz_bin_uiui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">j</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">row</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">row</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">))</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #004080;">string</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">row</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">19</span> <span style="color: #008080;">then</span>
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<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;">"%=96s\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #000080;font-style:italic;">-- to check the others against:</span>
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<span style="color: #000000;">rows</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rows</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<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>
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
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<span style="color: #000000;">arbitrary_precision</span><span style="color: #0000FF;">()</span>
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<span style="color: #000000;">sum_prior</span><span style="color: #0000FF;">()</span>
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<span style="color: #000000;">algebraic</span><span style="color: #0000FF;">()</span>
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<span style="color: #000000;">builtin</span><span style="color: #0000FF;">()</span>
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<!--
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16
Task/Pascals-triangle/V-(Vlang)/pascals-triangle.v
Normal file
16
Task/Pascals-triangle/V-(Vlang)/pascals-triangle.v
Normal file
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@ -0,0 +1,16 @@
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fn main() {rows(5)}
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fn rows(height int) [][]int {
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mut ret := [][]int{}
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mut cnum := 0
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for level := 1; level <= height; level++ {
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ret << []int{}
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cnum = 1
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for i := 1; i <= level; i++ {
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ret[level - 1] << cnum
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cnum = (cnum * (level - i)) / i
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}
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println(ret[level - 1])
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}
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return ret
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}
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