enhanced segment tree implementation and more pythonic (#1715)

* enhanced segment tree implementation and more pythonic

enhanced segment tree implementation and more pythonic

* add doctests for segment tree

* add type annotations

* unified processing sum min max segment tre

* delete source encoding in segment tree

* use a generator function instead of returning

* add doctests for methods

* add doctests for methods

* add doctests

* fix doctest

* fix doctest

* fix doctest

* fix function parameter and fix determine conditions

Author: lanzhiwang

data_structures/binary_tree/segment_tree_other.py

@@ -0,0 +1,237 @@
+"""
+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
+"""
+
+from queue import Queue
+from collections.abc import Sequence
+
+
+class SegmentTreeNode(object):
+    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 __str__(self):
+        return 'val: %s, start: %s, end: %s' % (self.val, self.start, self.end)
+
+
+class SegmentTree(object):
+    """
+    >>> import operator
+    >>> num_arr = SegmentTree([2, 1, 5, 3, 4], operator.add)
+    >>> for node in num_arr.traverse():
+    ...     print(node)
+    ...
+    val: 15, start: 0, end: 4
+    val: 8, start: 0, end: 2
+    val: 7, start: 3, end: 4
+    val: 3, start: 0, end: 1
+    val: 5, start: 2, end: 2
+    val: 3, start: 3, end: 3
+    val: 4, start: 4, end: 4
+    val: 2, start: 0, end: 0
+    val: 1, start: 1, end: 1
+    >>>
+    >>> num_arr.update(1, 5)
+    >>> for node in num_arr.traverse():
+    ...     print(node)
+    ...
+    val: 19, start: 0, end: 4
+    val: 12, start: 0, end: 2
+    val: 7, start: 3, end: 4
+    val: 7, start: 0, end: 1
+    val: 5, start: 2, end: 2
+    val: 3, start: 3, end: 3
+    val: 4, start: 4, end: 4
+    val: 2, start: 0, end: 0
+    val: 5, start: 1, end: 1
+    >>>
+    >>> 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)
+    ...
+    val: 5, start: 0, end: 4
+    val: 5, start: 0, end: 2
+    val: 4, start: 3, end: 4
+    val: 2, start: 0, end: 1
+    val: 5, start: 2, end: 2
+    val: 3, start: 3, end: 3
+    val: 4, start: 4, end: 4
+    val: 2, start: 0, end: 0
+    val: 1, start: 1, end: 1
+    >>>
+    >>> max_arr.update(1, 5)
+    >>> for node in max_arr.traverse():
+    ...     print(node)
+    ...
+    val: 5, start: 0, end: 4
+    val: 5, start: 0, end: 2
+    val: 4, start: 3, end: 4
+    val: 5, start: 0, end: 1
+    val: 5, start: 2, end: 2
+    val: 3, start: 3, end: 3
+    val: 4, start: 4, end: 4
+    val: 2, start: 0, end: 0
+    val: 5, start: 1, end: 1
+    >>>
+    >>> 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)
+    ...
+    val: 1, start: 0, end: 4
+    val: 1, start: 0, end: 2
+    val: 3, start: 3, end: 4
+    val: 1, start: 0, end: 1
+    val: 5, start: 2, end: 2
+    val: 3, start: 3, end: 3
+    val: 4, start: 4, end: 4
+    val: 2, start: 0, end: 0
+    val: 1, start: 1, end: 1
+    >>>
+    >>> min_arr.update(1, 5)
+    >>> for node in min_arr.traverse():
+    ...     print(node)
+    ...
+    val: 2, start: 0, end: 4
+    val: 2, start: 0, end: 2
+    val: 3, start: 3, end: 4
+    val: 2, start: 0, end: 1
+    val: 5, start: 2, end: 2
+    val: 3, start: 3, end: 3
+    val: 4, start: 4, end: 4
+    val: 2, start: 0, end: 0
+    val: 5, start: 1, end: 1
+    >>>
+    >>> 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
+        if self.collection:
+            self.root = self._build_tree(0, len(collection) - 1)
+
+    def update(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)
+
+    def query_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
+        >>>
+        """
+        return self._query_range(self.root, i, j)
+
+    def _build_tree(self, start, end):
+        if start == end:
+            return SegmentTreeNode(start, end, self.collection[start])
+        mid = (start + end) // 2
+        left = self._build_tree(start, mid)
+        right = self._build_tree(mid + 1, end)
+        return SegmentTreeNode(start, end, self.fn(left.val, right.val), left, right)
+
+    def _update_tree(self, node, i, val):
+        if node.start == i and node.end == i:
+            node.val = val
+            return
+        if i <= 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):
+        if node.start == i and node.end == j:
+            return node.val
+
+        if i <= node.mid:
+            if j <= node.mid:
+                # range in left child tree
+                return self._query_range(node.left, i, j)
+            else:
+                # range in left child tree and right child tree
+                return self.fn(self._query_range(node.left, i, node.mid), self._query_range(node.right, node.mid + 1, j))
+        else:
+            # range in right child tree
+            return self._query_range(node.right, i, j)
+
+    def traverse(self):
+        if self.root is not None:
+            queue = Queue()
+            queue.put(self.root)
+            while not queue.empty():
+                node = queue.get()
+                yield node
+
+                if node.left is not None:
+                    queue.put(node.left)
+
+                if node.right is not None:
+                    queue.put(node.right)
+
+
+if __name__ == '__main__':
+    import operator
+    for fn in [operator.add, max, min]:
+        print('*' * 50)
+        arr = SegmentTree([2, 1, 5, 3, 4], fn)
+        for node in arr.traverse():
+            print(node)
+        print()
+
+        arr.update(1, 5)
+        for node in arr.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()