Mercurial > hg > Members > tatsuki > functionaljava-master > core

comparison src/main/java/fj/data/Tree.java @ 0:fe80c1edf1be

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add getLoop
author tatsuki
date Fri, 20 Mar 2015 21:04:03 +0900
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1 package fj.data;
2
3 import fj.F;
4 import fj.F2;
5 import fj.F2Functions;
6 import fj.P;
7 import fj.P1;
8 import fj.P2;
9 import static fj.Function.*;
10 import static fj.data.Stream.*;
11 import fj.Monoid;
12 import fj.Show;
13
14 import java.util.Collection;
15 import java.util.Iterator;
16
17 /**
18 * Provides a lazy, immutable, non-empty, multi-way tree (a rose tree).
19 *
20 * @version %build.number%
21 */
22 public final class Tree<A> implements Iterable<A> {
23 /**
24 * Returns an iterator for this tree. This method exists to permit the use in a <code>for</code>-each loop.
25 *
26 * @return A iterator for this tree.
27 */
28 public Iterator<A> iterator() {
29 return flatten().iterator();
30 }
31
32 private final A root;
33 private final P1<Stream<Tree<A>>> subForest;
34
35 private Tree(final A root, final P1<Stream<Tree<A>>> subForest) {
36 this.root = root;
37 this.subForest = subForest;
38 }
39
40 /**
41 * Creates a nullary tree.
42 *
43 * @param root The root element of the tree.
44 * @return A nullary tree with the root element in it.
45 */
46 public static <A> Tree<A> leaf(final A root) {
47 return node(root, Stream.<Tree<A>>nil());
48 }
49
50 /**
51 * Creates a new tree given a root and a (potentially infinite) subforest.
52 *
53 * @param root The root element of the tree.
54 * @param forest A stream of the tree's subtrees.
55 * @return A newly sprouted tree.
56 */
57 public static <A> Tree<A> node(final A root, final P1<Stream<Tree<A>>> forest) {
58 return new Tree<A>(root, forest);
59 }
60
61 /**
62 * Creates a new tree given a root and a (potentially infinite) subforest.
63 *
64 * @param root The root element of the tree.
65 * @param forest A stream of the tree's subtrees.
66 * @return A newly sprouted tree.
67 */
68 public static <A> Tree<A> node(final A root, final Stream<Tree<A>> forest) {
69 return new Tree<A>(root, P.p(forest));
70 }
71
72 /**
73 * Creates a new n-ary given a root and a subforest of length n.
74 *
75 * @param root The root element of the tree.
76 * @param forest A list of the tree's subtrees.
77 * @return A newly sprouted tree.
78 */
79 public static <A> Tree<A> node(final A root, final List<Tree<A>> forest) {
80 return node(root, forest.toStream());
81 }
82
83 /**
84 * First-class constructor of trees.
85 *
86 * @return A function that constructs an n-ary tree given a root and a subforest or length n.
87 */
88 public static <A> F<A, F<P1<Stream<Tree<A>>>, Tree<A>>> node() {
89 return curry(new F2<A, P1<Stream<Tree<A>>>, Tree<A>>() {
90 public Tree<A> f(final A a, final P1<Stream<Tree<A>>> p1) {
91 return node(a, p1);
92 }
93 });
94 }
95
96 /**
97 * Returns the root element of the tree.
98 *
99 * @return The root element of the tree.
100 */
101 public A root() {
102 return root;
103 }
104
105 /**
106 * Returns a stream of the tree's subtrees.
107 *
108 * @return A stream of the tree's subtrees.
109 */
110 public P1<Stream<Tree<A>>> subForest() {
111 return subForest;
112 }
113
114 /**
115 * Provides a transformation from a tree to its root.
116 *
117 * @return A transformation from a tree to its root.
118 */
119 public static <A> F<Tree<A>, A> root_() {
120 return new F<Tree<A>, A>() {
121 public A f(final Tree<A> a) {
122 return a.root();
123 }
124 };
125 }
126
127 /**
128 * Provides a transformation from a tree to its subforest.
129 *
130 * @return A transformation from a tree to its subforest.
131 */
132 public static <A> F<Tree<A>, P1<Stream<Tree<A>>>> subForest_() {
133 return new F<Tree<A>, P1<Stream<Tree<A>>>>() {
134 public P1<Stream<Tree<A>>> f(final Tree<A> a) {
135 return a.subForest();
136 }
137 };
138 }
139
140 /**
141 * Puts the elements of the tree into a Stream, in pre-order.
142 *
143 * @return The elements of the tree in pre-order.
144 */
145 public Stream<A> flatten() {
146 final F2<Tree<A>, P1<Stream<A>>, Stream<A>> squish = new F2<Tree<A>, P1<Stream<A>>, Stream<A>>() {
147 public Stream<A> f(final Tree<A> t, final P1<Stream<A>> xs) {
148 return cons(t.root(), t.subForest().map(Stream.<Tree<A>, Stream<A>>foldRight().f(F2Functions.curry(this)).f(xs._1())));
149 }
150 };
151 return squish.f(this, P.p(Stream.<A>nil()));
152 }
153
154 /**
155 * flatten :: Tree a -> [a]
156 * flatten t = squish t []
157 * where squish (Node x ts) xs = x:Prelude.foldr squish xs ts
158 * Puts the elements of the tree into a Stream, in pre-order.
159 *
160 * @return The elements of the tree in pre-order.
161 */
162 public static <A> F<Tree<A>, Stream<A>> flatten_() {
163 return new F<Tree<A>, Stream<A>>() {
164 public Stream<A> f(final Tree<A> t) {
165 return t.flatten();
166 }
167 };
168 }
169
170 /**
171 * Provides a stream of the elements of the tree at each level, in level order.
172 *
173 * @return The elements of the tree at each level.
174 */
175 public Stream<Stream<A>> levels() {
176 final F<Stream<Tree<A>>, Stream<Tree<A>>> flatSubForests =
177 Stream.<Tree<A>, Tree<A>>bind_().f(compose(P1.<Stream<Tree<A>>>__1(), Tree.<A>subForest_()));
178 final F<Stream<Tree<A>>, Stream<A>> roots = Stream.<Tree<A>, A>map_().f(Tree.<A>root_());
179 return iterateWhile(flatSubForests, Stream.<Tree<A>>isNotEmpty_(), single(this)).map(roots);
180 }
181
182 /**
183 * Maps the given function over this tree.
184 *
185 * @param f The function to map over this tree.
186 * @return The new Tree after the function has been applied to each element in this Tree.
187 */
188 public <B> Tree<B> fmap(final F<A, B> f) {
189 return node(f.f(root()), subForest().map(Stream.<Tree<A>, Tree<B>>map_().f(Tree.<A, B>fmap_().f(f))));
190 }
191
192 /**
193 * Provides a transformation to lift any function so that it maps over Trees.
194 *
195 * @return A transformation to lift any function so that it maps over Trees.
196 */
197 public static <A, B> F<F<A, B>, F<Tree<A>, Tree<B>>> fmap_() {
198 return new F<F<A, B>, F<Tree<A>, Tree<B>>>() {
199 public F<Tree<A>, Tree<B>> f(final F<A, B> f) {
200 return new F<Tree<A>, Tree<B>>() {
201 public Tree<B> f(final Tree<A> a) {
202 return a.fmap(f);
203 }
204 };
205 }
206 };
207 }
208
209 /**
210 * Folds this tree using the given monoid.
211 *
212 * @param f A transformation from this tree's elements, to the monoid.
213 * @param m The monoid to fold this tree with.
214 * @return The result of folding the tree with the given monoid.
215 */
216 public <B> B foldMap(final F<A, B> f, final Monoid<B> m) {
217 return m.sum(f.f(root()), m.sumRight(subForest()._1().map(foldMap_(f, m)).toList()));
218 }
219
220 /**
221 * Projects an immutable collection of this tree.
222 *
223 * @return An immutable collection of this tree.
224 */
225 public Collection<A> toCollection() {
226 return flatten().toCollection();
227 }
228
229 /**
230 * Provides a function that folds a tree with the given monoid.
231 *
232 * @param f A transformation from a tree's elements to the monoid.
233 * @param m A monoid to fold the tree with.
234 * @return A function that, given a tree, folds it with the given monoid.
235 */
236 public static <A, B> F<Tree<A>, B> foldMap_(final F<A, B> f, final Monoid<B> m) {
237 return new F<Tree<A>, B>() {
238 public B f(final Tree<A> t) {
239 return t.foldMap(f, m);
240 }
241 };
242 }
243
244 /**
245 * Builds a tree from a seed value.
246 *
247 * @param f A function with which to build the tree.
248 * @return A function which, given a seed value, yields a tree.
249 */
250 public static <A, B> F<B, Tree<A>> unfoldTree(final F<B, P2<A, P1<Stream<B>>>> f) {
251 return new F<B, Tree<A>>() {
252 public Tree<A> f(final B b) {
253 final P2<A, P1<Stream<B>>> p = f.f(b);
254 return node(p._1(), p._2().map(Stream.<B, Tree<A>>map_().f(unfoldTree(f))));
255 }
256 };
257 }
258
259 /**
260 * Applies the given function to all subtrees of this tree, returning a tree of the results (comonad pattern).
261 *
262 * @param f A function to bind across all the subtrees of this tree.
263 * @return A new tree, with the results of applying the given function to each subtree of this tree. The result
264 * of applying the function to the entire tree is the root label, and the results of applying to the
265 * root's children are labels of the root's subforest, etc.
266 */
267 public <B> Tree<B> cobind(final F<Tree<A>, B> f) {
268 return unfoldTree(new F<Tree<A>, P2<B, P1<Stream<Tree<A>>>>>() {
269 public P2<B, P1<Stream<Tree<A>>>> f(final Tree<A> t) {
270 return P.p(f.f(t), t.subForest());
271 }
272 }).f(this);
273 }
274
275 /**
276 * Expands this tree into a tree of trees, with this tree as the root label, and subtrees as the labels of
277 * child nodes (comonad pattern).
278 *
279 * @return A tree of trees, with this tree as its root label, and subtrees of this tree as the labels of
280 * its child nodes.
281 */
282 public Tree<Tree<A>> cojoin() {
283 final F<Tree<A>, Tree<A>> id = identity();
284 return cobind(id);
285 }
286
287 private static <A> Stream<String> drawSubTrees(final Show<A> s, final Stream<Tree<A>> ts) {
288 return ts.isEmpty() ? Stream.<String>nil()
289 : ts.tail()._1().isEmpty() ? shift("`- ", " ", ts.head().drawTree(s)).cons("|")
290 : shift("+- ", "| ", ts.head().drawTree(s))
291 .append(drawSubTrees(s, ts.tail()._1()));
292 }
293
294 private static Stream<String> shift(final String f, final String o, final Stream<String> s) {
295 return Stream.repeat(o).cons(f).zipWith(s, Monoid.stringMonoid.sum());
296 }
297
298 private Stream<String> drawTree(final Show<A> s) {
299 return drawSubTrees(s, subForest._1()).cons(s.showS(root));
300 }
301
302 /**
303 * Draws a 2-dimensional representation of a tree.
304 *
305 * @param s A show instance for the elements of the tree.
306 * @return a String showing this tree in two dimensions.
307 */
308 public String draw(final Show<A> s) {
309 return Monoid.stringMonoid.join(drawTree(s), "\n");
310 }
311
312 /**
313 * Provides a show instance that draws a 2-dimensional representation of a tree.
314 *
315 * @param s A show instance for the elements of the tree.
316 * @return a show instance that draws a 2-dimensional representation of a tree.
317 */
318 public static <A> Show<Tree<A>> show2D(final Show<A> s) {
319 return Show.showS(new F<Tree<A>, String>() {
320 public String f(final Tree<A> tree) {
321 return tree.draw(s);
322 }
323 });
324 }
325
326 /**
327 * Zips this tree with another, using the given function. The resulting tree is the structural intersection
328 * of the two trees.
329 *
330 * @param bs A tree to zip this tree with.
331 * @param f A function with which to zip together the two trees.
332 * @return A new tree of the results of applying the given function over this tree and the given tree, position-wise.
333 */
334 public <B, C> Tree<C> zipWith(final Tree<B> bs, final F2<A, B, C> f) {
335 return F2Functions.zipTreeM(f).f(this, bs);
336 }
337
338 /**
339 * Zips this tree with another, using the given function. The resulting tree is the structural intersection
340 * of the two trees.
341 *
342 * @param bs A tree to zip this tree with.
343 * @param f A function with which to zip together the two trees.
344 * @return A new tree of the results of applying the given function over this tree and the given tree, position-wise.
345 */
346 public <B, C> Tree<C> zipWith(final Tree<B> bs, final F<A, F<B, C>> f) {
347 return zipWith(bs, uncurryF2(f));
348 }
349
350 /**
351 * Folds a Tree<A> into a Tree<B> by applying the function f from the bottom of the Tree to the top
352 *
353 * @param t A tree to fold from the bottom to the top.
354 * @param f A function transforming the current node and a stream of already transformed nodes (its children) into a new node
355 * @return The folded tree
356 */
357 public static <A, B> Tree<B> bottomUp(Tree<A> t, final F<P2<A, Stream<B>>, B> f) {
358 final F<Tree<A>, Tree<B>> recursiveCall = new F<Tree<A>, Tree<B>>() {
359 @Override public Tree<B> f(Tree<A> a) {
360 return bottomUp(a, f);
361 }
362 };
363
364 final Stream<Tree<B>> tbs = t.subForest()._1().map(recursiveCall);
365 return Tree.node(f.f(P.p(t.root(), tbs.map(Tree.<B> getRoot()))), tbs);
366 }
367
368 /**
369 * @return a function getting the root of a Tree
370 */
371 private static <A> F<Tree<A>, A> getRoot() {
372 return new F<Tree<A>, A>() {
373 @Override public A f(Tree<A> a) {
374 return a.root();
375 }
376 };
377 }
378
379 }