Pastable version of Pascal's Triangle

<div style="overflow:auto;border:solid 1px #ccc;background:#000;color:#F8F8F8">
          <div class="section">
            
            <pre style="float:left;margin:0 10px;border-right:0;color:#666;">1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57</pre>
            <pre class="sunburst"><span style="color:#65B042;"><span style="color:#65B042;">&quot;&quot;&quot;</span></span>
<span style="color:#65B042;">For a given number, prints Pascal's Triangle upside-down up to that line.</span>
<span style="color:#65B042;">Prints everything alligned at first, but starts screwing up at about 13.</span>
<span style="color:#65B042;"></span>
<span style="color:#65B042;">Some info:</span>
<span style="color:#65B042;">0. Takes advantage of the fact that the Triangle is symmetric.</span>
<span style="color:#65B042;">1. Uses the combinatorics property of the Triangle: </span>
<span style="color:#65B042;">	 For any NUMBER in position INDEX at row ROW:</span>
<span style="color:#65B042;">	 NUMBER = C(ROW, INDEX)</span>
<span style="color:#65B042;">2. A dictionary stores the values of the combinatorics already calculated,</span>
<span style="color:#65B042;">   so the comb function speeds up a little. Think of it as a recursive</span>
<span style="color:#65B042;">   function with a memory.</span>
<span style="color:#65B042;"></span>
<span style="color:#65B042;">Pablo A. Torres Navarrete</span>
<span style="color:#65B042;">tn.pablo@gmail.com</span>
<span style="color:#65B042;">03/09/07</span>
<span style="color:#65B042;"><span style="color:#65B042;">&quot;&quot;&quot;</span></span>

<span style="color:#AEAEAE;font-style:italic;"><span style="color:#AEAEAE;font-style:italic;">#</span>! /usr/bin/env python</span>

<span style="color:#E28964;">import</span> sys

<span style="color:#99CF50;">def</span> <span style="color:#89BDFF;">comb</span>(<span style="color:#3E87E3;">N</span>, <span style="color:#3E87E3;">n</span>, <span style="color:#3E87E3;">combs</span>):
	<span style="color:#65B042;"><span style="color:#65B042;">&quot;&quot;&quot;</span> </span>
<span style="color:#65B042;">	Returns the value of C(N,n). </span>
<span style="color:#65B042;">	First the function looks it up in a dictionary and only calculates</span>
<span style="color:#65B042;">	if it isn't present, in which case works recursively.</span>
<span style="color:#65B042;">	<span style="color:#65B042;">&quot;&quot;&quot;</span></span>
	<span style="color:#E28964;">try</span>:
		ans <span style="color:#E28964;">=</span> combs[(N,n)]
	<span style="color:#E28964;">except</span> <span style="color:#9B859D;">KeyError</span>:
		<span style="color:#E28964;">if</span> n <span style="color:#E28964;">==</span> <span style="color:#3387CC;">0</span>: ans<span style="color:#E28964;">=</span><span style="color:#3387CC;">1</span>
		<span style="color:#E28964;">elif</span> n <span style="color:#E28964;">==</span> <span style="color:#3387CC;">1</span>: ans<span style="color:#E28964;">=</span>N
		<span style="color:#E28964;">else</span>:
			<span style="color:#AEAEAE;font-style:italic;"><span style="color:#AEAEAE;font-style:italic;">#</span> A little maths...</span>
			ans <span style="color:#E28964;">=</span> (comb(N, n<span style="color:#E28964;">-</span><span style="color:#3387CC;">1</span>, combs) <span style="color:#E28964;">*</span> (N<span style="color:#E28964;">-</span>n<span style="color:#E28964;">+</span><span style="color:#3387CC;">1</span>) <span style="color:#E28964;">*</span> <span style="color:#3387CC;">1</span><span style="color:#E28964;">/</span>n)
			combs[(N,n)] <span style="color:#E28964;">=</span> ans
	<span style="color:#E28964;">return</span> ans

lines <span style="color:#E28964;">=</span> <span style="color:#9B859D;">int</span>(sys.argv[<span style="color:#3387CC;">1</span>])
<span style="color:#AEAEAE;font-style:italic;"><span style="color:#AEAEAE;font-style:italic;">#</span> stack that will contain the items of the row to be mirrored</span>
mirror <span style="color:#E28964;">=</span> []
<span style="color:#AEAEAE;font-style:italic;"><span style="color:#AEAEAE;font-style:italic;">#</span> dictionary of combinatoric-value pairs</span>
combs <span style="color:#E28964;">=</span> {}
<span style="color:#E28964;">for</span> row <span style="color:#E28964;">in</span> <span style="color:#DAD085;">range</span>(lines, <span style="color:#E28964;">-</span><span style="color:#3387CC;">1</span>, <span style="color:#E28964;">-</span><span style="color:#3387CC;">1</span>):
	<span style="color:#AEAEAE;font-style:italic;"><span style="color:#AEAEAE;font-style:italic;">#</span> insert indentation</span>
	<span style="color:#E28964;">print</span> <span style="color:#65B042;"><span style="color:#65B042;">'</span>    <span style="color:#65B042;">'</span></span> <span style="color:#E28964;">*</span> (lines <span style="color:#E28964;">-</span> row),
	<span style="color:#AEAEAE;font-style:italic;"><span style="color:#AEAEAE;font-style:italic;">#</span> first half of the row</span>
	limit <span style="color:#E28964;">=</span> (row<span style="color:#E28964;">/</span><span style="color:#E28964;">/</span><span style="color:#3387CC;">2</span>)<span style="color:#E28964;">+</span><span style="color:#3387CC;">1</span>
	<span style="color:#E28964;">for</span> index <span style="color:#E28964;">in</span> <span style="color:#DAD085;">range</span>(limit):
		num <span style="color:#E28964;">=</span> comb(row, index, combs)
		<span style="color:#E28964;">if</span> <span style="color:#E28964;">not</span>((row<span style="color:#E28964;">%</span><span style="color:#3387CC;">2</span> <span style="color:#E28964;">==</span> <span style="color:#3387CC;">0</span>) <span style="color:#E28964;">and</span> (index <span style="color:#E28964;">==</span> limit<span style="color:#E28964;">-</span><span style="color:#3387CC;">1</span>)): mirror.append(num)
		<span style="color:#E28964;">print</span> <span style="color:#65B042;"><span style="color:#65B042;">'</span><span style="color:#DDF2A4;">%i</span>      <span style="color:#65B042;">'</span></span> <span style="color:#E28964;">%</span> num,
	<span style="color:#AEAEAE;font-style:italic;"><span style="color:#AEAEAE;font-style:italic;">#</span> for the second half, mirror the first</span>
	<span style="color:#E28964;">while</span> mirror: <span style="color:#E28964;">print</span> <span style="color:#65B042;"><span style="color:#65B042;">'</span><span style="color:#DDF2A4;">%i</span>      <span style="color:#65B042;">'</span></span> <span style="color:#E28964;">%</span> mirror.pop(),
	<span style="color:#E28964;">print</span>
</pre>
          </div>
        </div>

<a href="http://refactormycode.com/codes/59-pascal-s-triangle" style="color:#fff" title="As seen on RefactorMyCode.com"><img alt="Small_logo" src="http://refactormycode.com/images/small_logo.gif" style="border:0" /></a>

counter free hit invisible