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25
26 /**
27 * <h1>java.util.stream</h1>
28 *
29 * Classes to support functional-style operations on streams of values, as in the following:
30 *
31 * <pre>{@code
32 * int sumOfWeights = blocks.stream().filter(b -> b.getColor() == RED)
33 * .mapToInt(b -> b.getWeight())
34 * .sum();
35 * }</pre>
36 *
37 * <p>Here we use {@code blocks}, which might be a {@code Collection}, as a source for a stream,
38 * and then perform a filter-map-reduce ({@code sum()} is an example of a <a href="package-summary.html#Reduction">reduction</a>
39 * operation) on the stream to obtain the sum of the weights of the red blocks.
40 *
41 * <p>The key abstraction used in this approach is {@link java.util.stream.Stream}, as well as its primitive
42 * specializations {@link java.util.stream.IntStream}, {@link java.util.stream.LongStream},
43 * and {@link java.util.stream.DoubleStream}. Streams differ from Collections in several ways:
44 *
45 * <ul>
46 * <li>No storage. A stream is not a data structure that stores elements; instead, they
47 * carry values from a source (which could be a data structure, a generator, an IO channel, etc)
48 * through a pipeline of computational operations.</li>
49 * <li>Functional in nature. An operation on a stream produces a result, but does not modify
50 * its underlying data source. For example, filtering a {@code Stream} produces a new {@code Stream},
51 * rather than removing elements from the underlying source.</li>
52 * <li>Laziness-seeking. Many stream operations, such as filtering, mapping, or duplicate removal,
53 * can be implemented lazily, exposing opportunities for optimization. (For example, "find the first
54 * {@code String} matching a pattern" need not examine all the input strings.) Stream operations
55 * are divided into intermediate ({@code Stream}-producing) operations and terminal (value-producing)
56 * operations; all intermediate operations are lazy.</li>
57 * <li>Possibly unbounded. While collections have a finite size, streams need not. Operations
58 * such as {@code limit(n)} or {@code findFirst()} can allow computations on infinite streams
59 * to complete in finite time.</li>
60 * </ul>
61 *
62 * <h2><a name="StreamPipelines">Stream pipelines</a></h2>
63 *
64 * <p>Streams are used to create <em>pipelines</em> of <a href="package-summary.html#StreamOps">operations</a>. A
65 * complete stream pipeline has several components: a source (which may be a {@code Collection},
66 * an array, a generator function, or an IO channel); zero or more <em>intermediate operations</em>
67 * such as {@code Stream.filter} or {@code Stream.map}; and a <em>terminal operation</em> such
68 * as {@code Stream.forEach} or {@code java.util.stream.Stream.reduce}. Stream operations may take as parameters
69 * <em>function values</em> (which are often lambda expressions, but could be method references
70 * or objects) which parameterize the behavior of the operation, such as a {@code Predicate}
71 * passed to the {@code Stream#filter} method.
72 *
73 * <p>Intermediate operations return a new {@code Stream}. They are lazy; executing an
74 * intermediate operation such as {@link java.util.stream.Stream#filter Stream.filter} does
75 * not actually perform any filtering, instead creating a new {@code Stream} that, when
76 * traversed, contains the elements of the initial {@code Stream} that match the
77 * given {@code Predicate}. Consuming elements from the stream source does not
78 * begin until the terminal operation is executed.
79 *
80 * <p>Terminal operations consume the {@code Stream} and produce a result or a side-effect.
81 * After a terminal operation is performed, the stream can no longer be used and you must
82 * return to the data source, or select a new data source, to get a new stream. For example,
83 * obtaining the sum of weights of all red blocks, and then of all blue blocks, requires a
84 * filter-map-reduce on two different streams:
85 * <pre>{@code
86 * int sumOfRedWeights = blocks.stream().filter(b -> b.getColor() == RED)
87 * .mapToInt(b -> b.getWeight())
88 * .sum();
89 * int sumOfBlueWeights = blocks.stream().filter(b -> b.getColor() == BLUE)
90 * .mapToInt(b -> b.getWeight())
91 * .sum();
92 * }</pre>
93 *
94 * <p>However, there are other techniques that allow you to obtain both results in a single
95 * pass if multiple traversal is impractical or inefficient. TODO provide link
96 *
97 * <h3><a name="StreamOps">Stream operations</a></h3>
98 *
99 * <p>Intermediate stream operation (such as {@code filter} or {@code sorted}) always produce a
100 * new {@code Stream}, and are always<em>lazy</em>. Executing a lazy operations does not
101 * trigger processing of the stream contents; all processing is deferred until the terminal
102 * operation commences. Processing streams lazily allows for significant efficiencies; in a
103 * pipeline such as the filter-map-sum example above, filtering, mapping, and addition can be
104 * fused into a single pass, with minimal intermediate state. Laziness also enables us to avoid
105 * examining all the data when it is not necessary; for operations such as "find the first
106 * string longer than 1000 characters", one need not examine all the input strings, just enough
107 * to find one that has the desired characteristics. (This behavior becomes even more important
108 * when the input stream is infinite and not merely large.)
109 *
110 * <p>Intermediate operations are further divided into <em>stateless</em> and <em>stateful</em>
111 * operations. Stateless operations retain no state from previously seen values when processing
112 * a new value; examples of stateless intermediate operations include {@code filter} and
113 * {@code map}. Stateful operations may incorporate state from previously seen elements in
114 * processing new values; examples of stateful intermediate operations include {@code distinct}
115 * and {@code sorted}. Stateful operations may need to process the entire input before
116 * producing a result; for example, one cannot produce any results from sorting a stream until
117 * one has seen all elements of the stream. As a result, under parallel computation, some
118 * pipelines containing stateful intermediate operations have to be executed in multiple passes.
119 * Pipelines containing exclusively stateless intermediate operations can be processed in a
120 * single pass, whether sequential or parallel.
121 *
122 * <p>Further, some operations are deemed <em>short-circuiting</em> operations. An intermediate
123 * operation is short-circuiting if, when presented with infinite input, it may produce a
124 * finite stream as a result. A terminal operation is short-circuiting if, when presented with
125 * infinite input, it may terminate in finite time. (Having a short-circuiting operation is a
126 * necessary, but not sufficient, condition for the processing of an infinite stream to
127 * terminate normally in finite time.)
128 *
129 * Terminal operations (such as {@code forEach} or {@code findFirst}) are always eager
130 * (they execute completely before returning), and produce a non-{@code Stream} result, such
131 * as a primitive value or a {@code Collection}, or have side-effects.
132 *
133 * <h3>Parallelism</h3>
134 *
135 * <p>By recasting aggregate operations as a pipeline of operations on a stream of values, many
136 * aggregate operations can be more easily parallelized. A {@code Stream} can execute either
137 * in serial or in parallel. When streams are created, they are either created as sequential
138 * or parallel streams; the parallel-ness of streams can also be switched by the
139 * {@link java.util.stream Stream#sequential()} and {@link java.util.stream.Stream#parallel()}
140 * operations. The {@code Stream} implementations in the JDK create serial streams unless
141 * parallelism is explicitly requested. For example, {@code Collection} has methods
142 * {@link java.util.Collection#stream} and {@link java.util.Collection#parallelStream},
143 * which produce sequential and parallel streams respectively; other stream-bearing methods
144 * such as {@link java.util.stream.IntStream#range(int, int)} produce sequential
145 * streams but these can be efficiently parallelized by calling {@code parallel()} on the
146 * result. The set of operations on serial and parallel streams is identical. To execute the
147 * "sum of weights of blocks" query in parallel, we would do:
148 *
149 * <pre>{@code
150 * int sumOfWeights = blocks.parallelStream().filter(b -> b.getColor() == RED)
151 * .mapToInt(b -> b.getWeight())
152 * .sum();
153 * }</pre>
154 *
155 * <p>The only difference between the serial and parallel versions of this example code is
156 * the creation of the initial {@code Stream}. Whether a {@code Stream} will execute in serial
157 * or parallel can be determined by the {@code Stream#isParallel} method. When the terminal
158 * operation is initiated, the entire stream pipeline is either executed sequentially or in
159 * parallel, determined by the last operation that affected the stream's serial-parallel
160 * orientation (which could be the stream source, or the {@code sequential()} or
161 * {@code parallel()} methods.)
162 *
163 * <p>In order for the results of parallel operations to be deterministic and consistent with
164 * their serial equivalent, the function values passed into the various stream operations should
165 * be <a href="#NonInteference"><em>stateless</em></a>.
166 *
167 * <h3><a name="Ordering">Ordering</a></h3>
168 *
169 * <p>Streams may or may not have an <em>encounter order</em>. An encounter
170 * order specifies the order in which elements are provided by the stream to the
171 * operations pipeline. Whether or not there is an encounter order depends on
172 * the source, the intermediate operations, and the terminal operation.
173 * Certain stream sources (such as {@code List} or arrays) are intrinsically
174 * ordered, whereas others (such as {@code HashSet}) are not. Some intermediate
175 * operations may impose an encounter order on an otherwise unordered stream,
176 * such as {@link java.util.stream.Stream#sorted()}, and others may render an
177 * ordered stream unordered (such as {@link java.util.stream.Stream#unordered()}).
178 * Some terminal operations may ignore encounter order, such as
179 * {@link java.util.stream.Stream#forEach}.
180 *
181 * <p>If a Stream is ordered, most operations are constrained to operate on the
182 * elements in their encounter order; if the source of a stream is a {@code List}
183 * containing {@code [1, 2, 3]}, then the result of executing {@code map(x -> x*2)}
184 * must be {@code [2, 4, 6]}. However, if the source has no defined encounter
185 * order, than any of the six permutations of the values {@code [2, 4, 6]} would
186 * be a valid result. Many operations can still be efficiently parallelized even
187 * under ordering constraints.
188 *
189 * <p>For sequential streams, ordering is only relevant to the determinism
190 * of operations performed repeatedly on the same source. (An {@code ArrayList}
191 * is constrained to iterate elements in order; a {@code HashSet} is not, and
192 * repeated iteration might produce a different order.)
193 *
194 * <p>For parallel streams, relaxing the ordering constraint can enable
195 * optimized implementation for some operations. For example, duplicate
196 * filtration on an ordered stream must completely process the first partition
197 * before it can return any elements from a subsequent partition, even if those
198 * elements are available earlier. On the other hand, without the constraint of
199 * ordering, duplicate filtration can be done more efficiently by using
200 * a shared {@code ConcurrentHashSet}. There will be cases where the stream
201 * is structurally ordered (the source is ordered and the intermediate
202 * operations are order-preserving), but the user does not particularly care
203 * about the encounter order. In some cases, explicitly de-ordering the stream
204 * with the {@link java.util.stream.Stream#unordered()} method may result in
205 * improved parallel performance for some stateful or terminal operations.
206 *
207 * <h3><a name="Non-Interference">Non-interference</a></h3>
208 *
209 * The {@code java.util.stream} package enables you to execute possibly-parallel
210 * bulk-data operations over a variety of data sources, including even non-thread-safe
211 * collections such as {@code ArrayList}. This is possible only if we can
212 * prevent <em>interference</em> with the data source during the execution of a
213 * stream pipeline. (Execution begins when the terminal operation is invoked, and ends
214 * when the terminal operation completes.) For most data sources, preventing interference
215 * means ensuring that the data source is <em>not modified at all</em> during the execution
216 * of the stream pipeline. (Some data sources, such as concurrent collections, are
217 * specifically designed to handle concurrent modification.)
218 *
219 * <p>Accordingly, lambda expressions (or other objects implementing the appropriate functional
220 * interface) passed to stream methods should never modify the stream's data source. An
221 * implementation is said to <em>interfere</em> with the data source if it modifies, or causes
222 * to be modified, the stream's data source. The need for non-interference applies to all
223 * pipelines, not just parallel ones. Unless the stream source is concurrent, modifying a
224 * stream's data source during execution of a stream pipeline can cause exceptions, incorrect
225 * answers, or nonconformant results.
226 *
227 * <p>Further, results may be nondeterministic or incorrect if the lambda expressions passed to
228 * stream operations are <em>stateful</em>. A stateful lambda (or other object implementing the
229 * appropriate functional interface) is one whose result depends on any state which might change
230 * during the execution of the stream pipeline. An example of a stateful lambda is:
231 * <pre>{@code
232 * Set<Integer> seen = Collections.synchronizedSet(new HashSet<>());
233 * stream.parallel().map(e -> { if (seen.add(e)) return 0; else return e; })...
234 * }</pre>
235 * Here, if the mapping operation is performed in parallel, the results for the same input
236 * could vary from run to run, due to thread scheduling differences, whereas, with a stateless
237 * lambda expression the results would always be the same.
238 *
239 * <h3>Side-effects</h3>
240 *
241 * <h2><a name="Reduction">Reduction operations</a></h2>
242 *
243 * A <em>reduction</em> operation takes a stream of elements and processes them in a way
244 * that reduces to a single value or summary description, such as finding the sum or maximum
245 * of a set of numbers. (In more complex scenarios, the reduction operation might need to
246 * extract data from the elements before reducing that data to a single value, such as
247 * finding the sum of weights of a set of blocks. This would require extracting the weight
248 * from each block before summing up the weights.)
249 *
250 * <p>Of course, such operations can be readily implemented as simple sequential loops, as in:
251 * <pre>{@code
252 * int sum = 0;
253 * for (int x : numbers) {
254 * sum += x;
255 * }
256 * }</pre>
257 * However, there may be a significant advantage to preferring a {@link java.util.stream.Stream#reduce reduce operation}
258 * over a mutative accumulation such as the above -- a properly constructed reduce operation is
259 * inherently parallelizable so long as the
260 * {@link java.util.function.BinaryOperator reduction operaterator}
261 * has the right characteristics. Specifically the operator must be
262 * <a href="#Associativity">associative</a>. For example, given a
263 * stream of numbers for which we want to find the sum, we can write:
264 * <pre>{@code
265 * int sum = numbers.reduce(0, (x,y) -> x+y);
266 * }</pre>
267 * or more succinctly:
268 * <pre>{@code
269 * int sum = numbers.reduce(0, Integer::sum);
270 * }</pre>
271 *
272 * <p>(The primitive specializations of {@link java.util.stream.Stream}, such as
273 * {@link java.util.stream.IntStream}, even have convenience methods for common reductions,
274 * such as {@link java.util.stream.IntStream#sum() sum} and {@link java.util.stream.IntStream#max() max},
275 * which are implemented as simple wrappers around reduce.)
276 *
277 * <p>Reduction parallellizes well since the implementation of {@code reduce} can operate on
278 * subsets of the stream in parallel, and then combine the intermediate results to get the final
279 * correct answer. Even if you were to use a parallelizable form of the
280 * {@link java.util.stream.Stream#forEach(Consumer) forEach()} method
281 * in place of the original for-each loop above, you would still have to provide thread-safe
282 * updates to the shared accumulating variable {@code sum}, and the required synchronization
283 * would likely eliminate any performance gain from parallelism. Using a {@code reduce} method
284 * instead removes all of the burden of parallelizing the reduction operation, and the library
285 * can provide an efficient parallel implementation with no additional synchronization needed.
286 *
287 * <p>The "blocks" examples shown earlier shows how reduction combines with other operations
288 * to replace for loops with bulk operations. If {@code blocks} is a collection of {@code Block}
289 * objects, which have a {@code getWeight} method, we can find the heaviest block with:
290 * <pre>{@code
291 * OptionalInt heaviest = blocks.stream()
292 * .mapToInt(Block::getWeight)
293 * .reduce(Integer::max);
294 * }</pre>
295 *
296 * <p>In its more general form, a {@code reduce} operation on elements of type {@code <T>}
297 * yielding a result of type {@code <U>} requires three parameters:
298 * <pre>{@code
299 * <U> U reduce(U identity,
300 * BiFunction<U, ? super T, U> accumlator,
301 * BinaryOperator<U> combiner);
302 * }</pre>
303 * Here, the <em>identity</em> element is both an initial seed for the reduction, and a default
304 * result if there are no elements. The <em>accumulator</em> function takes a partial result and
305 * the next element, and produce a new partial result. The <em>combiner</em> function combines
306 * the partial results of two accumulators to produce a new partial result, and eventually the
307 * final result.
308 *
309 * <p>This form is a generalization of the two-argument form, and is also a generalization of
310 * the map-reduce construct illustrated above. If we wanted to re-cast the simple {@code sum}
311 * example using the more general form, {@code 0} would be the identity element, while
312 * {@code Integer::sum} would be both the accumulator and combiner. For the sum-of-weights
313 * example, this could be re-cast as:
314 * <pre>{@code
315 * int sumOfWeights = blocks.stream().reduce(0,
316 * (sum, b) -> sum + b.getWeight())
317 * Integer::sum);
318 * }</pre>
319 * though the map-reduce form is more readable and generally preferable. The generalized form
320 * is provided for cases where significant work can be optimized away by combining mapping and
321 * reducing into a single function.
322 *
323 * <p>More formally, the {@code identity} value must be an <em>identity</em> for the combiner
324 * function. This means that for all {@code u}, {@code combiner.apply(identity, u)} is equal
325 * to {@code u}. Additionally, the {@code combiner} function must be
326 * <a href="#Associativity">associative</a> and must be compatible with the {@code accumulator}
327 * function; for all {@code u} and {@code t}, the following must hold:
328 * <pre>{@code
329 * combiner.apply(u, accumulator.apply(identity, t)) == accumulator.apply(u, t)
330 * }</pre>
331 *
332 * <h3><a name="MutableReduction">Mutable Reduction</a></h3>
333 *
334 * A <em>mutable</em> reduction operation is similar to an ordinary reduction, in that it reduces
335 * a stream of values to a single value, but instead of producing a distinct single-valued result, it
336 * mutates a general <em>result container</em>, such as a {@code Collection} or {@code StringBuilder},
337 * as it processes the elements in the stream.
338 *
339 * <p>For example, if we wanted to take a stream of strings and concatenate them into a single
340 * long string, we <em>could</em> achieve this with ordinary reduction:
341 * <pre>{@code
342 * String concatenated = strings.reduce("", String::concat)
343 * }</pre>
344 *
345 * We would get the desired result, and it would even work in parallel. However, we might not
346 * be happy about the performance! Such an implementation would do a great deal of string
347 * copying, and the run time would be <em>O(n^2)</em> in the number of elements. A more
348 * performant approach would be to accumulate the results into a {@link java.lang.StringBuilder}, which
349 * is a mutable container for accumulating strings. We can use the same technique to
350 * parallelize mutable reduction as we do with ordinary reduction.
351 *
352 * <p>The mutable reduction operation is called {@link java.util.stream.Stream#collect(Collector) collect()}, as it
353 * collects together the desired results into a result container such as {@code StringBuilder}.
354 * A {@code collect} operation requires three things: a factory function which will construct
355 * new instances of the result container, an accumulating function that will update a result
356 * container by incorporating a new element, and a combining function that can take two
357 * result containers and merge their contents. The form of this is very similar to the general
358 * form of ordinary reduction:
359 * <pre>{@code
360 * <R> R collect(Supplier<R> resultFactory,
361 * BiConsumer<R, ? super T> accumulator,
362 * BiConsumer<R, R> combiner);
363 * }</pre>
364 * As with {@code reduce()}, the benefit of expressing {@code collect} in this abstract way is
365 * that it is directly amenable to parallelization: we can accumulate partial results in parallel
366 * and then combine them. For example, to collect the String representations of the elements
367 * in a stream into an {@code ArrayList}, we could write the obvious sequential for-each form:
368 * <pre>{@code
369 * ArrayList<String> strings = new ArrayList<>();
370 * for (T element : stream) {
371 * strings.add(element.toString());
372 * }
373 * }</pre>
374 * Or we could use a parallelizable collect form:
375 * <pre>{@code
376 * ArrayList<String> strings = stream.collect(() -> new ArrayList<>(),
377 * (c, e) -> c.add(e.toString()),
378 * (c1, c2) -> c1.addAll(c2));
379 * }</pre>
380 * or, noting that we have buried a mapping operation inside the accumulator function, more
381 * succinctly as:
382 * <pre>{@code
383 * ArrayList<String> strings = stream.map(Object::toString)
384 * .collect(ArrayList::new, ArrayList::add, ArrayList::addAll);
385 * }</pre>
386 * Here, our supplier is just the {@link java.util.ArrayList#ArrayList() ArrayList constructor}, the
387 * accumulator adds the stringified element to an {@code ArrayList}, and the combiner simply
388 * uses {@link java.util.ArrayList#addAll addAll} to copy the strings from one container into the other.
389 *
390 * <p>As with the regular reduction operation, the ability to parallelize only comes if an
391 * <a href="package-summary.html#Associativity">associativity</a> condition is met. The {@code combiner} is associative
392 * if for result containers {@code r1}, {@code r2}, and {@code r3}:
393 * <pre>{@code
394 * combiner.accept(r1, r2);
395 * combiner.accept(r1, r3);
396 * }</pre>
397 * is equivalent to
398 * <pre>{@code
399 * combiner.accept(r2, r3);
400 * combiner.accept(r1, r2);
401 * }</pre>
402 * where equivalence means that {@code r1} is left in the same state (according to the meaning
403 * of {@link java.lang.Object#equals equals} for the element types). Similarly, the {@code resultFactory}
404 * must act as an <em>identity</em> with respect to the {@code combiner} so that for any result
405 * container {@code r}:
406 * <pre>{@code
407 * combiner.accept(r, resultFactory.get());
408 * }</pre>
409 * does not modify the state of {@code r} (again according to the meaning of
410 * {@link java.lang.Object#equals equals}). Finally, the {@code accumulator} and {@code combiner} must be
411 * compatible such that for a result container {@code r} and element {@code t}:
412 * <pre>{@code
413 * r2 = resultFactory.get();
414 * accumulator.accept(r2, t);
415 * combiner.accept(r, r2);
416 * }</pre>
417 * is equivalent to:
418 * <pre>{@code
419 * accumulator.accept(r,t);
420 * }</pre>
421 * where equivalence means that {@code r} is left in the same state (again according to the
422 * meaning of {@link java.lang.Object#equals equals}).
423 *
424 * <p> The three aspects of {@code collect}: supplier, accumulator, and combiner, are often very
425 * tightly coupled, and it is convenient to introduce the notion of a {@link java.util.stream.Collector} as
426 * being an object that embodies all three aspects. There is a {@link java.util.stream.Stream#collect(Collector) collect}
427 * method that simply takes a {@code Collector} and returns the resulting container.
428 * The above example for collecting strings into a {@code List} can be rewritten using a
429 * standard {@code Collector} as:
430 * <pre>{@code
431 * ArrayList<String> strings = stream.map(Object::toString)
432 * .collect(Collectors.toList());
433 * }</pre>
434 *
435 * <h3><a name="ConcurrentReduction">Reduction, Concurrency, and Ordering</a></h3>
436 *
437 * With some complex reduction operations, for example a collect that produces a
438 * {@code Map}, such as:
439 * <pre>{@code
440 * Map<Buyer, List<Transaction>> salesByBuyer
441 * = txns.parallelStream()
442 * .collect(Collectors.groupingBy(Transaction::getBuyer));
443 * }</pre>
444 * (where {@link java.util.stream.Collectors#groupingBy} is a utility function
445 * that returns a {@link java.util.stream.Collector} for grouping sets of elements based on some key)
446 * it may actually be counterproductive to perform the operation in parallel.
447 * This is because the combining step (merging one {@code Map} into another by key)
448 * can be expensive for some {@code Map} implementations.
449 *
450 * <p>Suppose, however, that the result container used in this reduction
451 * was a concurrently modifiable collection -- such as a
452 * {@link java.util.concurrent.ConcurrentHashMap ConcurrentHashMap}. In that case,
453 * the parallel invocations of the accumulator could actually deposit their results
454 * concurrently into the same shared result container, eliminating the need for the combiner to
455 * merge distinct result containers. This potentially provides a boost
456 * to the parallel execution performance. We call this a <em>concurrent</em> reduction.
457 *
458 * <p>A {@link java.util.stream.Collector} that supports concurrent reduction is marked with the
459 * {@link java.util.stream.Collector.Characteristics#CONCURRENT} characteristic.
460 * Having a concurrent collector is a necessary condition for performing a
461 * concurrent reduction, but that alone is not sufficient. If you imagine multiple
462 * accumulators depositing results into a shared container, the order in which
463 * results are deposited is non-deterministic. Consequently, a concurrent reduction
464 * is only possible if ordering is not important for the stream being processed.
465 * The {@link java.util.stream.Stream#collect(Collector)}
466 * implementation will only perform a concurrent reduction if
467 * <ul>
468 * <li>The stream is parallel;</li>
469 * <li>The collector has the
470 * {@link java.util.stream.Collector.Characteristics#CONCURRENT} characteristic,
471 * and;</li>
472 * <li>Either the stream is unordered, or the collector has the
473 * {@link java.util.stream.Collector.Characteristics#UNORDERED} characteristic.
474 * </ul>
475 * For example:
476 * <pre>{@code
477 * Map<Buyer, List<Transaction>> salesByBuyer
478 * = txns.parallelStream()
479 * .unordered()
480 * .collect(groupingByConcurrent(Transaction::getBuyer));
481 * }</pre>
482 * (where {@link java.util.stream.Collectors#groupingByConcurrent} is the concurrent companion
483 * to {@code groupingBy}).
484 *
485 * <p>Note that if it is important that the elements for a given key appear in the
486 * order they appear in the source, then we cannot use a concurrent reduction,
487 * as ordering is one of the casualties of concurrent insertion. We would then
488 * be constrained to implement either a sequential reduction or a merge-based
489 * parallel reduction.
490 *
491 * <h2><a name="Associativity">Associativity</a></h2>
492 *
493 * An operator or function {@code op} is <em>associative</em> if the following holds:
494 * <pre>{@code
495 * (a op b) op c == a op (b op c)
496 * }</pre>
497 * The importance of this to parallel evaluation can be seen if we expand this to four terms:
498 * <pre>{@code
499 * a op b op c op d == (a op b) op (c op d)
500 * }</pre>
501 * So we can evaluate {@code (a op b)} in parallel with {@code (c op d)} and then invoke {@code op} on
502 * the results.
503 * TODO what does associative mean for mutative combining functions?
504 * FIXME: we described mutative associativity above.
505 *
506 * <h2><a name="StreamSources">Stream sources</a></h2>
507 * TODO where does this section go?
508 *
509 * XXX - change to section to stream construction gradually introducing more
510 * complex ways to construct
511 * - construction from Collection
512 * - construction from Iterator
513 * - construction from array
514 * - construction from generators
515 * - construction from spliterator
516 *
517 * XXX - the following is quite low-level but important aspect of stream constriction
518 *
519 * <p>A pipeline is initially constructed from a spliterator (see {@link java.util.Spliterator}) supplied by a stream source.
520 * The spliterator covers elements of the source and provides element traversal operations
521 * for a possibly-parallel computation. See methods on {@link java.util.stream.Streams} for construction
522 * of pipelines using spliterators.
523 *
524 * <p>A source may directly supply a spliterator. If so, the spliterator is traversed, split, or queried
525 * for estimated size after, and never before, the terminal operation commences. It is strongly recommended
526 * that the spliterator report a characteristic of {@code IMMUTABLE} or {@code CONCURRENT}, or be
527 * <em>late-binding</em> and not bind to the elements it covers until traversed, split or queried for
528 * estimated size.
529 *
530 * <p>If a source cannot directly supply a recommended spliterator then it may indirectly supply a spliterator
531 * using a {@code Supplier}. The spliterator is obtained from the supplier after, and never before, the terminal
532 * operation of the stream pipeline commences.
533 *
534 * <p>Such requirements significantly reduce the scope of potential interference to the interval starting
535 * with the commencing of the terminal operation and ending with the producing a result or side-effect. See
536 * <a href="package-summary.html#Non-Interference">Non-Interference</a> for
537 * more details.
538 *
539 * XXX - move the following to the non-interference section
540 *
541 * <p>A source can be modified before the terminal operation commences and those modifications will be reflected in
542 * the covered elements. Afterwards, and depending on the properties of the source, further modifications
543 * might not be reflected and the throwing of a {@code ConcurrentModificationException} may occur.
544 *
545 * <p>For example, consider the following code:
546 * <pre>{@code
547 * List<String> l = new ArrayList(Arrays.asList("one", "two"));
548 * Stream<String> sl = l.stream();
549 * l.add("three");
550 * String s = sl.collect(toStringJoiner(" ")).toString();
551 * }</pre>
552 * First a list is created consisting of two strings: "one"; and "two". Then a stream is created from that list.
553 * Next the list is modified by adding a third string: "three". Finally the elements of the stream are collected
554 * and joined together. Since the list was modified before the terminal {@code collect} operation commenced
555 * the result will be a string of "one two three". However, if the list is modified after the terminal operation
556 * commences, as in:
557 * <pre>{@code
558 * List<String> l = new ArrayList(Arrays.asList("one", "two"));
559 * Stream<String> sl = l.stream();
560 * String s = sl.peek(s -> l.add("BAD LAMBDA")).collect(toStringJoiner(" ")).toString();
561 * }</pre>
562 * then a {@code ConcurrentModificationException} will be thrown since the {@code peek} operation will attempt
563 * to add the string "BAD LAMBDA" to the list after the terminal operation has commenced.
564 */
565
566 package java.util.stream;