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"""
Segment_tree creates a segment tree with a given array and function,
allowing queries to be done later in log(N) time
function takes 2 values and returns a same type value
"""
fromcollections.abcimportSequence
fromqueueimportQueue
classSegmentTreeNode:
def__init__(self, start, end, val, left=None, right=None):
self.start=start
self.end=end
self.val=val
self.mid= (start+end) //2
self.left=left
self.right=right
def__repr__(self):
returnf"SegmentTreeNode(start={self.start}, end={self.end}, val={self.val})"
classSegmentTree:
"""
>>> import operator
>>> num_arr = SegmentTree([2, 1, 5, 3, 4], operator.add)
>>> tuple(num_arr.traverse()) # doctest: +NORMALIZE_WHITESPACE
(SegmentTreeNode(start=0, end=4, val=15),
SegmentTreeNode(start=0, end=2, val=8),
SegmentTreeNode(start=3, end=4, val=7),
SegmentTreeNode(start=0, end=1, val=3),
SegmentTreeNode(start=2, end=2, val=5),
SegmentTreeNode(start=3, end=3, val=3),
SegmentTreeNode(start=4, end=4, val=4),
SegmentTreeNode(start=0, end=0, val=2),
SegmentTreeNode(start=1, end=1, val=1))
>>>
>>> num_arr.update(1, 5)
>>> tuple(num_arr.traverse()) # doctest: +NORMALIZE_WHITESPACE
(SegmentTreeNode(start=0, end=4, val=19),
SegmentTreeNode(start=0, end=2, val=12),
SegmentTreeNode(start=3, end=4, val=7),
SegmentTreeNode(start=0, end=1, val=7),
SegmentTreeNode(start=2, end=2, val=5),
SegmentTreeNode(start=3, end=3, val=3),
SegmentTreeNode(start=4, end=4, val=4),
SegmentTreeNode(start=0, end=0, val=2),
SegmentTreeNode(start=1, end=1, val=5))
>>>
>>> num_arr.query_range(3, 4)
7
>>> num_arr.query_range(2, 2)
5
>>> num_arr.query_range(1, 3)
13
>>>
>>> max_arr = SegmentTree([2, 1, 5, 3, 4], max)
>>> for node in max_arr.traverse():
... print(node)
...
SegmentTreeNode(start=0, end=4, val=5)
SegmentTreeNode(start=0, end=2, val=5)
SegmentTreeNode(start=3, end=4, val=4)
SegmentTreeNode(start=0, end=1, val=2)
SegmentTreeNode(start=2, end=2, val=5)
SegmentTreeNode(start=3, end=3, val=3)
SegmentTreeNode(start=4, end=4, val=4)
SegmentTreeNode(start=0, end=0, val=2)
SegmentTreeNode(start=1, end=1, val=1)
>>>
>>> max_arr.update(1, 5)
>>> for node in max_arr.traverse():
... print(node)
...
SegmentTreeNode(start=0, end=4, val=5)
SegmentTreeNode(start=0, end=2, val=5)
SegmentTreeNode(start=3, end=4, val=4)
SegmentTreeNode(start=0, end=1, val=5)
SegmentTreeNode(start=2, end=2, val=5)
SegmentTreeNode(start=3, end=3, val=3)
SegmentTreeNode(start=4, end=4, val=4)
SegmentTreeNode(start=0, end=0, val=2)
SegmentTreeNode(start=1, end=1, val=5)
>>>
>>> max_arr.query_range(3, 4)
4
>>> max_arr.query_range(2, 2)
5
>>> max_arr.query_range(1, 3)
5
>>>
>>> min_arr = SegmentTree([2, 1, 5, 3, 4], min)
>>> for node in min_arr.traverse():
... print(node)
...
SegmentTreeNode(start=0, end=4, val=1)
SegmentTreeNode(start=0, end=2, val=1)
SegmentTreeNode(start=3, end=4, val=3)
SegmentTreeNode(start=0, end=1, val=1)
SegmentTreeNode(start=2, end=2, val=5)
SegmentTreeNode(start=3, end=3, val=3)
SegmentTreeNode(start=4, end=4, val=4)
SegmentTreeNode(start=0, end=0, val=2)
SegmentTreeNode(start=1, end=1, val=1)
>>>
>>> min_arr.update(1, 5)
>>> for node in min_arr.traverse():
... print(node)
...
SegmentTreeNode(start=0, end=4, val=2)
SegmentTreeNode(start=0, end=2, val=2)
SegmentTreeNode(start=3, end=4, val=3)
SegmentTreeNode(start=0, end=1, val=2)
SegmentTreeNode(start=2, end=2, val=5)
SegmentTreeNode(start=3, end=3, val=3)
SegmentTreeNode(start=4, end=4, val=4)
SegmentTreeNode(start=0, end=0, val=2)
SegmentTreeNode(start=1, end=1, val=5)
>>>
>>> min_arr.query_range(3, 4)
3
>>> min_arr.query_range(2, 2)
5
>>> min_arr.query_range(1, 3)
3
>>>
"""
def__init__(self, collection: Sequence, function):
self.collection=collection
self.fn=function
ifself.collection:
self.root=self._build_tree(0, len(collection) -1)
defupdate(self, i, val):
"""
Update an element in log(N) time
:param i: position to be update
:param val: new value
>>> import operator
>>> num_arr = SegmentTree([2, 1, 5, 3, 4], operator.add)
>>> num_arr.update(1, 5)
>>> num_arr.query_range(1, 3)
13
"""
self._update_tree(self.root, i, val)
defquery_range(self, i, j):
"""
Get range query value in log(N) time
:param i: left element index
:param j: right element index
:return: element combined in the range [i, j]
>>> import operator
>>> num_arr = SegmentTree([2, 1, 5, 3, 4], operator.add)
>>> num_arr.update(1, 5)
>>> num_arr.query_range(3, 4)
7
>>> num_arr.query_range(2, 2)
5
>>> num_arr.query_range(1, 3)
13
>>>
"""
returnself._query_range(self.root, i, j)
def_build_tree(self, start, end):
ifstart==end:
returnSegmentTreeNode(start, end, self.collection[start])
mid= (start+end) //2
left=self._build_tree(start, mid)
right=self._build_tree(mid+1, end)
returnSegmentTreeNode(start, end, self.fn(left.val, right.val), left, right)
def_update_tree(self, node, i, val):
ifnode.start==iandnode.end==i:
node.val=val
return
ifi<=node.mid:
self._update_tree(node.left, i, val)
else:
self._update_tree(node.right, i, val)
node.val=self.fn(node.left.val, node.right.val)
def_query_range(self, node, i, j):
ifnode.start==iandnode.end==j:
returnnode.val
ifi<=node.mid:
ifj<=node.mid:
# range in left child tree
returnself._query_range(node.left, i, j)
else:
# range in left child tree and right child tree
returnself.fn(
self._query_range(node.left, i, node.mid),
self._query_range(node.right, node.mid+1, j),
)
else:
# range in right child tree
returnself._query_range(node.right, i, j)
deftraverse(self):
ifself.rootisnotNone:
queue=Queue()
queue.put(self.root)
whilenotqueue.empty():
node=queue.get()
yieldnode
ifnode.leftisnotNone:
queue.put(node.left)
ifnode.rightisnotNone:
queue.put(node.right)
if__name__=="__main__":
importoperator
forfnin [operator.add, max, min]:
print("*"*50)
arr=SegmentTree([2, 1, 5, 3, 4], fn)
fornodeinarr.traverse():
print(node)
print()
arr.update(1, 5)
fornodeinarr.traverse():
print(node)
print()
print(arr.query_range(3, 4)) # 7
print(arr.query_range(2, 2)) # 5
print(arr.query_range(1, 3)) # 13
print()