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
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<!-- NewPage -->
<html lang="en">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>CombinatoricsUtils (Apache Commons Math 3.6.1 API)</title>
<link rel="stylesheet" type="text/css" href="../../../../../stylesheet.css" title="Style">
</head>
<body>
<script type="text/javascript"><!--
if (location.href.indexOf('is-external=true') == -1) {
parent.document.title="CombinatoricsUtils (Apache Commons Math 3.6.1 API)";
}
//-->
</script>
<noscript>
<div>JavaScript is disabled on your browser.</div>
</noscript>
<!-- ========= START OF TOP NAVBAR ======= -->
<div class="topNav"><a name="navbar_top">
<!-- -->
</a><a href="#skip-navbar_top" title="Skip navigation links"></a><a name="navbar_top_firstrow">
<!-- -->
</a>
<ul class="navList" title="Navigation">
<li><a href="../../../../../overview-summary.html">Overview</a></li>
<li><a href="package-summary.html">Package</a></li>
<li class="navBarCell1Rev">Class</li>
<li><a href="class-use/CombinatoricsUtils.html">Use</a></li>
<li><a href="package-tree.html">Tree</a></li>
<li><a href="../../../../../deprecated-list.html">Deprecated</a></li>
<li><a href="../../../../../index-all.html">Index</a></li>
<li><a href="../../../../../help-doc.html">Help</a></li>
</ul>
<div class="aboutLanguage"><em><script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script></em></div>
</div>
<div class="subNav">
<ul class="navList">
<li><a href="../../../../../org/apache/commons/math3/util/Combinations.html" title="class in org.apache.commons.math3.util"><span class="strong">Prev Class</span></a></li>
<li><a href="../../../../../org/apache/commons/math3/util/CompositeFormat.html" title="class in org.apache.commons.math3.util"><span class="strong">Next Class</span></a></li>
</ul>
<ul class="navList">
<li><a href="../../../../../index.html?org/apache/commons/math3/util/CombinatoricsUtils.html" target="_top">Frames</a></li>
<li><a href="CombinatoricsUtils.html" target="_top">No Frames</a></li>
</ul>
<ul class="navList" id="allclasses_navbar_top">
<li><a href="../../../../../allclasses-noframe.html">All Classes</a></li>
</ul>
<div>
<script type="text/javascript"><!--
allClassesLink = document.getElementById("allclasses_navbar_top");
if(window==top) {
allClassesLink.style.display = "block";
}
else {
allClassesLink.style.display = "none";
}
//-->
</script>
</div>
<div>
<ul class="subNavList">
<li>Summary: </li>
<li>Nested | </li>
<li>Field | </li>
<li>Constr | </li>
<li><a href="#method_summary">Method</a></li>
</ul>
<ul class="subNavList">
<li>Detail: </li>
<li>Field | </li>
<li>Constr | </li>
<li><a href="#method_detail">Method</a></li>
</ul>
</div>
<a name="skip-navbar_top">
<!-- -->
</a></div>
<!-- ========= END OF TOP NAVBAR ========= -->
<!-- ======== START OF CLASS DATA ======== -->
<div class="header">
<div class="subTitle">org.apache.commons.math3.util</div>
<h2 title="Class CombinatoricsUtils" class="title">Class CombinatoricsUtils</h2>
</div>
<div class="contentContainer">
<ul class="inheritance">
<li><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</a></li>
<li>
<ul class="inheritance">
<li>org.apache.commons.math3.util.CombinatoricsUtils</li>
</ul>
</li>
</ul>
<div class="description">
<ul class="blockList">
<li class="blockList">
<hr>
<br>
<pre>public final class <span class="strong">CombinatoricsUtils</span>
extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
<div class="block">Combinatorial utilities.</div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>3.3</dd></dl>
</li>
</ul>
</div>
<div class="summary">
<ul class="blockList">
<li class="blockList">
<!-- ========== METHOD SUMMARY =========== -->
<ul class="blockList">
<li class="blockList"><a name="method_summary">
<!-- -->
</a>
<h3>Method Summary</h3>
<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation">
<caption><span>Methods</span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static long</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/CombinatoricsUtils.html#binomialCoefficient(int,%20int)">binomialCoefficient</a></strong>(int n,
int k)</code>
<div class="block">Returns an exact representation of the <a
href="http://mathworld.wolfram.com/BinomialCoefficient.html"> Binomial
Coefficient</a>, "<code>n choose k</code>", the number of
<code>k</code>-element subsets that can be selected from an
<code>n</code>-element set.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/CombinatoricsUtils.html#binomialCoefficientDouble(int,%20int)">binomialCoefficientDouble</a></strong>(int n,
int k)</code>
<div class="block">Returns a <code>double</code> representation of the <a
href="http://mathworld.wolfram.com/BinomialCoefficient.html"> Binomial
Coefficient</a>, "<code>n choose k</code>", the number of
<code>k</code>-element subsets that can be selected from an
<code>n</code>-element set.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/CombinatoricsUtils.html#binomialCoefficientLog(int,%20int)">binomialCoefficientLog</a></strong>(int n,
int k)</code>
<div class="block">Returns the natural <code>log</code> of the <a
href="http://mathworld.wolfram.com/BinomialCoefficient.html"> Binomial
Coefficient</a>, "<code>n choose k</code>", the number of
<code>k</code>-element subsets that can be selected from an
<code>n</code>-element set.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/CombinatoricsUtils.html#checkBinomial(int,%20int)">checkBinomial</a></strong>(int n,
int k)</code>
<div class="block">Check binomial preconditions.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static <a href="http://docs.oracle.com/javase/7/docs/api/java/util/Iterator.html?is-external=true" title="class or interface in java.util">Iterator</a><int[]></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/CombinatoricsUtils.html#combinationsIterator(int,%20int)">combinationsIterator</a></strong>(int n,
int k)</code>
<div class="block">Returns an iterator whose range is the k-element subsets of {0, ..., n - 1}
represented as <code>int[]</code> arrays.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static long</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/CombinatoricsUtils.html#factorial(int)">factorial</a></strong>(int n)</code>
<div class="block">Returns n!.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/CombinatoricsUtils.html#factorialDouble(int)">factorialDouble</a></strong>(int n)</code>
<div class="block">Compute n!, the<a href="http://mathworld.wolfram.com/Factorial.html">
factorial</a> of <code>n</code> (the product of the numbers 1 to n), as a
<code>double</code>.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/CombinatoricsUtils.html#factorialLog(int)">factorialLog</a></strong>(int n)</code>
<div class="block">Compute the natural logarithm of the factorial of <code>n</code>.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static long</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/CombinatoricsUtils.html#stirlingS2(int,%20int)">stirlingS2</a></strong>(int n,
int k)</code>
<div class="block">Returns the <a
href="http://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html">
Stirling number of the second kind</a>, "<code>S(n,k)</code>", the number of
ways of partitioning an <code>n</code>-element set into <code>k</code> non-empty
subsets.</div>
</td>
</tr>
</table>
<ul class="blockList">
<li class="blockList"><a name="methods_inherited_from_class_java.lang.Object">
<!-- -->
</a>
<h3>Methods inherited from class java.lang.<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3>
<code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long,%20int)" title="class or interface in java.lang">wait</a></code></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
<div class="details">
<ul class="blockList">
<li class="blockList">
<!-- ============ METHOD DETAIL ========== -->
<ul class="blockList">
<li class="blockList"><a name="method_detail">
<!-- -->
</a>
<h3>Method Detail</h3>
<a name="binomialCoefficient(int, int)">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>binomialCoefficient</h4>
<pre>public static long binomialCoefficient(int n,
int k)
throws <a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a>,
<a href="../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a>,
<a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></pre>
<div class="block">Returns an exact representation of the <a
href="http://mathworld.wolfram.com/BinomialCoefficient.html"> Binomial
Coefficient</a>, "<code>n choose k</code>", the number of
<code>k</code>-element subsets that can be selected from an
<code>n</code>-element set.
<p>
<Strong>Preconditions</strong>:
<ul>
<li> <code>0 <= k <= n </code> (otherwise
<code>MathIllegalArgumentException</code> is thrown)</li>
<li> The result is small enough to fit into a <code>long</code>. The
largest value of <code>n</code> for which all coefficients are
<code>< Long.MAX_VALUE</code> is 66. If the computed value exceeds
<code>Long.MAX_VALUE</code> a <code>MathArithMeticException</code> is
thrown.</li>
</ul></p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>n</code> - the size of the set</dd><dd><code>k</code> - the size of the subsets to be counted</dd>
<dt><span class="strong">Returns:</span></dt><dd><code>n choose k</code></dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if <code>n < 0</code>.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a></code> - if <code>k > n</code>.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></code> - if the result is too large to be
represented by a long integer.</dd></dl>
</li>
</ul>
<a name="binomialCoefficientDouble(int, int)">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>binomialCoefficientDouble</h4>
<pre>public static double binomialCoefficientDouble(int n,
int k)
throws <a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a>,
<a href="../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a>,
<a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></pre>
<div class="block">Returns a <code>double</code> representation of the <a
href="http://mathworld.wolfram.com/BinomialCoefficient.html"> Binomial
Coefficient</a>, "<code>n choose k</code>", the number of
<code>k</code>-element subsets that can be selected from an
<code>n</code>-element set.
<p>
<Strong>Preconditions</strong>:
<ul>
<li> <code>0 <= k <= n </code> (otherwise
<code>IllegalArgumentException</code> is thrown)</li>
<li> The result is small enough to fit into a <code>double</code>. The
largest value of <code>n</code> for which all coefficients are less than
Double.MAX_VALUE is 1029. If the computed value exceeds Double.MAX_VALUE,
Double.POSITIVE_INFINITY is returned</li>
</ul></p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>n</code> - the size of the set</dd><dd><code>k</code> - the size of the subsets to be counted</dd>
<dt><span class="strong">Returns:</span></dt><dd><code>n choose k</code></dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if <code>n < 0</code>.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a></code> - if <code>k > n</code>.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></code> - if the result is too large to be
represented by a long integer.</dd></dl>
</li>
</ul>
<a name="binomialCoefficientLog(int, int)">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>binomialCoefficientLog</h4>
<pre>public static double binomialCoefficientLog(int n,
int k)
throws <a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a>,
<a href="../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a>,
<a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></pre>
<div class="block">Returns the natural <code>log</code> of the <a
href="http://mathworld.wolfram.com/BinomialCoefficient.html"> Binomial
Coefficient</a>, "<code>n choose k</code>", the number of
<code>k</code>-element subsets that can be selected from an
<code>n</code>-element set.
<p>
<Strong>Preconditions</strong>:
<ul>
<li> <code>0 <= k <= n </code> (otherwise
<code>MathIllegalArgumentException</code> is thrown)</li>
</ul></p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>n</code> - the size of the set</dd><dd><code>k</code> - the size of the subsets to be counted</dd>
<dt><span class="strong">Returns:</span></dt><dd><code>n choose k</code></dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if <code>n < 0</code>.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a></code> - if <code>k > n</code>.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></code> - if the result is too large to be
represented by a long integer.</dd></dl>
</li>
</ul>
<a name="factorial(int)">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>factorial</h4>
<pre>public static long factorial(int n)
throws <a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a>,
<a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></pre>
<div class="block">Returns n!. Shorthand for <code>n</code> <a
href="http://mathworld.wolfram.com/Factorial.html"> Factorial</a>, the
product of the numbers <code>1,...,n</code>.
<p>
<Strong>Preconditions</strong>:
<ul>
<li> <code>n >= 0</code> (otherwise
<code>MathIllegalArgumentException</code> is thrown)</li>
<li> The result is small enough to fit into a <code>long</code>. The
largest value of <code>n</code> for which <code>n!</code> does not exceed
Long.MAX_VALUE} is 20. If the computed value exceeds <code>Long.MAX_VALUE</code>
an <code>MathArithMeticException </code> is thrown.</li>
</ul>
</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>n</code> - argument</dd>
<dt><span class="strong">Returns:</span></dt><dd><code>n!</code></dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></code> - if the result is too large to be represented
by a <code>long</code>.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if <code>n < 0</code>.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></code> - if <code>n > 20</code>: The factorial value is too
large to fit in a <code>long</code>.</dd></dl>
</li>
</ul>
<a name="factorialDouble(int)">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>factorialDouble</h4>
<pre>public static double factorialDouble(int n)
throws <a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></pre>
<div class="block">Compute n!, the<a href="http://mathworld.wolfram.com/Factorial.html">
factorial</a> of <code>n</code> (the product of the numbers 1 to n), as a
<code>double</code>.
The result should be small enough to fit into a <code>double</code>: The
largest <code>n</code> for which <code>n!</code> does not exceed
<code>Double.MAX_VALUE</code> is 170. If the computed value exceeds
<code>Double.MAX_VALUE</code>, <code>Double.POSITIVE_INFINITY</code> is returned.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>n</code> - Argument.</dd>
<dt><span class="strong">Returns:</span></dt><dd><code>n!</code></dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if <code>n < 0</code>.</dd></dl>
</li>
</ul>
<a name="factorialLog(int)">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>factorialLog</h4>
<pre>public static double factorialLog(int n)
throws <a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></pre>
<div class="block">Compute the natural logarithm of the factorial of <code>n</code>.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>n</code> - Argument.</dd>
<dt><span class="strong">Returns:</span></dt><dd><code>n!</code></dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if <code>n < 0</code>.</dd></dl>
</li>
</ul>
<a name="stirlingS2(int, int)">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>stirlingS2</h4>
<pre>public static long stirlingS2(int n,
int k)
throws <a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a>,
<a href="../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a>,
<a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></pre>
<div class="block">Returns the <a
href="http://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html">
Stirling number of the second kind</a>, "<code>S(n,k)</code>", the number of
ways of partitioning an <code>n</code>-element set into <code>k</code> non-empty
subsets.
<p>
The preconditions are <code>0 <= k <= n </code> (otherwise
<code>NotPositiveException</code> is thrown)
</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>n</code> - the size of the set</dd><dd><code>k</code> - the number of non-empty subsets</dd>
<dt><span class="strong">Returns:</span></dt><dd><code>S(n,k)</code></dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if <code>k < 0</code>.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a></code> - if <code>k > n</code>.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></code> - if some overflow happens, typically for n exceeding 25 and
k between 20 and n-2 (S(n,n-1) is handled specifically and does not overflow)</dd><dt><span class="strong">Since:</span></dt>
<dd>3.1</dd></dl>
</li>
</ul>
<a name="combinationsIterator(int, int)">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>combinationsIterator</h4>
<pre>public static <a href="http://docs.oracle.com/javase/7/docs/api/java/util/Iterator.html?is-external=true" title="class or interface in java.util">Iterator</a><int[]> combinationsIterator(int n,
int k)</pre>
<div class="block">Returns an iterator whose range is the k-element subsets of {0, ..., n - 1}
represented as <code>int[]</code> arrays.
<p>
The arrays returned by the iterator are sorted in descending order and
they are visited in lexicographic order with significance from right to
left. For example, combinationsIterator(4, 2) returns an Iterator that
will generate the following sequence of arrays on successive calls to
<code>next()</code>:</p><p>
<code>[0, 1], [0, 2], [1, 2], [0, 3], [1, 3], [2, 3]</code>
</p><p>
If <code>k == 0</code> an Iterator containing an empty array is returned and
if <code>k == n</code> an Iterator containing [0, ..., n -1] is returned.</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>n</code> - Size of the set from which subsets are selected.</dd><dd><code>k</code> - Size of the subsets to be enumerated.</dd>
<dt><span class="strong">Returns:</span></dt><dd>an <a href="http://docs.oracle.com/javase/7/docs/api/java/util/Iterator.html?is-external=true" title="class or interface in java.util"><code>iterator</code></a> over the k-sets in n.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if <code>n < 0</code>.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a></code> - if <code>k > n</code>.</dd></dl>
</li>
</ul>
<a name="checkBinomial(int, int)">
<!-- -->
</a>
<ul class="blockListLast">
<li class="blockList">
<h4>checkBinomial</h4>
<pre>public static void checkBinomial(int n,
int k)
throws <a href="../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a>,
<a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></pre>
<div class="block">Check binomial preconditions.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>n</code> - Size of the set.</dd><dd><code>k</code> - Size of the subsets to be counted.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if <code>n < 0</code>.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a></code> - if <code>k > n</code>.</dd></dl>
</li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
</div>
<!-- ========= END OF CLASS DATA ========= -->
<!-- ======= START OF BOTTOM NAVBAR ====== -->
<div class="bottomNav"><a name="navbar_bottom">
<!-- -->
</a><a href="#skip-navbar_bottom" title="Skip navigation links"></a><a name="navbar_bottom_firstrow">
<!-- -->
</a>
<ul class="navList" title="Navigation">
<li><a href="../../../../../overview-summary.html">Overview</a></li>
<li><a href="package-summary.html">Package</a></li>
<li class="navBarCell1Rev">Class</li>
<li><a href="class-use/CombinatoricsUtils.html">Use</a></li>
<li><a href="package-tree.html">Tree</a></li>
<li><a href="../../../../../deprecated-list.html">Deprecated</a></li>
<li><a href="../../../../../index-all.html">Index</a></li>
<li><a href="../../../../../help-doc.html">Help</a></li>
</ul>
<div class="aboutLanguage"><em><script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script></em></div>
</div>
<div class="subNav">
<ul class="navList">
<li><a href="../../../../../org/apache/commons/math3/util/Combinations.html" title="class in org.apache.commons.math3.util"><span class="strong">Prev Class</span></a></li>
<li><a href="../../../../../org/apache/commons/math3/util/CompositeFormat.html" title="class in org.apache.commons.math3.util"><span class="strong">Next Class</span></a></li>
</ul>
<ul class="navList">
<li><a href="../../../../../index.html?org/apache/commons/math3/util/CombinatoricsUtils.html" target="_top">Frames</a></li>
<li><a href="CombinatoricsUtils.html" target="_top">No Frames</a></li>
</ul>
<ul class="navList" id="allclasses_navbar_bottom">
<li><a href="../../../../../allclasses-noframe.html">All Classes</a></li>
</ul>
<div>
<script type="text/javascript"><!--
allClassesLink = document.getElementById("allclasses_navbar_bottom");
if(window==top) {
allClassesLink.style.display = "block";
}
else {
allClassesLink.style.display = "none";
}
//-->
</script>
</div>
<div>
<ul class="subNavList">
<li>Summary: </li>
<li>Nested | </li>
<li>Field | </li>
<li>Constr | </li>
<li><a href="#method_summary">Method</a></li>
</ul>
<ul class="subNavList">
<li>Detail: </li>
<li>Field | </li>
<li>Constr | </li>
<li><a href="#method_detail">Method</a></li>
</ul>
</div>
<a name="skip-navbar_bottom">
<!-- -->
</a></div>
<!-- ======== END OF BOTTOM NAVBAR ======= -->
<p class="legalCopy"><small>Copyright © 2003–2016 <a href="http://www.apache.org/">The Apache Software Foundation</a>. All rights reserved.</small></p>
</body>
</html>
|
