From e94b42d0f2b704cd8e293ac372d4980061d5a870 Mon Sep 17 00:00:00 2001
From: lanzhiwang <hzhilamp@163.com>
Date: Sat, 25 Jan 2020 22:23:30 +0800
Subject: [PATCH 01/13] enhanced segment tree implementation and more pythonic

enhanced segment tree implementation and more pythonic
---
 .../binary_tree/segment_tree_other.py         | 249 ++++++++++++++++++
 1 file changed, 249 insertions(+)
 create mode 100644 data_structures/binary_tree/segment_tree_other.py

diff --git a/data_structures/binary_tree/segment_tree_other.py b/data_structures/binary_tree/segment_tree_other.py
new file mode 100644
index 000000000000..b0cf9da380fb
--- /dev/null
+++ b/data_structures/binary_tree/segment_tree_other.py
@@ -0,0 +1,249 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+
+from queue import Queue
+
+
+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 NumArray:
+    def __init__(self, nums):
+        self.nums = nums
+        if self.nums:
+            self.root = self._build_tree(0, len(nums) - 1)
+
+    def update(self, i, val):
+        self._update_tree(self.root, i, val)
+
+    def sum_range(self, i, j):
+        return self._sum_range(self.root, i, j)
+
+    def _build_tree(self, start, end):
+        if start == end:
+            return SegmentTreeNode(start, end, self.nums[start])
+        mid = (start + end) // 2
+        left = self._build_tree(start, mid)
+        right = self._build_tree(mid + 1, end)
+        return SegmentTreeNode(start, end, left.val + right.val, left, right)
+
+    def _update_tree(self, root, i, val):
+        if root.start == i and root.end == i:
+            root.val = val
+            return
+        if i <= root.mid:
+            self._update_tree(root.left, i, val)
+        else:
+            self._update_tree(root.right, i, val)
+        root.val = root.left.val + root.right.val
+
+    def _sum_range(self, root, i, j):
+        if root.start == i and root.end == j:
+            return root.val
+        """
+         [i, j] [i, j] [i, j]
+        [start mid] [mid+1 end]
+        """
+        if j <= root.mid:
+            return self._sum_range(root.left, i, j)
+        elif i > root.mid:
+            return self._sum_range(root.right, i, j)
+        else:
+            return self._sum_range(root.left, i, root.mid) + self._sum_range(root.right, root.mid + 1, j)
+
+    def traverse(self):
+        result = []
+        if self.root is not None:
+            queue = Queue()
+            queue.put(self.root)
+            while not queue.empty():
+                node = queue.get()
+                result.append(node)
+
+                if node.left is not None:
+                    queue.put(node.left)
+
+                if node.right is not None:
+                    queue.put(node.right)
+            return result
+
+
+class MaxArray:
+    def __init__(self, nums):
+        self.nums = nums
+        if self.nums:
+            self.root = self._build_tree(0, len(nums) - 1)
+
+    def update(self, i, val):
+        self._update_tree(self.root, i, val)
+
+    def max_range(self, i, j):
+        return self._max_range(self.root, i, j)
+
+    def _build_tree(self, start, end):
+        if start == end:
+            return SegmentTreeNode(start, end, self.nums[start])
+        mid = (start + end) // 2
+        left = self._build_tree(start, mid)
+        right = self._build_tree(mid + 1, end)
+        return SegmentTreeNode(start, end, max([left.val, right.val]), left, right)
+
+    def _update_tree(self, root, i, val):
+        if root.start == i and root.end == i:
+            root.val = val
+            return
+        if i <= root.mid:
+            self._update_tree(root.left, i, val)
+        else:
+            self._update_tree(root.right, i, val)
+        root.val = max([root.left.val, root.right.val])
+
+    def _max_range(self, root, i, j):
+        if root.start == i and root.end == j:
+            return root.val
+        """
+         [i, j] [i, j] [i, j]
+        [start mid] [mid+1 end]
+        """
+        if j <= root.mid:
+            return self._max_range(root.left, i, j)
+        elif i > root.mid:
+            return self._max_range(root.right, i, j)
+        else:
+            return max([self._max_range(root.left, i, root.mid), self._max_range(root.right, root.mid + 1, j)])
+
+    def traverse(self):
+        result = []
+        if self.root is not None:
+            queue = Queue()
+            queue.put(self.root)
+            while not queue.empty():
+                node = queue.get()
+                result.append(node)
+
+                if node.left is not None:
+                    queue.put(node.left)
+
+                if node.right is not None:
+                    queue.put(node.right)
+            return result
+
+
+class MinArray:
+    def __init__(self, nums):
+        self.nums = nums
+        if self.nums:
+            self.root = self._build_tree(0, len(nums) - 1)
+
+    def update(self, i, val):
+        self._update_tree(self.root, i, val)
+
+    def min_range(self, i, j):
+        return self._min_range(self.root, i, j)
+
+    def _build_tree(self, start, end):
+        if start == end:
+            return SegmentTreeNode(start, end, self.nums[start])
+        mid = (start + end) // 2
+        left = self._build_tree(start, mid)
+        right = self._build_tree(mid + 1, end)
+        return SegmentTreeNode(start, end, min([left.val, right.val]), left, right)
+
+    def _update_tree(self, root, i, val):
+        if root.start == i and root.end == i:
+            root.val = val
+            return
+        if i <= root.mid:
+            self._update_tree(root.left, i, val)
+        else:
+            self._update_tree(root.right, i, val)
+        root.val = min([root.left.val, root.right.val])
+
+    def _min_range(self, root, i, j):
+        if root.start == i and root.end == j:
+            return root.val
+        """
+         [i, j] [i, j] [i, j]
+        [start mid] [mid+1 end]
+        """
+        if j <= root.mid:
+            return self._min_range(root.left, i, j)
+        elif i > root.mid:
+            return self._min_range(root.right, i, j)
+        else:
+            return min([self._min_range(root.left, i, root.mid), self._min_range(root.right, root.mid + 1, j)])
+
+    def traverse(self):
+        result = []
+        if self.root is not None:
+            queue = Queue()
+            queue.put(self.root)
+            while not queue.empty():
+                node = queue.get()
+                result.append(node)
+
+                if node.left is not None:
+                    queue.put(node.left)
+
+                if node.right is not None:
+                    queue.put(node.right)
+            return result
+
+
+if __name__ == '__main__':
+    print('求和线段树')
+    num_arr = NumArray([2, 1, 5, 3, 4])
+    for node in num_arr.traverse():
+        print(node)
+    print()
+
+    num_arr.update(1, 5)
+    for node in num_arr.traverse():
+        print(node)
+    print()
+
+    print(num_arr.sum_range(3, 4))  # 7
+    print(num_arr.sum_range(2, 2))  # 5
+    print(num_arr.sum_range(1, 3))  # 13
+
+    print()
+    print('求最大值线段树')
+    max_arr = MaxArray([2, 1, 5, 3, 4])
+    for node in max_arr.traverse():
+        print(node)
+    print()
+
+    max_arr.update(1, 5)
+    for node in max_arr.traverse():
+        print(node)
+    print()
+
+    print(max_arr.max_range(3, 4))  # 4
+    print(max_arr.max_range(2, 2))  # 5
+    print(max_arr.max_range(1, 3))  # 5
+
+    print()
+    print('求最小值线段树')
+    min_arr = MinArray([2, 1, 5, 3, 4])
+    for node in min_arr.traverse():
+        print(node)
+    print()
+
+    min_arr.update(1, 5)
+    for node in min_arr.traverse():
+        print(node)
+    print()
+
+    print(min_arr.min_range(3, 4))  # 3
+    print(min_arr.min_range(2, 2))  # 5
+    print(min_arr.min_range(1, 3))  # 3

From 2880d47ce9bcb396f32a794e3aabee26d3709eaf Mon Sep 17 00:00:00 2001
From: lanzhiwang <hzhilamp@163.com>
Date: Sun, 26 Jan 2020 10:08:50 +0800
Subject: [PATCH 02/13] add doctests for segment tree

---
 .../binary_tree/segment_tree_other.py         | 111 ++++++++++++++++++
 1 file changed, 111 insertions(+)

diff --git a/data_structures/binary_tree/segment_tree_other.py b/data_structures/binary_tree/segment_tree_other.py
index b0cf9da380fb..496a415cbc1c 100644
--- a/data_structures/binary_tree/segment_tree_other.py
+++ b/data_structures/binary_tree/segment_tree_other.py
@@ -18,6 +18,43 @@ def __str__(self):
 
 
 class NumArray:
+    """NumArray is sum tree of object. Parent node is sum of two child nodes.
+    >>> num_arr = NumArray([2, 1, 5, 3, 4])
+    >>> 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.sum_range(3, 4)
+    7
+    >>> num_arr.sum_range(2, 2)
+    5
+    >>> num_arr.sum_range(1, 3)
+    13
+    >>>
+    """
     def __init__(self, nums):
         self.nums = nums
         if self.nums:
@@ -79,6 +116,43 @@ def traverse(self):
 
 
 class MaxArray:
+    """MaxArray is max tree of object. Parent node is max of two child nodes.
+    >>> max_arr = MaxArray([2, 1, 5, 3, 4])
+    >>> 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.max_range(3, 4)
+    4
+    >>> max_arr.max_range(2, 2)
+    5
+    >>> max_arr.max_range(1, 3)
+    5
+    >>>
+    """
     def __init__(self, nums):
         self.nums = nums
         if self.nums:
@@ -140,6 +214,43 @@ def traverse(self):
 
 
 class MinArray:
+    """MinArray is min tree of object. Parent node is min of two child nodes.
+    >>> min_arr = MinArray([2, 1, 5, 3, 4])
+    >>> 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.min_range(3, 4)
+    3
+    >>> min_arr.min_range(2, 2)
+    5
+    >>> min_arr.min_range(1, 3)
+    3
+    >>>
+    """
     def __init__(self, nums):
         self.nums = nums
         if self.nums:

From 030a55d9d84313fc6963a19f94793a017bc2ef9b Mon Sep 17 00:00:00 2001
From: lanzhiwang <hzhilamp@163.com>
Date: Sun, 26 Jan 2020 10:22:16 +0800
Subject: [PATCH 03/13] add type annotations

---
 .../binary_tree/segment_tree_other.py         | 31 ++++++++++---------
 1 file changed, 16 insertions(+), 15 deletions(-)

diff --git a/data_structures/binary_tree/segment_tree_other.py b/data_structures/binary_tree/segment_tree_other.py
index 496a415cbc1c..3d2c5b86e3ca 100644
--- a/data_structures/binary_tree/segment_tree_other.py
+++ b/data_structures/binary_tree/segment_tree_other.py
@@ -2,6 +2,7 @@
 # -*- coding: utf-8 -*-
 
 from queue import Queue
+from collections.abc import Sequence
 
 
 class SegmentTreeNode(object):
@@ -55,10 +56,10 @@ class NumArray:
     13
     >>>
     """
-    def __init__(self, nums):
-        self.nums = nums
-        if self.nums:
-            self.root = self._build_tree(0, len(nums) - 1)
+    def __init__(self, collection: Sequence):
+        self.collection = collection
+        if self.collection:
+            self.root = self._build_tree(0, len(collection) - 1)
 
     def update(self, i, val):
         self._update_tree(self.root, i, val)
@@ -68,7 +69,7 @@ def sum_range(self, i, j):
 
     def _build_tree(self, start, end):
         if start == end:
-            return SegmentTreeNode(start, end, self.nums[start])
+            return SegmentTreeNode(start, end, self.collection[start])
         mid = (start + end) // 2
         left = self._build_tree(start, mid)
         right = self._build_tree(mid + 1, end)
@@ -153,10 +154,10 @@ class MaxArray:
     5
     >>>
     """
-    def __init__(self, nums):
-        self.nums = nums
-        if self.nums:
-            self.root = self._build_tree(0, len(nums) - 1)
+    def __init__(self, collection: Sequence):
+        self.collection = collection
+        if self.collection:
+            self.root = self._build_tree(0, len(collection) - 1)
 
     def update(self, i, val):
         self._update_tree(self.root, i, val)
@@ -166,7 +167,7 @@ def max_range(self, i, j):
 
     def _build_tree(self, start, end):
         if start == end:
-            return SegmentTreeNode(start, end, self.nums[start])
+            return SegmentTreeNode(start, end, self.collection[start])
         mid = (start + end) // 2
         left = self._build_tree(start, mid)
         right = self._build_tree(mid + 1, end)
@@ -251,10 +252,10 @@ class MinArray:
     3
     >>>
     """
-    def __init__(self, nums):
-        self.nums = nums
-        if self.nums:
-            self.root = self._build_tree(0, len(nums) - 1)
+    def __init__(self, collection: Sequence):
+        self.collection = collection
+        if self.collection:
+            self.root = self._build_tree(0, len(collection) - 1)
 
     def update(self, i, val):
         self._update_tree(self.root, i, val)
@@ -264,7 +265,7 @@ def min_range(self, i, j):
 
     def _build_tree(self, start, end):
         if start == end:
-            return SegmentTreeNode(start, end, self.nums[start])
+            return SegmentTreeNode(start, end, self.collection[start])
         mid = (start + end) // 2
         left = self._build_tree(start, mid)
         right = self._build_tree(mid + 1, end)

From e0c1b062a3587a2a700a5d04f110a62e486cafb8 Mon Sep 17 00:00:00 2001
From: lanzhiwang <hzhilamp@163.com>
Date: Sun, 26 Jan 2020 18:56:59 +0800
Subject: [PATCH 04/13] unified processing sum min max segment tre

---
 .../binary_tree/segment_tree_other.py         | 243 ++++--------------
 1 file changed, 48 insertions(+), 195 deletions(-)

diff --git a/data_structures/binary_tree/segment_tree_other.py b/data_structures/binary_tree/segment_tree_other.py
index 3d2c5b86e3ca..69903d38ccc4 100644
--- a/data_structures/binary_tree/segment_tree_other.py
+++ b/data_structures/binary_tree/segment_tree_other.py
@@ -1,5 +1,10 @@
 #!/usr/bin/env python3
 # -*- coding: utf-8 -*-
+"""
+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
@@ -18,9 +23,10 @@ def __str__(self):
         return 'val: %s, start: %s, end: %s' % (self.val, self.start, self.end)
 
 
-class NumArray:
-    """NumArray is sum tree of object. Parent node is sum of two child nodes.
-    >>> num_arr = NumArray([2, 1, 5, 3, 4])
+class SegmentTree(object):
+    """
+    >>> import operator
+    >>> num_arr = SegmentTree([2, 1, 5, 3, 4], operator.add)
     >>> for node in num_arr.traverse():
     ...     print(node)
     ...
@@ -48,77 +54,14 @@ class NumArray:
     val: 2, start: 0, end: 0
     val: 5, start: 1, end: 1
     >>>
-    >>> num_arr.sum_range(3, 4)
+    >>> num_arr.query_range(3, 4)
     7
-    >>> num_arr.sum_range(2, 2)
+    >>> num_arr.query_range(2, 2)
     5
-    >>> num_arr.sum_range(1, 3)
+    >>> num_arr.query_range(1, 3)
     13
     >>>
-    """
-    def __init__(self, collection: Sequence):
-        self.collection = collection
-        if self.collection:
-            self.root = self._build_tree(0, len(collection) - 1)
-
-    def update(self, i, val):
-        self._update_tree(self.root, i, val)
-
-    def sum_range(self, i, j):
-        return self._sum_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, left.val + right.val, left, right)
-
-    def _update_tree(self, root, i, val):
-        if root.start == i and root.end == i:
-            root.val = val
-            return
-        if i <= root.mid:
-            self._update_tree(root.left, i, val)
-        else:
-            self._update_tree(root.right, i, val)
-        root.val = root.left.val + root.right.val
-
-    def _sum_range(self, root, i, j):
-        if root.start == i and root.end == j:
-            return root.val
-        """
-         [i, j] [i, j] [i, j]
-        [start mid] [mid+1 end]
-        """
-        if j <= root.mid:
-            return self._sum_range(root.left, i, j)
-        elif i > root.mid:
-            return self._sum_range(root.right, i, j)
-        else:
-            return self._sum_range(root.left, i, root.mid) + self._sum_range(root.right, root.mid + 1, j)
-
-    def traverse(self):
-        result = []
-        if self.root is not None:
-            queue = Queue()
-            queue.put(self.root)
-            while not queue.empty():
-                node = queue.get()
-                result.append(node)
-
-                if node.left is not None:
-                    queue.put(node.left)
-
-                if node.right is not None:
-                    queue.put(node.right)
-            return result
-
-
-class MaxArray:
-    """MaxArray is max tree of object. Parent node is max of two child nodes.
-    >>> max_arr = MaxArray([2, 1, 5, 3, 4])
+    >>> max_arr = SegmentTree([2, 1, 5, 3, 4], max)
     >>> for node in max_arr.traverse():
     ...     print(node)
     ...
@@ -146,77 +89,14 @@ class MaxArray:
     val: 2, start: 0, end: 0
     val: 5, start: 1, end: 1
     >>>
-    >>> max_arr.max_range(3, 4)
+    >>> max_arr.query_range(3, 4)
     4
-    >>> max_arr.max_range(2, 2)
+    >>> max_arr.query_range(2, 2)
     5
-    >>> max_arr.max_range(1, 3)
+    >>> max_arr.query_range(1, 3)
     5
     >>>
-    """
-    def __init__(self, collection: Sequence):
-        self.collection = collection
-        if self.collection:
-            self.root = self._build_tree(0, len(collection) - 1)
-
-    def update(self, i, val):
-        self._update_tree(self.root, i, val)
-
-    def max_range(self, i, j):
-        return self._max_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, max([left.val, right.val]), left, right)
-
-    def _update_tree(self, root, i, val):
-        if root.start == i and root.end == i:
-            root.val = val
-            return
-        if i <= root.mid:
-            self._update_tree(root.left, i, val)
-        else:
-            self._update_tree(root.right, i, val)
-        root.val = max([root.left.val, root.right.val])
-
-    def _max_range(self, root, i, j):
-        if root.start == i and root.end == j:
-            return root.val
-        """
-         [i, j] [i, j] [i, j]
-        [start mid] [mid+1 end]
-        """
-        if j <= root.mid:
-            return self._max_range(root.left, i, j)
-        elif i > root.mid:
-            return self._max_range(root.right, i, j)
-        else:
-            return max([self._max_range(root.left, i, root.mid), self._max_range(root.right, root.mid + 1, j)])
-
-    def traverse(self):
-        result = []
-        if self.root is not None:
-            queue = Queue()
-            queue.put(self.root)
-            while not queue.empty():
-                node = queue.get()
-                result.append(node)
-
-                if node.left is not None:
-                    queue.put(node.left)
-
-                if node.right is not None:
-                    queue.put(node.right)
-            return result
-
-
-class MinArray:
-    """MinArray is min tree of object. Parent node is min of two child nodes.
-    >>> min_arr = MinArray([2, 1, 5, 3, 4])
+    >>> min_arr = SegmentTree([2, 1, 5, 3, 4], min)
     >>> for node in min_arr.traverse():
     ...     print(node)
     ...
@@ -244,24 +124,26 @@ class MinArray:
     val: 2, start: 0, end: 0
     val: 5, start: 1, end: 1
     >>>
-    >>> min_arr.min_range(3, 4)
+    >>> min_arr.query_range(3, 4)
     3
-    >>> min_arr.min_range(2, 2)
+    >>> min_arr.query_range(2, 2)
     5
-    >>> min_arr.min_range(1, 3)
+    >>> min_arr.query_range(1, 3)
     3
     >>>
+
     """
-    def __init__(self, collection: Sequence):
+    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):
         self._update_tree(self.root, i, val)
 
-    def min_range(self, i, j):
-        return self._min_range(self.root, i, j)
+    def query_range(self, i, j):
+        return self._query_range(self.root, i, j)
 
     def _build_tree(self, start, end):
         if start == end:
@@ -269,7 +151,7 @@ def _build_tree(self, start, end):
         mid = (start + end) // 2
         left = self._build_tree(start, mid)
         right = self._build_tree(mid + 1, end)
-        return SegmentTreeNode(start, end, min([left.val, right.val]), left, right)
+        return SegmentTreeNode(start, end, self.fn(left.val, right.val), left, right)
 
     def _update_tree(self, root, i, val):
         if root.start == i and root.end == i:
@@ -279,9 +161,9 @@ def _update_tree(self, root, i, val):
             self._update_tree(root.left, i, val)
         else:
             self._update_tree(root.right, i, val)
-        root.val = min([root.left.val, root.right.val])
+        root.val = self.fn(root.left.val, root.right.val)
 
-    def _min_range(self, root, i, j):
+    def _query_range(self, root, i, j):
         if root.start == i and root.end == j:
             return root.val
         """
@@ -289,11 +171,11 @@ def _min_range(self, root, i, j):
         [start mid] [mid+1 end]
         """
         if j <= root.mid:
-            return self._min_range(root.left, i, j)
+            return self._query_range(root.left, i, j)
         elif i > root.mid:
-            return self._min_range(root.right, i, j)
+            return self._query_range(root.right, i, j)
         else:
-            return min([self._min_range(root.left, i, root.mid), self._min_range(root.right, root.mid + 1, j)])
+            return self.fn(self._query_range(root.left, i, root.mid), self._query_range(root.right, root.mid + 1, j))
 
     def traverse(self):
         result = []
@@ -313,49 +195,20 @@ def traverse(self):
 
 
 if __name__ == '__main__':
-    print('求和线段树')
-    num_arr = NumArray([2, 1, 5, 3, 4])
-    for node in num_arr.traverse():
-        print(node)
-    print()
-
-    num_arr.update(1, 5)
-    for node in num_arr.traverse():
-        print(node)
-    print()
-
-    print(num_arr.sum_range(3, 4))  # 7
-    print(num_arr.sum_range(2, 2))  # 5
-    print(num_arr.sum_range(1, 3))  # 13
-
-    print()
-    print('求最大值线段树')
-    max_arr = MaxArray([2, 1, 5, 3, 4])
-    for node in max_arr.traverse():
-        print(node)
-    print()
-
-    max_arr.update(1, 5)
-    for node in max_arr.traverse():
-        print(node)
-    print()
-
-    print(max_arr.max_range(3, 4))  # 4
-    print(max_arr.max_range(2, 2))  # 5
-    print(max_arr.max_range(1, 3))  # 5
-
-    print()
-    print('求最小值线段树')
-    min_arr = MinArray([2, 1, 5, 3, 4])
-    for node in min_arr.traverse():
-        print(node)
-    print()
-
-    min_arr.update(1, 5)
-    for node in min_arr.traverse():
-        print(node)
-    print()
-
-    print(min_arr.min_range(3, 4))  # 3
-    print(min_arr.min_range(2, 2))  # 5
-    print(min_arr.min_range(1, 3))  # 3
+    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()

From 1e2b002458c3b58aed1226b42eec7c644781de1f Mon Sep 17 00:00:00 2001
From: lanzhiwang <hzhilamp@163.com>
Date: Mon, 27 Jan 2020 14:29:13 +0800
Subject: [PATCH 05/13] delete source encoding in segment tree

---
 data_structures/binary_tree/segment_tree_other.py | 2 --
 1 file changed, 2 deletions(-)

diff --git a/data_structures/binary_tree/segment_tree_other.py b/data_structures/binary_tree/segment_tree_other.py
index 69903d38ccc4..d743ac8a7a3f 100644
--- a/data_structures/binary_tree/segment_tree_other.py
+++ b/data_structures/binary_tree/segment_tree_other.py
@@ -1,5 +1,3 @@
-#!/usr/bin/env python3
-# -*- coding: utf-8 -*-
 """
 Segment_tree creates a segment tree with a given array and function,
 allowing queries to be done later in log(N) time

From 78134bf1d1009087e236019e44866ac69b08baca Mon Sep 17 00:00:00 2001
From: lanzhiwang <hzhilamp@163.com>
Date: Mon, 27 Jan 2020 18:58:15 +0800
Subject: [PATCH 06/13] use a generator function instead of returning

---
 data_structures/binary_tree/segment_tree_other.py | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/data_structures/binary_tree/segment_tree_other.py b/data_structures/binary_tree/segment_tree_other.py
index d743ac8a7a3f..822b65808246 100644
--- a/data_structures/binary_tree/segment_tree_other.py
+++ b/data_structures/binary_tree/segment_tree_other.py
@@ -176,20 +176,18 @@ def _query_range(self, root, i, j):
             return self.fn(self._query_range(root.left, i, root.mid), self._query_range(root.right, root.mid + 1, j))
 
     def traverse(self):
-        result = []
         if self.root is not None:
             queue = Queue()
             queue.put(self.root)
             while not queue.empty():
                 node = queue.get()
-                result.append(node)
+                yield node
 
                 if node.left is not None:
                     queue.put(node.left)
 
                 if node.right is not None:
                     queue.put(node.right)
-            return result
 
 
 if __name__ == '__main__':

From ac028db7cdcee3855712cba35c856b78b8559218 Mon Sep 17 00:00:00 2001
From: lanzhiwang <hzhilamp@163.com>
Date: Mon, 27 Jan 2020 19:30:28 +0800
Subject: [PATCH 07/13] add doctests for methods

---
 .../binary_tree/segment_tree_other.py         | 23 +++++++++++++++++++
 1 file changed, 23 insertions(+)

diff --git a/data_structures/binary_tree/segment_tree_other.py b/data_structures/binary_tree/segment_tree_other.py
index 822b65808246..6f14fa31e72d 100644
--- a/data_structures/binary_tree/segment_tree_other.py
+++ b/data_structures/binary_tree/segment_tree_other.py
@@ -138,9 +138,32 @@ def __init__(self, collection: Sequence, function):
             self.root = self._build_tree(0, len(collection) - 1)
 
     def update(self, i, val):
+        """
+        update value in collection
+        :param i: index of collection
+        :param val: new value
+        :return:
+        >>> num_arr = SegmentTree([2, 1, 5, 3, 4], operator.add)
+        >>> num_arr.update(1, 5)
+        """
         self._update_tree(self.root, i, val)
 
     def query_range(self, i, j):
+        """
+        Sum, Max, Min operation in intervals i and j([i, j])
+        :param i:  left index
+        :param j:  right index
+        :return:  Sum, Max, Min
+        >>> 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):

From 6928b3287fac1598a96a1e31135e61bbae0e7187 Mon Sep 17 00:00:00 2001
From: lanzhiwang <hzhilamp@163.com>
Date: Mon, 27 Jan 2020 19:45:26 +0800
Subject: [PATCH 08/13] add doctests for methods

---
 data_structures/binary_tree/segment_tree_other.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/data_structures/binary_tree/segment_tree_other.py b/data_structures/binary_tree/segment_tree_other.py
index 6f14fa31e72d..36a1185acb0c 100644
--- a/data_structures/binary_tree/segment_tree_other.py
+++ b/data_structures/binary_tree/segment_tree_other.py
@@ -143,6 +143,7 @@ def update(self, i, val):
         :param i: index of collection
         :param val: new value
         :return:
+        >>> import operator
         >>> num_arr = SegmentTree([2, 1, 5, 3, 4], operator.add)
         >>> num_arr.update(1, 5)
         """
@@ -154,6 +155,7 @@ def query_range(self, i, j):
         :param i:  left index
         :param j:  right index
         :return:  Sum, Max, Min
+        >>> import operator
         >>> num_arr = SegmentTree([2, 1, 5, 3, 4], operator.add)
         >>> num_arr.update(1, 5)
         >>> num_arr.query_range(3, 4)

From 0508a9914b0c1d3d344ca274675e346d2861f192 Mon Sep 17 00:00:00 2001
From: lanzhiwang <hzhilamp@163.com>
Date: Wed, 29 Jan 2020 14:12:07 +0800
Subject: [PATCH 09/13] add doctests

---
 .../binary_tree/segment_tree_other.py         | 43 +++++++++++++++++++
 1 file changed, 43 insertions(+)

diff --git a/data_structures/binary_tree/segment_tree_other.py b/data_structures/binary_tree/segment_tree_other.py
index 36a1185acb0c..0f45f40f2af2 100644
--- a/data_structures/binary_tree/segment_tree_other.py
+++ b/data_structures/binary_tree/segment_tree_other.py
@@ -169,6 +169,40 @@ def query_range(self, i, j):
         return self._query_range(self.root, i, j)
 
     def _build_tree(self, start, end):
+        r"""build segment tree
+        collection: [2, 1, 5, 3, 4]
+
+        _build_tree(0, 4)  -> 15 = 8 + 7
+            _build_tree(0, 2)  -> 8 = 3 + 5
+                _build_tree(0, 1)  -> 3 = 2 + 1
+                    _build_tree(0, 0) -> 2
+                    _build_tree(1, 1) -> 1
+                _build_tree(2, 2)  -> 5
+            _build_tree(3, 4)  -> 7 = 3 + 4
+                _build_tree(3, 3)  -> 3
+                _build_tree(4, 4)  -> 4
+
+        1. determine the interval of each node
+
+                    0-4(2)
+                   /     \
+               0-2(1)   3-4(3)
+              /    \     / \
+           0-1(0) 2-2  3-3 4-4
+          /  \
+        0-0 1-1
+
+        2. determine the value of each node.
+
+               15
+             /    \
+            8      7
+           / \    / \
+          3   5  3   4
+         / \
+        2   1
+
+        """
         if start == end:
             return SegmentTreeNode(start, end, self.collection[start])
         mid = (start + end) // 2
@@ -177,6 +211,12 @@ def _build_tree(self, start, end):
         return SegmentTreeNode(start, end, self.fn(left.val, right.val), left, right)
 
     def _update_tree(self, root, i, val):
+        r"""update segment tree
+        _update_tree(15, 1, 5)  -> update value of node with value of left child add value of right child
+            _update_tree(8, 1, 5)  -> update value of node with value of left child add value of right child
+                _update_tree(3, 1, 5)  -> update value of node with value of left child add value of right child
+                    _update_tree(1, 1, 5)  -> update value of leaf node
+        """
         if root.start == i and root.end == i:
             root.val = val
             return
@@ -193,10 +233,13 @@ def _query_range(self, root, i, j):
          [i, j] [i, j] [i, j]
         [start mid] [mid+1 end]
         """
+        # interval in left child tree
         if j <= root.mid:
             return self._query_range(root.left, i, j)
+        # interval in child child tree
         elif i > root.mid:
             return self._query_range(root.right, i, j)
+        # interval in left child tree and right child tree
         else:
             return self.fn(self._query_range(root.left, i, root.mid), self._query_range(root.right, root.mid + 1, j))
 

From e6254a9ae6f9f6b459d7e59194ed3c31cdff04ba Mon Sep 17 00:00:00 2001
From: lanzhiwang <hzhilamp@163.com>
Date: Thu, 30 Jan 2020 15:40:50 +0800
Subject: [PATCH 10/13] fix doctest

---
 .../binary_tree/segment_tree_other.py         | 65 ++++---------------
 1 file changed, 11 insertions(+), 54 deletions(-)

diff --git a/data_structures/binary_tree/segment_tree_other.py b/data_structures/binary_tree/segment_tree_other.py
index 0f45f40f2af2..8250c82035b9 100644
--- a/data_structures/binary_tree/segment_tree_other.py
+++ b/data_structures/binary_tree/segment_tree_other.py
@@ -139,22 +139,23 @@ def __init__(self, collection: Sequence, function):
 
     def update(self, i, val):
         """
-        update value in collection
-        :param i: index of collection
+        Update an element in log(N) time
+        :param i: position to be update
         :param val: new value
-        :return:
         >>> import operator
         >>> num_arr = SegmentTree([2, 1, 5, 3, 4], operator.add)
         >>> num_arr.update(1, 5)
+        >>> max_arr.query_range(1, 3)
+        5
         """
         self._update_tree(self.root, i, val)
 
     def query_range(self, i, j):
         """
-        Sum, Max, Min operation in intervals i and j([i, j])
-        :param i:  left index
-        :param j:  right index
-        :return:  Sum, Max, Min
+        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)
@@ -169,40 +170,6 @@ def query_range(self, i, j):
         return self._query_range(self.root, i, j)
 
     def _build_tree(self, start, end):
-        r"""build segment tree
-        collection: [2, 1, 5, 3, 4]
-
-        _build_tree(0, 4)  -> 15 = 8 + 7
-            _build_tree(0, 2)  -> 8 = 3 + 5
-                _build_tree(0, 1)  -> 3 = 2 + 1
-                    _build_tree(0, 0) -> 2
-                    _build_tree(1, 1) -> 1
-                _build_tree(2, 2)  -> 5
-            _build_tree(3, 4)  -> 7 = 3 + 4
-                _build_tree(3, 3)  -> 3
-                _build_tree(4, 4)  -> 4
-
-        1. determine the interval of each node
-
-                    0-4(2)
-                   /     \
-               0-2(1)   3-4(3)
-              /    \     / \
-           0-1(0) 2-2  3-3 4-4
-          /  \
-        0-0 1-1
-
-        2. determine the value of each node.
-
-               15
-             /    \
-            8      7
-           / \    / \
-          3   5  3   4
-         / \
-        2   1
-
-        """
         if start == end:
             return SegmentTreeNode(start, end, self.collection[start])
         mid = (start + end) // 2
@@ -211,12 +178,6 @@ def _build_tree(self, start, end):
         return SegmentTreeNode(start, end, self.fn(left.val, right.val), left, right)
 
     def _update_tree(self, root, i, val):
-        r"""update segment tree
-        _update_tree(15, 1, 5)  -> update value of node with value of left child add value of right child
-            _update_tree(8, 1, 5)  -> update value of node with value of left child add value of right child
-                _update_tree(3, 1, 5)  -> update value of node with value of left child add value of right child
-                    _update_tree(1, 1, 5)  -> update value of leaf node
-        """
         if root.start == i and root.end == i:
             root.val = val
             return
@@ -229,17 +190,13 @@ def _update_tree(self, root, i, val):
     def _query_range(self, root, i, j):
         if root.start == i and root.end == j:
             return root.val
-        """
-         [i, j] [i, j] [i, j]
-        [start mid] [mid+1 end]
-        """
-        # interval in left child tree
+        # range in left child tree
         if j <= root.mid:
             return self._query_range(root.left, i, j)
-        # interval in child child tree
+        # range in child child tree
         elif i > root.mid:
             return self._query_range(root.right, i, j)
-        # interval in left child tree and right child tree
+        # range in left child tree and right child tree
         else:
             return self.fn(self._query_range(root.left, i, root.mid), self._query_range(root.right, root.mid + 1, j))
 

From 4197e8bb7b77801b9db3262ed7677e2399190067 Mon Sep 17 00:00:00 2001
From: lanzhiwang <hzhilamp@163.com>
Date: Thu, 30 Jan 2020 16:46:49 +0800
Subject: [PATCH 11/13] fix doctest

---
 data_structures/binary_tree/segment_tree_other.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/data_structures/binary_tree/segment_tree_other.py b/data_structures/binary_tree/segment_tree_other.py
index 8250c82035b9..2c3c1895fa17 100644
--- a/data_structures/binary_tree/segment_tree_other.py
+++ b/data_structures/binary_tree/segment_tree_other.py
@@ -145,7 +145,7 @@ def update(self, i, val):
         >>> import operator
         >>> num_arr = SegmentTree([2, 1, 5, 3, 4], operator.add)
         >>> num_arr.update(1, 5)
-        >>> max_arr.query_range(1, 3)
+        >>> num_arr.query_range(1, 3)
         5
         """
         self._update_tree(self.root, i, val)

From d3365b152c4e0924925c6af548cf98e715369c87 Mon Sep 17 00:00:00 2001
From: lanzhiwang <hzhilamp@163.com>
Date: Thu, 30 Jan 2020 17:09:35 +0800
Subject: [PATCH 12/13] fix doctest

---
 data_structures/binary_tree/segment_tree_other.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/data_structures/binary_tree/segment_tree_other.py b/data_structures/binary_tree/segment_tree_other.py
index 2c3c1895fa17..7871efd23027 100644
--- a/data_structures/binary_tree/segment_tree_other.py
+++ b/data_structures/binary_tree/segment_tree_other.py
@@ -146,7 +146,7 @@ def update(self, i, val):
         >>> num_arr = SegmentTree([2, 1, 5, 3, 4], operator.add)
         >>> num_arr.update(1, 5)
         >>> num_arr.query_range(1, 3)
-        5
+        13
         """
         self._update_tree(self.root, i, val)
 

From cc9da55b04093cb9713a408e0f87dd275a915921 Mon Sep 17 00:00:00 2001
From: lanzhiwang <hzhilamp@163.com>
Date: Tue, 3 Mar 2020 18:17:24 +0800
Subject: [PATCH 13/13] fix function parameter and fix determine conditions

---
 .../binary_tree/segment_tree_other.py         | 40 ++++++++++---------
 1 file changed, 21 insertions(+), 19 deletions(-)

diff --git a/data_structures/binary_tree/segment_tree_other.py b/data_structures/binary_tree/segment_tree_other.py
index 7871efd23027..93b603cdc7a2 100644
--- a/data_structures/binary_tree/segment_tree_other.py
+++ b/data_structures/binary_tree/segment_tree_other.py
@@ -177,28 +177,30 @@ def _build_tree(self, start, end):
         right = self._build_tree(mid + 1, end)
         return SegmentTreeNode(start, end, self.fn(left.val, right.val), left, right)
 
-    def _update_tree(self, root, i, val):
-        if root.start == i and root.end == i:
-            root.val = val
+    def _update_tree(self, node, i, val):
+        if node.start == i and node.end == i:
+            node.val = val
             return
-        if i <= root.mid:
-            self._update_tree(root.left, i, val)
+        if i <= node.mid:
+            self._update_tree(node.left, i, val)
         else:
-            self._update_tree(root.right, i, val)
-        root.val = self.fn(root.left.val, root.right.val)
-
-    def _query_range(self, root, i, j):
-        if root.start == i and root.end == j:
-            return root.val
-        # range in left child tree
-        if j <= root.mid:
-            return self._query_range(root.left, i, j)
-        # range in child child tree
-        elif i > root.mid:
-            return self._query_range(root.right, i, j)
-        # range in left child tree and right child tree
+            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:
-            return self.fn(self._query_range(root.left, i, root.mid), self._query_range(root.right, root.mid + 1, j))
+            # range in right child tree
+            return self._query_range(node.right, i, j)
 
     def traverse(self):
         if self.root is not None: