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25 
26 /**
27  * Classes to support functional-style operations on streams of elements, such
28  * as map-reduce transformations on collections.  For example:
29  *
30  * <pre>{@code
31  *     int sum = widgets.stream()
32  *                      .filter(b -> b.getColor() == RED)
33  *                      .mapToInt(b -> b.getWeight())
34  *                      .sum();
35  * }</pre>
36  *
37  * <p>Here we use {@code widgets}, a {@code Collection<Widget>},
38  * as a source for a stream, and then perform a filter-map-reduce on the stream
39  * to obtain the sum of the weights of the red widgets.  (Summation is an
40  * example of a <a href="package-summary.html#Reduction">reduction</a>
41  * operation.)
42  *
43  * <p>The key abstraction introduced in this package is <em>stream</em>.  The
44  * classes {@link java.util.stream.Stream}, {@link java.util.stream.IntStream},
45  * {@link java.util.stream.LongStream}, and {@link java.util.stream.DoubleStream}
46  * are streams over objects and the primitive {@code int}, {@code long} and
47  * {@code double} types.  Streams differ from collections in several ways:
48  *
49  * <ul>
50  *     <li>No storage.  A stream is not a data structure that stores elements;
51  *     instead, it conveys elements from a source such as a data structure,
52  *     an array, a generator function, or an I/O channel, through a pipeline of
53  *     computational operations.</li>
54  *     <li>Functional in nature.  An operation on a stream produces a result,
55  *     but does not modify its source.  For example, filtering a {@code Stream}
56  *     obtained from a collection produces a new {@code Stream} without the
57  *     filtered elements, rather than removing elements from the source
58  *     collection.</li>
59  *     <li>Laziness-seeking.  Many stream operations, such as filtering, mapping,
60  *     or duplicate removal, can be implemented lazily, exposing opportunities
61  *     for optimization.  For example, "find the first {@code String} with
62  *     three consecutive vowels" need not examine all the input strings.
63  *     Stream operations are divided into intermediate ({@code Stream}-producing)
64  *     operations and terminal (value- or side-effect-producing) operations.
65  *     Intermediate operations are always lazy.</li>
66  *     <li>Possibly unbounded.  While collections have a finite size, streams
67  *     need not.  Short-circuiting operations such as {@code limit(n)} or
68  *     {@code findFirst()} can allow computations on infinite streams to
69  *     complete in finite time.</li>
70  *     <li>Consumable. The elements of a stream are only visited once during
71  *     the life of a stream. Like an {@link java.util.Iterator}, a new stream
72  *     must be generated to revisit the same elements of the source.
73  *     </li>
74  * </ul>
75  *
76  * Streams can be obtained in a number of ways. Some examples include:
77  * <ul>
78  *     <li>From a {@link java.util.Collection} via the {@code stream()} and
79  *     {@code parallelStream()} methods;</li>
80  *     <li>From an array via {@link java.util.Arrays#stream(Object[])};</li>
81  *     <li>From static factory methods on the stream classes, such as
82  *     {@link java.util.stream.Stream#of(Object[])},
83  *     {@link java.util.stream.IntStream#range(int, int)}
84  *     or {@link java.util.stream.Stream#iterate(Object, UnaryOperator)};</li>
85  *     <li>The lines of a file can be obtained from {@link java.io.BufferedReader#lines()};</li>
86  *     <li>Streams of file paths can be obtained from methods in {@link java.nio.file.Files};</li>
87  *     <li>Streams of random numbers can be obtained from {@link java.util.Random#ints()};</li>
88  *     <li>Numerous other stream-bearing methods in the JDK, including
89  *     {@link java.util.BitSet#stream()},
90  *     {@link java.util.regex.Pattern#splitAsStream(java.lang.CharSequence)},
91  *     and {@link java.util.jar.JarFile#stream()}.</li>
92  * </ul>
93  *
94  * <p>Additional stream sources can be provided by third-party libraries using
95  * <a href="package-summary.html#StreamSources">these techniques</a>.
96  *
97  * <h2><a name="StreamOps">Stream operations and pipelines</a></h2>
98  *
99  * <p>Stream operations are divided into <em>intermediate</em> and
100  * <em>terminal</em> operations, and are combined to form <em>stream
101  * pipelines</em>.  A stream pipeline consists of a source (such as a
102  * {@code Collection}, an array, a generator function, or an I/O channel);
103  * followed by zero or more intermediate operations such as
104  * {@code Stream.filter} or {@code Stream.map}; and a terminal operation such
105  * as {@code Stream.forEach} or {@code Stream.reduce}.
106  *
107  * <p>Intermediate operations return a new stream.  They are always
108  * <em>lazy</em>; executing an intermediate operation such as
109  * {@code filter()} does not actually perform any filtering, but instead
110  * creates a new stream that, when traversed, contains the elements of
111  * the initial stream that match the given predicate.  Traversal
112  * of the pipeline source does not begin until the terminal operation of the
113  * pipeline is executed.
114  *
115  * <p>Terminal operations, such as {@code Stream.forEach} or
116  * {@code IntStream.sum}, may traverse the stream to produce a result or a
117  * side-effect. After the terminal operation is performed, the stream pipeline
118  * is considered consumed, and can no longer be used; if you need to traverse
119  * the same data source again, you must return to the data source to get a new
120  * stream.  In almost all cases, terminal operations are <em>eager</em>,
121  * completing their traversal of the data source and processing of the pipeline
122  * before returning.  Only the terminal operations {@code iterator()} and
123  * {@code spliterator()} are not; these are provided as an "escape hatch" to enable
124  * arbitrary client-controlled pipeline traversals in the event that the
125  * existing operations are not sufficient to the task.
126  *
127  * <p> Processing streams lazily allows for significant efficiencies; in a
128  * pipeline such as the filter-map-sum example above, filtering, mapping, and
129  * summing can be fused into a single pass on the data, with minimal
130  * intermediate state. Laziness also allows avoiding examining all the data
131  * when it is not necessary; for operations such as "find the first string
132  * longer than 1000 characters", it is only necessary to examine just enough
133  * strings to find one that has the desired characteristics without examining
134  * all of the strings available from the source. (This behavior becomes even
135  * more important when the input stream is infinite and not merely large.)
136  *
137  * <p>Intermediate operations are further divided into <em>stateless</em>
138  * and <em>stateful</em> operations. Stateless operations, such as {@code filter}
139  * and {@code map}, retain no state from previously seen element when processing
140  * a new element -- each element can be processed
141  * independently of operations on other elements.  Stateful operations, such as
142  * {@code distinct} and {@code sorted}, may incorporate state from previously
143  * seen elements when processing new elements.
144  *
145  * <p>Stateful operations may need to process the entire input
146  * before producing a result.  For example, one cannot produce any results from
147  * sorting a stream until one has seen all elements of the stream.  As a result,
148  * under parallel computation, some pipelines containing stateful intermediate
149  * operations may require multiple passes on the data or may need to buffer
150  * significant data.  Pipelines containing exclusively stateless intermediate
151  * operations can be processed in a single pass, whether sequential or parallel,
152  * with minimal data buffering.
153  *
154  * <p>Further, some operations are deemed <em>short-circuiting</em> operations.
155  * An intermediate operation is short-circuiting if, when presented with
156  * infinite input, it may produce a finite stream as a result.  A terminal
157  * operation is short-circuiting if, when presented with infinite input, it may
158  * terminate in finite time.  Having a short-circuiting operation in the pipeline
159  * is a necessary, but not sufficient, condition for the processing of an infinite
160  * stream to terminate normally in finite time.
161  *
162  * <h3>Parallelism</h3>
163  *
164  * <p>Processing elements with an explicit {@code for-}loop is inherently serial.
165  * Streams facilitate parallel execution by reframing the computation as a pipeline of
166  * aggregate operations, rather than as imperative operations on each individual
167  * element.  All streams operations can execute either in serial or in parallel.
168  * The stream implementations in the JDK create serial streams unless parallelism is
169  * explicitly requested.  For example, {@code Collection} has methods
170  * {@link java.util.Collection#stream} and {@link java.util.Collection#parallelStream},
171  * which produce sequential and parallel streams respectively; other
172  * stream-bearing methods such as {@link java.util.stream.IntStream#range(int, int)}
173  * produce sequential streams but these streams can be efficiently parallelized by
174  * invoking their {@link java.util.stream.BaseStream#parallel()} method.
175  * To execute the prior "sum of weights of widgets" query in parallel, we would
176  * do:
177  *
178  * <pre>{@code
179  *     int sumOfWeights = widgets.}<code><b>parallelStream()</b></code>{@code
180  *                               .filter(b -> b.getColor() == RED)
181  *                               .mapToInt(b -> b.getWeight())
182  *                               .sum();
183  * }</pre>
184  *
185  * <p>The only difference between the serial and parallel versions of this
186  * example is the creation of the initial stream, using "{@code parallelStream()}"
187  * instead of "{@code stream()}".  When the terminal operation is initiated,
188  * the stream pipeline is executed sequentially or in parallel depending on the
189  * orientation of the stream on which it is invoked.  Whether a stream will execute in serial or
190  * parallel can be determined with the {@code isParallel()} method, and the
191  * orientation of a stream can be modified with the
192  * {@link java.util.stream.BaseStream#sequential()} and
193  * {@link java.util.stream.BaseStream#parallel()} operations.  When the terminal
194  * operation is initiated, the stream pipeline is executed sequentially or in
195  * parallel depending on the mode of the stream on which it is invoked.
196  *
197  * <p>Except for operations identified as explicitly nondeterministic, such
198  * as {@code findAny()}, whether a stream executes sequentially or in parallel
199  * should not change the result of the computation.
200  *
201  * <p>Most stream operations accept parameters that describe user-specified
202  * behavior, which are often lambda expressions.  To preserve correct behavior,
203  * these <em>behavioral parameters</em> must be <em>non-interfering</em>, and in
204  * most cases must be <em>stateless</em>.  Such parameters are always instances
205  * of a <a href="../function/package-summary.html">functional interface</a> such
206  * as {@link java.util.function.Function}, and are often lambda expressions or
207  * method references.
208  *
209  * <h3><a name="NonInterference">Non-interference</a></h3>
210  *
211  * Streams enable you to execute possibly-parallel aggregate operations over a
212  * variety of data sources, including even non-thread-safe collections such as
213  * {@code ArrayList}. This is possible only if we can prevent
214  * <em>interference</em> with the data source during the execution of a stream
215  * pipeline.  Except for the escape-hatch operations {@code iterator()} and
216  * {@code spliterator()}, execution begins when the terminal operation is
217  * invoked, and ends when the terminal operation completes.  For most data
218  * sources, preventing interference means ensuring that the data source is
219  * <em>not modified at all</em> during the execution of the stream pipeline.
220  * The notable exception to this are streams whose sources are concurrent
221  * collections, which are specifically designed to handle concurrent modification.
222  * Concurrent stream sources are those whose {@code Spliterator} reports the
223  * {@code CONCURRENT} characteristic.
224  *
225  * <p>Accordingly, behavioral parameters in stream pipelines whose source might
226  * not be concurrent should never modify the stream's data source.
227  * A behavioral parameter is said to <em>interfere</em> with a non-concurrent
228  * data source if it modifies, or causes to be
229  * modified, the stream's data source.  The need for non-interference applies
230  * to all pipelines, not just parallel ones.  Unless the stream source is
231  * concurrent, modifying a stream's data source during execution of a stream
232  * pipeline can cause exceptions, incorrect answers, or nonconformant behavior.
233  *
234  * For well-behaved stream sources, the source can be modified before the
235  * terminal operation commences and those modifications will be reflected in
236  * the covered elements.  For example, consider the following code:
237  *
238  * <pre>{@code
239  *     List<String> l = new ArrayList(Arrays.asList("one", "two"));
240  *     Stream<String> sl = l.stream();
241  *     l.add("three");
242  *     String s = sl.collect(joining(" "));
243  * }</pre>
244  *
245  * First a list is created consisting of two strings: "one"; and "two". Then a
246  * stream is created from that list. Next the list is modified by adding a third
247  * string: "three". Finally the elements of the stream are collected and joined
248  * together. Since the list was modified before the terminal {@code collect}
249  * operation commenced the result will be a string of "one two three". All the
250  * streams returned from JDK collections, and most other JDK classes,
251  * are well-behaved in this manner; for streams generated by other libraries, see
252  * <a href="package-summary.html#StreamSources">Low-level stream
253  * construction</a> for requirements for building well-behaved streams.
254  *
255  * <h3><a name="Statelessness">Stateless behaviors</a></h3>
256  *
257  * Stream pipeline results may be nondeterministic or incorrect if the behavioral
258  * parameters to the stream operations are <em>stateful</em>.  A stateful lambda
259  * (or other object implementing the appropriate functional interface) is one
260  * whose result depends on any state which might change during the execution
261  * of the stream pipeline.  An example of a stateful lambda is the parameter
262  * to {@code map()} in:
263  *
264  * <pre>{@code
265  *     Set<Integer> seen = Collections.synchronizedSet(new HashSet<>());
266  *     stream.parallel().map(e -> { if (seen.add(e)) return 0; else return e; })...
267  * }</pre>
268  *
269  * Here, if the mapping operation is performed in parallel, the results for the
270  * same input could vary from run to run, due to thread scheduling differences,
271  * whereas, with a stateless lambda expression the results would always be the
272  * same.
273  *
274  * <p>Note also that attempting to access mutable state from behavioral parameters
275  * presents you with a bad choice with respect to safety and performance; if
276  * you do not synchronize access to that state, you have a data race and
277  * therefore your code is broken, but if you do synchronize access to that
278  * state, you risk having contention undermine the parallelism you are seeking
279  * to benefit from.  The best approach is to avoid stateful behavioral
280  * parameters to stream operations entirely; there is usually a way to
281  * restructure the stream pipeline to avoid statefulness.
282  *
283  * <h3>Side-effects</h3>
284  *
285  * Side-effects in behavioral parameters to stream operations are, in general,
286  * discouraged, as they can often lead to unwitting violations of the
287  * statelessness requirement, as well as other thread-safety hazards.
288  *
289  * <p>If the behavioral parameters do have side-effects, unless explicitly
290  * stated, there are no guarantees as to the
291  * <a href="../concurrent/package-summary.html#MemoryVisibility"><i>visibility</i></a>
292  * of those side-effects to other threads, nor are there any guarantees that
293  * different operations on the "same" element within the same stream pipeline
294  * are executed in the same thread.  Further, the ordering of those effects
295  * may be surprising.  Even when a pipeline is constrained to produce a
296  * <em>result</em> that is consistent with the encounter order of the stream
297  * source (for example, {@code IntStream.range(0,5).parallel().map(x -> x*2).toArray()}
298  * must produce {@code [0, 2, 4, 6, 8]}), no guarantees are made as to the order
299  * in which the mapper function is applied to individual elements, or in what
300  * thread any behavioral parameter is executed for a given element.
301  *
302  * <p>Many computations where one might be tempted to use side effects can be more
303  * safely and efficiently expressed without side-effects, such as using
304  * <a href="package-summary.html#Reduction">reduction</a> instead of mutable
305  * accumulators. However, side-effects such as using {@code println()} for debugging
306  * purposes are usually harmless.  A small number of stream operations, such as
307  * {@code forEach()} and {@code peek()}, can operate only via side-effects;
308  * these should be used with care.
309  *
310  * <p>As an example of how to transform a stream pipeline that inappropriately
311  * uses side-effects to one that does not, the following code searches a stream
312  * of strings for those matching a given regular expression, and puts the
313  * matches in a list.
314  *
315  * <pre>{@code
316  *     ArrayList<String> results = new ArrayList<>();
317  *     stream.filter(s -> pattern.matcher(s).matches())
318  *           .forEach(s -> results.add(s));  // Unnecessary use of side-effects!
319  * }</pre>
320  *
321  * This code unnecessarily uses side-effects.  If executed in parallel, the
322  * non-thread-safety of {@code ArrayList} would cause incorrect results, and
323  * adding needed synchronization would cause contention, undermining the
324  * benefit of parallelism.  Furthermore, using side-effects here is completely
325  * unnecessary; the {@code forEach()} can simply be replaced with a reduction
326  * operation that is safer, more efficient, and more amenable to
327  * parallelization:
328  *
329  * <pre>{@code
330  *     List<String>results =
331  *         stream.filter(s -> pattern.matcher(s).matches())
332  *               .collect(Collectors.toList());  // No side-effects!
333  * }</pre>
334  *
335  * <h3><a name="Ordering">Ordering</a></h3>
336  *
337  * <p>Streams may or may not have a defined <em>encounter order</em>.  Whether
338  * or not a stream has an encounter order depends on the source and the
339  * intermediate operations.  Certain stream sources (such as {@code List} or
340  * arrays) are intrinsically ordered, whereas others (such as {@code HashSet})
341  * are not.  Some intermediate operations, such as {@code sorted()}, may impose
342  * an encounter order on an otherwise unordered stream, and others may render an
343  * ordered stream unordered, such as {@link java.util.stream.BaseStream#unordered()}.
344  * Further, some terminal operations may ignore encounter order, such as
345  * {@code forEach()}.
346  *
347  * <p>If a stream is ordered, most operations are constrained to operate on the
348  * elements in their encounter order; if the source of a stream is a {@code List}
349  * containing {@code [1, 2, 3]}, then the result of executing {@code map(x -> x*2)}
350  * must be {@code [2, 4, 6]}.  However, if the source has no defined encounter
351  * order, then any permutation of the values {@code [2, 4, 6]} would be a valid
352  * result.
353  *
354  * <p>For sequential streams, the presence or absence of an encounter order does
355  * not affect performance, only determinism.  If a stream is ordered, repeated
356  * execution of identical stream pipelines on an identical source will produce
357  * an identical result; if it is not ordered, repeated execution might produce
358  * different results.
359  *
360  * <p>For parallel streams, relaxing the ordering constraint can sometimes enable
361  * more efficient execution.  Certain aggregate operations,
362  * such as filtering duplicates ({@code distinct()}) or grouped reductions
363  * ({@code Collectors.groupingBy()}) can be implemented more efficiently if ordering of elements
364  * is not relevant.  Similarly, operations that are intrinsically tied to encounter order,
365  * such as {@code limit()}, may require
366  * buffering to ensure proper ordering, undermining the benefit of parallelism.
367  * In cases where the stream has an encounter order, but the user does not
368  * particularly <em>care</em> about that encounter order, explicitly de-ordering
369  * the stream with {@link java.util.stream.BaseStream#unordered() unordered()} may
370  * improve parallel performance for some stateful or terminal operations.
371  * However, most stream pipelines, such as the "sum of weight of blocks" example
372  * above, still parallelize efficiently even under ordering constraints.
373  *
374  * <h2><a name="Reduction">Reduction operations</a></h2>
375  *
376  * A <em>reduction</em> operation (also called a <em>fold</em>) takes a sequence
377  * of input elements and combines them into a single summary result by repeated
378  * application of a combining operation, such as finding the sum or maximum of
379  * a set of numbers, or accumulating elements into a list.  The streams classes have
380  * multiple forms of general reduction operations, called
381  * {@link java.util.stream.Stream#reduce(java.util.function.BinaryOperator) reduce()}
382  * and {@link java.util.stream.Stream#collect(java.util.stream.Collector) collect()},
383  * as well as multiple specialized reduction forms such as
384  * {@link java.util.stream.IntStream#sum() sum()}, {@link java.util.stream.IntStream#max() max()},
385  * or {@link java.util.stream.IntStream#count() count()}.
386  *
387  * <p>Of course, such operations can be readily implemented as simple sequential
388  * loops, as in:
389  * <pre>{@code
390  *    int sum = 0;
391  *    for (int x : numbers) {
392  *       sum += x;
393  *    }
394  * }</pre>
395  * However, there are good reasons to prefer a reduce operation
396  * over a mutative accumulation such as the above.  Not only is a reduction
397  * "more abstract" -- it operates on the stream as a whole rather than individual
398  * elements -- but a properly constructed reduce operation is inherently
399  * parallelizable, so long as the function(s) used to process the elements
400  * are <a href="package-summary.html#Associativity">associative</a> and
401  * <a href="package-summary.html#NonInterfering">stateless</a>.
402  * For example, given a stream of numbers for which we want to find the sum, we
403  * can write:
404  * <pre>{@code
405  *    int sum = numbers.stream().reduce(0, (x,y) -> x+y);
406  * }</pre>
407  * or:
408  * <pre>{@code
409  *    int sum = numbers.stream().reduce(0, Integer::sum);
410  * }</pre>
411  *
412  * <p>These reduction operations can run safely in parallel with almost no
413  * modification:
414  * <pre>{@code
415  *    int sum = numbers.parallelStream().reduce(0, Integer::sum);
416  * }</pre>
417  *
418  * <p>Reduction parallellizes well because the implementation
419  * can operate on subsets of the data in parallel, and then combine the
420  * intermediate results to get the final correct answer.  (Even if the language
421  * had a "parallel for-each" construct, the mutative accumulation approach would
422  * still required the developer to provide
423  * thread-safe updates to the shared accumulating variable {@code sum}, and
424  * the required synchronization would then likely eliminate any performance gain from
425  * parallelism.)  Using {@code reduce()} instead removes all of the
426  * burden of parallelizing the reduction operation, and the library can provide
427  * an efficient parallel implementation with no additional synchronization
428  * required.
429  *
430  * <p>The "widgets" examples shown earlier shows how reduction combines with
431  * other operations to replace for loops with bulk operations.  If {@code widgets}
432  * is a collection of {@code Widget} objects, which have a {@code getWeight} method,
433  * we can find the heaviest widget with:
434  * <pre>{@code
435  *     OptionalInt heaviest = widgets.parallelStream()
436  *                                   .mapToInt(Widget::getWeight)
437  *                                   .max();
438  * }</pre>
439  *
440  * <p>In its more general form, a {@code reduce} operation on elements of type
441  * {@code <T>} yielding a result of type {@code <U>} requires three parameters:
442  * <pre>{@code
443  * <U> U reduce(U identity,
444  *              BiFunction<U, ? super T, U> accumulator,
445  *              BinaryOperator<U> combiner);
446  * }</pre>
447  * Here, the <em>identity</em> element is both an initial seed value for the reduction
448  * and a default result if there are no input elements. The <em>accumulator</em>
449  * function takes a partial result and the next element, and produces a new
450  * partial result. The <em>combiner</em> function combines two partial results
451  * to produce a new partial result.  (The combiner is necessary in parallel
452  * reductions, where the input is partitioned, a partial accumulation computed
453  * for each partition, and then the partial results are combined to produce a
454  * final result.)
455  *
456  * <p>More formally, the {@code identity} value must be an <em>identity</em> for
457  * the combiner function. This means that for all {@code u},
458  * {@code combiner.apply(identity, u)} is equal to {@code u}. Additionally, the
459  * {@code combiner} function must be <a href="package-summary.html#Associativity">associative</a> and
460  * must be compatible with the {@code accumulator} function: for all {@code u}
461  * and {@code t}, {@code combiner.apply(u, accumulator.apply(identity, t))} must
462  * be {@code equals()} to {@code accumulator.apply(u, t)}.
463  *
464  * <p>The three-argument form is a generalization of the two-argument form,
465  * incorporating a mapping step into the accumulation step.  We could
466  * re-cast the simple sum-of-weights example using the more general form as
467  * follows:
468  * <pre>{@code
469  *     int sumOfWeights = widgets.stream()
470  *                               .reduce(0,
471  *                                       (sum, b) -> sum + b.getWeight())
472  *                                       Integer::sum);
473  * }</pre>
474  * though the explicit map-reduce form is more readable and therefore should
475  * usually be preferred. The generalized form is provided for cases where
476  * significant work can be optimized away by combining mapping and reducing
477  * into a single function.
478  *
479  * <h3><a name="MutableReduction">Mutable reduction</a></h3>
480  *
481  * A <em>mutable reduction operation</em> accumulates input elements into a
482  * mutable result container, such as a {@code Collection} or {@code StringBuilder},
483  * as it processes the elements in the stream.
484  *
485  * <p>If we wanted to take a stream of strings and concatenate them into a
486  * single long string, we <em>could</em> achieve this with ordinary reduction:
487  * <pre>{@code
488  *     String concatenated = strings.reduce("", String::concat)
489  * }</pre>
490  *
491  * <p>We would get the desired result, and it would even work in parallel.  However,
492  * we might not be happy about the performance!  Such an implementation would do
493  * a great deal of string copying, and the run time would be <em>O(n^2)</em> in
494  * the number of characters.  A more performant approach would be to accumulate
495  * the results into a {@link java.lang.StringBuilder}, which is a mutable
496  * container for accumulating strings.  We can use the same technique to
497  * parallelize mutable reduction as we do with ordinary reduction.
498  *
499  * <p>The mutable reduction operation is called
500  * {@link java.util.stream.Stream#collect(Collector) collect()},
501  * as it collects together the desired results into a result container such
502  * as a {@code Collection}.
503  * A {@code collect} operation requires three functions:
504  * a supplier function to construct new instances of the result container, an
505  * accumulator function to incorporate an input element into a result
506  * container, and a combining function to merge the contents of one result
507  * container into another.  The form of this is very similar to the general
508  * form of ordinary reduction:
509  * <pre>{@code
510  * <R> R collect(Supplier<R> supplier,
511  *               BiConsumer<R, ? super T> accumulator,
512  *               BiConsumer<R, R> combiner);
513  * }</pre>
514  * <p>As with {@code reduce()}, a benefit of expressing {@code collect} in this
515  * abstract way is that it is directly amenable to parallelization: we can
516  * accumulate partial results in parallel and then combine them, so long as the
517  * accumulation and combining functions satisfy the appropriate requirements.
518  * For example, to collect the String representations of the elements in a
519  * stream into an {@code ArrayList}, we could write the obvious sequential
520  * for-each form:
521  * <pre>{@code
522  *     ArrayList<String> strings = new ArrayList<>();
523  *     for (T element : stream) {
524  *         strings.add(element.toString());
525  *     }
526  * }</pre>
527  * Or we could use a parallelizable collect form:
528  * <pre>{@code
529  *     ArrayList<String> strings = stream.collect(() -> new ArrayList<>(),
530  *                                                (c, e) -> c.add(e.toString()),
531  *                                                (c1, c2) -> c1.addAll(c2));
532  * }</pre>
533  * or, pulling the mapping operation out of the accumulator function, we could
534  * express it more succinctly as:
535  * <pre>{@code
536  *     List<String> strings = stream.map(Object::toString)
537  *                                  .collect(ArrayList::new, ArrayList::add, ArrayList::addAll);
538  * }</pre>
539  * Here, our supplier is just the {@link java.util.ArrayList#ArrayList()
540  * ArrayList constructor}, the accumulator adds the stringified element to an
541  * {@code ArrayList}, and the combiner simply uses {@link java.util.ArrayList#addAll addAll}
542  * to copy the strings from one container into the other.
543  *
544  * <p>The three aspects of {@code collect} -- supplier, accumulator, and
545  * combiner -- are tightly coupled.  We can use the abstraction of a
546  * {@link java.util.stream.Collector} to capture all three aspects.  The
547  * above example for collecting strings into a {@code List} can be rewritten
548  * using a standard {@code Collector} as:
549  * <pre>{@code
550  *     List<String> strings = stream.map(Object::toString)
551  *                                  .collect(Collectors.toList());
552  * }</pre>
553  *
554  * <p>Packaging mutable reductions into a Collector has another advantage:
555  * composability.  The class {@link java.util.stream.Collectors} contains a
556  * number of predefined factories for collectors, including combinators
557  * that transform one collector into another.  For example, suppose we have a
558  * collector that computes the sum of the salaries of a stream of
559  * employees, as follows:
560  *
561  * <pre>{@code
562  *     Collector<Employee, ?, Integer> summingSalaries
563  *         = Collectors.summingInt(Employee::getSalary);
564  * }</pre>
565  *
566  * (The {@code ?} for the second type parameter merely indicates that we don't
567  * care about the intermediate representation used by this collector.)
568  * If we wanted to create a collector to tabulate the sum of salaries by
569  * department, we could reuse {@code summingSalaries} using
570  * {@link java.util.stream.Collectors#groupingBy(java.util.function.Function, java.util.stream.Collector) groupingBy}:
571  *
572  * <pre>{@code
573  *     Map<Department, Integer> salariesByDept
574  *         = employees.stream().collect(Collectors.groupingBy(Employee::getDepartment,
575  *                                                            summingSalaries));
576  * }</pre>
577  *
578  * <p>As with the regular reduction operation, {@code collect()} operations can
579  * only be parallelized if appropriate conditions are met.  For any partially
580  * accumulated result, combining it with an empty result container must
581  * produce an equivalent result.  That is, for a partially accumulated result
582  * {@code p} that is the result of any series of accumulator and combiner
583  * invocations, {@code p} must be equivalent to
584  * {@code combiner.apply(p, supplier.get())}.
585  *
586  * <p>Further, however the computation is split, it must produce an equivalent
587  * result.  For any input elements {@code t1} and {@code t2}, the results
588  * {@code r1} and {@code r2} in the computation below must be equivalent:
589  * <pre>{@code
590  *     A a1 = supplier.get();
591  *     accumulator.accept(a1, t1);
592  *     accumulator.accept(a1, t2);
593  *     R r1 = finisher.apply(a1);  // result without splitting
594  *
595  *     A a2 = supplier.get();
596  *     accumulator.accept(a2, t1);
597  *     A a3 = supplier.get();
598  *     accumulator.accept(a3, t2);
599  *     R r2 = finisher.apply(combiner.apply(a2, a3));  // result with splitting
600  * }</pre>
601  *
602  * <p>Here, equivalence generally means according to {@link java.lang.Object#equals(Object)}.
603  * but in some cases equivalence may be relaxed to account for differences in
604  * order.
605  *
606  * <h3><a name="ConcurrentReduction">Reduction, concurrency, and ordering</a></h3>
607  *
608  * With some complex reduction operations, for example a {@code collect()} that
609  * produces a {@code Map}, such as:
610  * <pre>{@code
611  *     Map<Buyer, List<Transaction>> salesByBuyer
612  *         = txns.parallelStream()
613  *               .collect(Collectors.groupingBy(Transaction::getBuyer));
614  * }</pre>
615  * it may actually be counterproductive to perform the operation in parallel.
616  * This is because the combining step (merging one {@code Map} into another by
617  * key) can be expensive for some {@code Map} implementations.
618  *
619  * <p>Suppose, however, that the result container used in this reduction
620  * was a concurrently modifiable collection -- such as a
621  * {@link java.util.concurrent.ConcurrentHashMap}. In that case, the parallel
622  * invocations of the accumulator could actually deposit their results
623  * concurrently into the same shared result container, eliminating the need for
624  * the combiner to merge distinct result containers. This potentially provides
625  * a boost to the parallel execution performance. We call this a
626  * <em>concurrent</em> reduction.
627  *
628  * <p>A {@link java.util.stream.Collector} that supports concurrent reduction is
629  * marked with the {@link java.util.stream.Collector.Characteristics#CONCURRENT}
630  * characteristic.  However, a concurrent collection also has a downside.  If
631  * multiple threads are depositing results concurrently into a shared container,
632  * the order in which results are deposited is non-deterministic. Consequently,
633  * a concurrent reduction is only possible if ordering is not important for the
634  * stream being processed. The {@link java.util.stream.Stream#collect(Collector)}
635  * implementation will only perform a concurrent reduction if
636  * <ul>
637  * <li>The stream is parallel;</li>
638  * <li>The collector has the
639  * {@link java.util.stream.Collector.Characteristics#CONCURRENT} characteristic,
640  * and;</li>
641  * <li>Either the stream is unordered, or the collector has the
642  * {@link java.util.stream.Collector.Characteristics#UNORDERED} characteristic.
643  * </ul>
644  * You can ensure the stream is unordered by using the
645  * {@link java.util.stream.BaseStream#unordered()} method.  For example:
646  * <pre>{@code
647  *     Map<Buyer, List<Transaction>> salesByBuyer
648  *         = txns.parallelStream()
649  *               .unordered()
650  *               .collect(groupingByConcurrent(Transaction::getBuyer));
651  * }</pre>
652  * (where {@link java.util.stream.Collectors#groupingByConcurrent} is the
653  * concurrent equivalent of {@code groupingBy}).
654  *
655  * <p>Note that if it is important that the elements for a given key appear in
656  * the order they appear in the source, then we cannot use a concurrent
657  * reduction, as ordering is one of the casualties of concurrent insertion.
658  * We would then be constrained to implement either a sequential reduction or
659  * a merge-based parallel reduction.
660  *
661  * <h3><a name="Associativity">Associativity</a></h3>
662  *
663  * An operator or function {@code op} is <em>associative</em> if the following
664  * holds:
665  * <pre>{@code
666  *     (a op b) op c == a op (b op c)
667  * }</pre>
668  * The importance of this to parallel evaluation can be seen if we expand this
669  * to four terms:
670  * <pre>{@code
671  *     a op b op c op d == (a op b) op (c op d)
672  * }</pre>
673  * So we can evaluate {@code (a op b)} in parallel with {@code (c op d)}, and
674  * then invoke {@code op} on the results.
675  *
676  * <p>Examples of associative operations include numeric addition, min, and
677  * max, and string concatenation.
678  *
679  * <h2><a name="StreamSources">Low-level stream construction</a></h2>
680  *
681  * So far, all the stream examples have used methods like
682  * {@link java.util.Collection#stream()} or {@link java.util.Arrays#stream(Object[])}
683  * to obtain a stream.  How are those stream-bearing methods implemented?
684  *
685  * <p>The class {@link java.util.stream.StreamSupport} has a number of
686  * low-level methods for creating a stream, all using some form of a
687  * {@link java.util.Spliterator}. A spliterator is the parallel analogue of an
688  * {@link java.util.Iterator}; it describes a (possibly infinite) collection of
689  * elements, with support for sequentially advancing, bulk traversal, and
690  * splitting off some portion of the input into another spliterator which can
691  * be processed in parallel.  At the lowest level, all streams are driven by a
692  * spliterator.
693  *
694  * <p>There are a number of implementation choices in implementing a
695  * spliterator, nearly all of which are tradeoffs between simplicity of
696  * implementation and runtime performance of streams using that spliterator.
697  * The simplest, but least performant, way to create a spliterator is to
698  * create one from an iterator using
699  * {@link java.util.Spliterators#spliteratorUnknownSize(java.util.Iterator, int)}.
700  * While such a spliterator will work, it will likely offer poor parallel
701  * performance, since we have lost sizing information (how big is the
702  * underlying data set), as well as being constrained to a simplistic
703  * splitting algorithm.
704  *
705  * <p>A higher-quality spliterator will provide balanced and known-size
706  * splits, accurate sizing information, and a number of other
707  * {@link java.util.Spliterator#characteristics() characteristics} of the
708  * spliterator or data that can be used by implementations to optimize
709  * execution.
710  *
711  * <p>Spliterators for mutable data sources have an additional challenge;
712  * timing of binding to the data, since the data could change between the time
713  * the spliterator is created and the time the stream pipeline is executed.
714  * Ideally, a spliterator for a stream would report a characteristic of
715 
716  * {@code IMMUTABLE} or {@code CONCURRENT}; if not it should be
717  * <a href="../Spliterator.html#binding"><em>late-binding</em></a>. If a source
718  * cannot directly supply a recommended spliterator, it may indirectly supply
719  * a spliterator using a {@code Supplier}, and construct a stream via the
720  * {@code Supplier}-accepting versions of
721  * {@link java.util.stream.StreamSupport#stream(Supplier, int, boolean) stream()}.
722  * The spliterator is obtained from the supplier only after the terminal
723  * operation of the stream pipeline commences.
724  *
725  * <p>These requirements significantly reduce the scope of potential
726  * interference between mutations of the stream source and execution of stream
727  * pipelines. Streams based on spliterators with the desired characteristics,
728  * or those using the Supplier-based factory forms, are immune to
729  * modifications of the data source prior to commencement of the terminal
730  * operation (provided the behavioral parameters to the stream operations meet
731  * the required criteria for non-interference and statelessness).  See
732  * <a href="package-summary.html#NonInterference">Non-Interference</a>
733  * for more details.
734  *
735  * @since 1.8
736  */
737 package java.util.stream;
738 
739 import java.util.function.BinaryOperator;
740 import java.util.function.UnaryOperator;
741