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12 # See the License for the specific language governing permissions and
13 # limitations under the License.
15 # Binary Tree data-structure
16 # A binary tree is a tree data structure in which each node has at most two children
17 # (referred to as the left child and the right child).
18 # In a binary tree, the degree of each node can be at most two.
19 # Binary trees are used to implement binary search trees and binary heaps,
20 # and are used for efficient searching and sorting.
29 # * node.left.key < node.key
30 # * node.right.key > node.key
31 # * no duplicates allowed
34 # * search average O(lg n) worst O(n)
35 # * insert average O(lg n) worst O(n)
36 # * delete average O(lg n) worst O(n)
39 # var tree = new BinTreeMap[Int, String]
41 # assert tree.min == "n1"
42 class BinTreeMap[K
: Comparable, E
]
45 redef type N
: BinTreeNode[K
, E
]
48 private var first_node
: nullable BinTreeNode[K
, E
] = null
49 private var last_node
: nullable BinTreeNode[K
, E
] = null
51 # O(n) in worst case, average is O(h) with h: tree height
53 # var tree = new BinTreeMap[Int, String]
54 # assert tree.is_empty
56 # assert not tree.is_empty
57 redef fun is_empty
do return root
== null
59 # O(n) in worst case, average is O(h) with h: tree height
61 # var tree = new BinTreeMap[Int, String]
62 # assert not tree.has_key(1)
63 # for i in [4, 2, 1, 5, 3] do tree[i] = "n{i}"
64 # assert not tree.has_key(0)
65 # assert tree.has_key(2)
66 # assert not tree.has_key(6)
67 redef fun has_key
(key
: K
): Bool do
68 if is_empty
then return false
69 var res
= search_down
(root
.as(not null), key
)
77 private var cache_node
: nullable N
= null
79 # Get the node value associated to `key`
80 # O(n) in worst case, average is O(h) with h: tree height
82 # var tree = new BinTreeMap[Int, String]
83 # for i in [4, 2, 1, 5, 3] do tree[i] = "n{i}"
84 # assert tree.has_key(1)
85 # assert tree[1] == "n1"
86 # assert tree.has_key(1)
87 # assert tree[2] == "n2"
88 redef fun [](key
: K
): E
do
89 assert not_empty
: not is_empty
90 if cache_node
!= null and cache_node
.key
== key
then return cache_node
.value
91 var res
= search_down
(root
.as(not null), key
)
92 assert has_key
: res
!= null
96 # Search `key` in `from` and its children nodes.
97 protected fun search_down
(from
: N
, key
: K
): nullable N
do
98 var cmp
= key
<=> from
.key
99 if cmp
== 0 then return from
100 if from
.left
!= null and cmp
< 0 then
101 return search_down
(from
.left
.as(not null), key
)
102 else if from
.right
!= null then
103 return search_down
(from
.right
.as(not null), key
)
108 # Get the node with the minimum key
109 # O(n) in worst case, average is O(h) with h: tree height
111 # var tree = new BinTreeMap[Int, String]
112 # for i in [4, 2, 1, 5, 3] do tree[i] = "n{i}"
113 # assert tree.min == "n1"
115 assert not_empty
: root
!= null
116 return min_from
(root
.as(not null)).value
119 # Get the left-most child from `node`.
120 protected fun min_from
(node
: N
): N
do
121 if node
.left
== null then return node
122 return min_from
(node
.left
.as(not null))
125 # Get the node with the maximum key
126 # O(n) in worst case, average is O(h) with h: tree height
128 # var tree = new BinTreeMap[Int, String]
129 # for i in [4, 2, 1, 5, 3, 6, 7, 8] do tree[i] = "n{i}"
130 # assert tree.max == "n8"
132 assert not_empty
: root
!= null
133 return max_from
(root
.as(not null)).value
136 # Get the right-most child from `node`.
137 protected fun max_from
(node
: N
): N
do
138 if node
.right
== null then return node
139 return max_from
(node
.right
.as(not null))
142 # Insert a new node in tree using `key` and `item`
143 # O(n) in worst case, average is O(h) with h: tree height
145 # var tree = new BinTreeMap[Int, String]
147 # assert tree.max == "n1"
149 # assert tree.max == "n3"
150 redef fun []=(key
, item
) do
151 insert_node
(new BinTreeNode[K
, E
](key
, item
))
154 # Add `node` in the tree.
155 protected fun insert_node
(node
: N
) do
160 shift_down
(root
.as(not null), node
)
162 if first_node
== null then
165 if last_node
!= null then
166 last_node
.next
= node
167 node
.prev
= last_node
172 # Push down the `node` in tree from a specified `from` index
173 protected fun shift_down
(from
, node
: N
) do
174 var cmp
= node
.key
<=> from
.key
176 if from
.left
== null then
180 shift_down
(from
.left
.as(not null), node
)
183 if from
.right
== null then
187 shift_down
(from
.right
.as(not null), node
)
192 # Delete node at `key` (also return the deleted node value)
193 # O(n) in worst case, average is O(h) with h: tree height
195 # var tree = new BinTreeMap[Int, String]
197 # assert tree.max == "n1"
199 # assert tree.max == "n3"
201 # assert tree.max == "n1"
202 fun delete
(key
: K
): nullable E
do
203 assert is_empty
: root
!= null
205 var node
= search_down
(root
.as(not null), key
)
206 if node
== null then return null
207 if node
.left
== null then
208 transplant
(node
, node
.right
)
209 else if node
.right
== null then
210 transplant
(node
, node
.left
)
212 var min
= min_from
(node
.right
.as(not null))
213 if min
.parent
!= node
then
214 transplant
(min
, min
.right
)
215 min
.right
= node
.right
216 min
.right
.parent
= min
218 transplant
(node
, min
)
220 min
.left
.parent
= min
222 if first_node
== node
then
225 if last_node
== node
then
226 last_node
= node
.prev
227 last_node
.next
= null
229 node
.prev
.next
= node
.next
230 node
.next
.prev
= node
.prev
235 # Swap a `node` with the `other` in this Tree
236 # note: Nodes parents are updated, children still untouched
237 protected fun transplant
(node
, other
: nullable N
) do
238 if node
== null then return
239 if node
.parent
== null then
241 else if node
== node
.parent
.left
then
242 node
.parent
.left
= other
244 node
.parent
.right
= other
246 if other
!= null then other
.parent
= node
.parent
249 # Perform left rotation on `node`
259 protected fun rotate_left
(node
: N
) do
262 if y
.left
!= null then
265 y
.parent
= node
.parent
266 if node
.parent
== null then
268 else if node
== node
.parent
.left
then
271 node
.parent
.right
= y
277 # Perform right rotation on `node`
287 protected fun rotate_right
(node
: N
) do
290 if y
.right
!= null then
291 y
.right
.parent
= node
293 y
.parent
= node
.parent
294 if node
.parent
== null then
296 else if node
== node
.parent
.right
then
297 node
.parent
.right
= y
305 # Sort the tree into an array
308 # var tree = new BinTreeMap[Int, String]
309 # for i in [4, 2, 1, 5, 3] do tree[i] = "n{i}"
310 # assert tree.sort == ["n1", "n2", "n3", "n4", "n5"]
311 fun sort
: Array[E
] do
312 var sorted
= new Array[E
]
313 if root
== null then return sorted
314 sort_down
(root
.as(not null), sorted
)
318 # Sort the tree from `node` and place results in `sorted`.
319 protected fun sort_down
(node
: N
, sorted
: Array[E
]) do
320 if node
.left
!= null then sort_down
(node
.left
.as(not null), sorted
)
321 sorted
.add
(node
.value
)
322 if node
.right
!= null then sort_down
(node
.right
.as(not null), sorted
)
327 if root
== null then return "[]"
328 return "[{print_tree(root)}]"
331 # Print the tree starting from `node`.
332 protected fun print_tree
(node
: N
): String do
333 var s
= new FlatBuffer
335 if node
.left
!= null then s
.append
(print_tree
(node
.left
.as(not null)))
336 if node
.right
!= null then s
.append
(print_tree
(node
.right
.as(not null)))
340 redef fun show_dot
do
341 assert not_empty
: root
!= null
342 var f
= new OProcess("dot", "-Txlib")
343 f
.write
"digraph \{\n"
344 dot_down
(root
.as(not null), f
)
349 # Translate the tree in dot format starting from `node`.
350 protected fun dot_down
(node
: N
, f
: OProcess) do
351 if node
.left
!= null then dot_down
(node
.left
.as(not null), f
)
353 if node
.right
!= null then dot_down
(node
.right
.as(not null), f
)
358 # var tree = new BinTreeMap[Int, String]
359 # assert tree.length == 0
360 # for i in [4, 2, 1, 5, 3] do tree[i] = "n{i}"
361 # assert tree.length == 5
362 redef fun length
do return len
364 # Nodes are iterated in the same order in which they were added to the tree.
367 # var tree = new BinTreeMap[Int, String]
368 # for i in [4, 2, 1, 5, 3] do tree[i] = "n{i}"
369 # var keys = new Array[Int]
370 # for k, v in tree do
373 # assert keys == [4, 2, 1, 5, 3]
374 redef fun iterator
do return new BinTreeMapIterator[K
, E
](self)
377 # TreeNode used by BinTree
378 class BinTreeNode[K
: Comparable, E
]
381 private var prev
: nullable BinTreeNode[K
, E
] = null
382 private var next
: nullable BinTreeNode[K
, E
] = null
384 redef type N
: BinTreeNode[K
, E
]
386 private var left_node
: nullable N
= null
388 # `left` tree node child (null if node has no left child)
389 fun left
: nullable N
do return left_node
391 # set `left` child for this node (or null if left no child)
392 # ENSURE: node.key < key (only if node != null)
393 fun left
=(node
: nullable N
) do
394 #assert node != null implies node.key < key
398 private var right_node
: nullable N
= null
400 # `right` tree node child (null if node has no right child)
401 fun right
: nullable N
do return right_node
403 # set `right` child for this node (or null if right no child)
404 # ENSURE: node.key < key (only if node != null)
405 fun right
=(node
: nullable N
) do
406 #assert node != null implies node.key > key
410 # `parent` of the `parent` of this node (null if root)
411 fun grandparent
: nullable N
do
412 if parent
== null then
419 # Other child of the `grandparent`
420 # `left` or `right` depends on the position of the current node against its parent
421 fun uncle
: nullable N
do
426 if parent
== g
.left
then
434 # Other child of the parent
435 # `left` or `right` depends on the position of the current node against its parent
436 fun sibling
: nullable N
do
437 if parent
== null then
439 else if self == parent
.left
then
441 else if self == parent
.right
then
448 redef fun to_s
do return "\{{key}: {value or else ""}\}"
451 private class BinTreeMapIterator[K
: Comparable, E
]
452 super MapIterator[K
, E
]
454 var tree
: BinTreeMap[K
, E
]
455 var current
: nullable BinTreeNode[K
, E
] = null
457 init do current
= tree
.first_node
459 redef fun is_ok
do return not current
== null
460 redef fun next
do current
= current
.next
461 redef fun item
do return current
.value
462 redef fun key
do do return current
.key