Add iterative segment tree (keon#587)

* Added an iterative version of segment tree

* Added test for the iterative segment tree

* Added readme index to iterative segment tree

* Add an additional example and moves examples to the top

README.md

@@ -341,6 +341,7 @@ If you want to uninstall algorithms, it is as simple as:
         - [red_black_tree](algorithms/tree/red_black_tree/red_black_tree.py)
     - [segment_tree](algorithms/tree/segment_tree)
         - [segment_tree](algorithms/tree/segment_tree/segment_tree.py)
+        - [iterative_segment_tree](algorithms/tree/segment_tree/iterative_segment_tree.py)
     - [traversal](algorithms/tree/traversal)
         - [inorder](algorithms/tree/traversal/inorder.py)
         - [level_order](algorithms/tree/traversal/level_order.py)

algorithms/tree/segment_tree/iterative_segment_tree.py

@@ -0,0 +1,53 @@
+"""
+SegmentTree creates a segment tree with a given array and a "commutative" function,
+this non-recursive version uses less memory than the recursive version and include:
+1. range queries in log(N) time
+2. update an element in log(N) time
+the function should be commutative and takes 2 values and returns the same type value
+
+Examples -
+mytree = SegmentTree([2, 4, 5, 3, 4],max)
+print(mytree.query(2, 4))
+mytree.update(3, 6)
+print(mytree.query(0, 3)) ...
+
+mytree = SegmentTree([4, 5, 2, 3, 4, 43, 3], lambda a, b: a + b)
+print(mytree.query(0, 6))
+mytree.update(2, -10)
+print(mytree.query(0, 6)) ...
+
+mytree = SegmentTree([(1, 2), (4, 6), (4, 5)], lambda a, b: (a[0] + b[0], a[1] + b[1]))
+print(mytree.query(0, 2))
+mytree.update(2, (-1, 2))
+print(mytree.query(0, 2)) ...
+"""
+
+
+class SegmentTree:
+    def __init__(self, arr, function):
+        self.tree = [None for _ in range(len(arr))] + arr
+        self.size = len(arr)
+        self.fn = function
+        self.build_tree()
+
+    def build_tree(self):
+        for i in range(self.size - 1, 0, -1):
+            self.tree[i] = self.fn(self.tree[i * 2], self.tree[i * 2 + 1])
+
+    def update(self, p, v):
+        p += self.size
+        self.tree[p] = v
+        while p > 1:
+            p = p // 2
+            self.tree[p] = self.fn(self.tree[p * 2], self.tree[p * 2 + 1])
+
+    def query(self, l, r):
+        l, r = l + self.size, r + self.size
+        res = None
+        while l <= r:
+            if l % 2 == 1:
+                res = self.tree[l] if res is None else self.fn(res, self.tree[l])
+            if r % 2 == 0:
+                res = self.tree[r] if res is None else self.fn(res, self.tree[r])
+            l, r = (l + 1) // 2, (r - 1) // 2
+        return res

tests/test_iterative_segment_tree.py

@@ -0,0 +1,91 @@
+from algorithms.tree.segment_tree.iterative_segment_tree import SegmentTree
+from functools import reduce
+
+import unittest
+
+
+def gcd(a, b):
+    if b == 0:
+        return a
+    return gcd(b, a % b)
+
+
+class TestSegmentTree(unittest.TestCase):
+    """
+    Test for the Iterative Segment Tree data structure
+    """
+
+    def test_segment_tree_creation(self):
+        arr = [2, 4, 3, 6, 8, 9, 3]
+        max_segment_tree = SegmentTree(arr, max)
+        min_segment_tree = SegmentTree(arr, min)
+        sum_segment_tree = SegmentTree(arr, lambda a, b: a + b)
+        gcd_segment_tree = SegmentTree(arr, gcd)
+        self.assertEqual(max_segment_tree.tree, [None, 9, 8, 9, 4, 8, 9, 2, 4, 3, 6, 8, 9, 3])
+        self.assertEqual(min_segment_tree.tree, [None, 2, 3, 2, 3, 6, 3, 2, 4, 3, 6, 8, 9, 3])
+        self.assertEqual(sum_segment_tree.tree, [None, 35, 21, 14, 7, 14, 12, 2, 4, 3, 6, 8, 9, 3])
+        self.assertEqual(gcd_segment_tree.tree, [None, 1, 1, 1, 1, 2, 3, 2, 4, 3, 6, 8, 9, 3])
+
+    def test_max_segment_tree(self):
+        arr = [-1, 1, 10, 2, 9, -3, 8, 4, 7, 5, 6, 0]
+        self.__test_all_segments(arr, max)
+
+    def test_min_segment_tree(self):
+        arr = [1, 10, -2, 9, -3, 8, 4, -7, 5, 6, 11, -12]
+        self.__test_all_segments(arr, min)
+
+    def test_sum_segment_tree(self):
+        arr = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6, -11, -12]
+        self.__test_all_segments(arr, lambda a, b: a + b)
+
+    def test_gcd_segment_tree(self):
+        arr = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6, 11, 12, 14]
+        self.__test_all_segments(arr, gcd)
+
+    def test_max_segment_tree_with_updates(self):
+        arr = [-1, 1, 10, 2, 9, -3, 8, 4, 7, 5, 6, 0]
+        updates = {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9, 9: 10, 10: 11, 11: 12}
+        self.__test_all_segments_with_updates(arr, max, updates)
+
+    def test_min_segment_tree_with_updates(self):
+        arr = [1, 10, -2, 9, -3, 8, 4, -7, 5, 6, 11, -12]
+        updates = {0: 7, 1: 2, 2: 6, 3: -14, 4: 5, 5: 4, 6: 7, 7: -10, 8: 9, 9: 10, 10: 12, 11: 1}
+        self.__test_all_segments_with_updates(arr, min, updates)
+
+    def test_sum_segment_tree_with_updates(self):
+        arr = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6, -11, -12]
+        updates = {0: 12, 1: 11, 2: 10, 3: 9, 4: 8, 5: 7, 6: 6, 7: 5, 8: 4, 9: 3, 10: 2, 11: 1}
+        self.__test_all_segments_with_updates(arr, lambda a, b: a + b, updates)
+
+    def test_gcd_segment_tree_with_updates(self):
+        arr = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6, 11, 12, 14]
+        updates = {0: 4, 1: 2, 2: 3, 3: 9, 4: 21, 5: 7, 6: 4, 7: 4, 8: 2, 9: 5, 10: 17, 11: 12, 12: 3}
+        self.__test_all_segments_with_updates(arr, gcd, updates)
+
+    def __test_all_segments(self, arr, fnc):
+        """
+        Test all possible segments in the tree
+        :param arr: array to test
+        :param fnc: function of the segment tree
+        """
+        segment_tree = SegmentTree(arr, fnc)
+        self.__test_segments_helper(segment_tree, fnc, arr)
+
+    def __test_all_segments_with_updates(self, arr, fnc, upd):
+        """
+        Test all possible segments in the tree with updates
+        :param arr: array to test
+        :param fnc: function of the segment tree
+        :param upd: updates to test
+        """
+        segment_tree = SegmentTree(arr, fnc)
+        for index, value in upd.items():
+            arr[index] = value
+            segment_tree.update(index, value)
+            self.__test_segments_helper(segment_tree, fnc, arr)
+
+    def __test_segments_helper(self, seg_tree, fnc, arr):
+        for i in range(0, len(arr)):
+            for j in range(i, len(arr)):
+                range_value = reduce(fnc, arr[i:j + 1])
+                self.assertEqual(seg_tree.query(i, j), range_value)