lowest_common_ancestor.py static type checking (TheAlgorithms#2329)

* adding static type checking to basic_binary_tree.py

* Add static type checking to functions with None return type

* Applying code review comments

* Added missing import statement

* fix spaciing

* "cleaned up depth_of_tree"

* Add doctests and then streamline display() and is_full_binary_tree()

* added static typing to lazy_segment_tree.py

* added missing import statement

* modified variable names for left and right elements

* added static typing to lowest_common_ancestor.py

* fixed formatting

* modified files to meet style guidelines, edited docstrings and added some doctests

* added and fixed doctests in lazy_segment_tree.py

* fixed errors in doctests

Co-authored-by: Christian Clauss <[email protected]>

Author: kanthuc

data_structures/binary_tree/lazy_segment_tree.py

@@ -1,84 +1,119 @@
 import math
+from typing import List
 
 
 class SegmentTree:
-    def __init__(self, N):
+    def __init__(self, N: int) -> None:
         self.N = N
-        self.st = [
-            0 for i in range(0, 4 * N)
-        ]  # approximate the overall size of segment tree with array N
-        self.lazy = [0 for i in range(0, 4 * N)]  # create array to store lazy update
-        self.flag = [0 for i in range(0, 4 * N)]  # flag for lazy update
+        # approximate the overall size of segment tree with array N
+        self.st: List[int] = [0 for i in range(0, 4 * N)]
+        # create array to store lazy update
+        self.lazy: List[int] = [0 for i in range(0, 4 * N)]
+        self.flag: List[int] = [0 for i in range(0, 4 * N)]  # flag for lazy update
 
-    def left(self, idx):
+    def left(self, idx: int) -> int:
+        """
+        >>> segment_tree = SegmentTree(15)
+        >>> segment_tree.left(1)
+        2
+        >>> segment_tree.left(2)
+        4
+        >>> segment_tree.left(12)
+        24
+        """
         return idx * 2
 
-    def right(self, idx):
+    def right(self, idx: int) -> int:
+        """
+        >>> segment_tree = SegmentTree(15)
+        >>> segment_tree.right(1)
+        3
+        >>> segment_tree.right(2)
+        5
+        >>> segment_tree.right(12)
+        25
+        """
         return idx * 2 + 1
 
-    def build(self, idx, l, r, A):  # noqa: E741
-        if l == r:  # noqa: E741
-            self.st[idx] = A[l - 1]
+    def build(
+        self, idx: int, left_element: int, right_element: int, A: List[int]
+    ) -> None:
+        if left_element == right_element:
+            self.st[idx] = A[left_element - 1]
         else:
-            mid = (l + r) // 2
-            self.build(self.left(idx), l, mid, A)
-            self.build(self.right(idx), mid + 1, r, A)
+            mid = (left_element + right_element) // 2
+            self.build(self.left(idx), left_element, mid, A)
+            self.build(self.right(idx), mid + 1, right_element, A)
             self.st[idx] = max(self.st[self.left(idx)], self.st[self.right(idx)])
 
-    # update with O(lg N) (Normal segment tree without lazy update will take O(Nlg N)
-    # for each update)
-    def update(self, idx, l, r, a, b, val):  # noqa: E741
+    def update(
+        self, idx: int, left_element: int, right_element: int, a: int, b: int, val: int
+    ) -> bool:
         """
+        update with O(lg N) (Normal segment tree without lazy update will take O(Nlg N)
+        for each update)
+
         update(1, 1, N, a, b, v) for update val v to [a,b]
         """
         if self.flag[idx] is True:
             self.st[idx] = self.lazy[idx]
             self.flag[idx] = False
-            if l != r:  # noqa: E741
+            if left_element != right_element:
                 self.lazy[self.left(idx)] = self.lazy[idx]
                 self.lazy[self.right(idx)] = self.lazy[idx]
                 self.flag[self.left(idx)] = True
                 self.flag[self.right(idx)] = True
 
-        if r < a or l > b:
+        if right_element < a or left_element > b:
             return True
-        if l >= a and r <= b:  # noqa: E741
+        if left_element >= a and right_element <= b:
             self.st[idx] = val
-            if l != r:  # noqa: E741
+            if left_element != right_element:
                 self.lazy[self.left(idx)] = val
                 self.lazy[self.right(idx)] = val
                 self.flag[self.left(idx)] = True
                 self.flag[self.right(idx)] = True
             return True
-        mid = (l + r) // 2
-        self.update(self.left(idx), l, mid, a, b, val)
-        self.update(self.right(idx), mid + 1, r, a, b, val)
+        mid = (left_element + right_element) // 2
+        self.update(self.left(idx), left_element, mid, a, b, val)
+        self.update(self.right(idx), mid + 1, right_element, a, b, val)
         self.st[idx] = max(self.st[self.left(idx)], self.st[self.right(idx)])
         return True
 
     # query with O(lg N)
-    def query(self, idx, l, r, a, b):  # noqa: E741
+    def query(
+        self, idx: int, left_element: int, right_element: int, a: int, b: int
+    ) -> int:
         """
         query(1, 1, N, a, b) for query max of [a,b]
+        >>> A = [1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
+        >>> segment_tree = SegmentTree(15)
+        >>> segment_tree.build(1, 1, 15, A)
+        >>> segment_tree.query(1, 1, 15, 4, 6)
+        7
+        >>> segment_tree.query(1, 1, 15, 7, 11)
+        14
+        >>> segment_tree.query(1, 1, 15, 7, 12)
+        15
         """
         if self.flag[idx] is True:
             self.st[idx] = self.lazy[idx]
             self.flag[idx] = False
-            if l != r:  # noqa: E741
+            if left_element != right_element:
                 self.lazy[self.left(idx)] = self.lazy[idx]
                 self.lazy[self.right(idx)] = self.lazy[idx]
                 self.flag[self.left(idx)] = True
                 self.flag[self.right(idx)] = True
-        if r < a or l > b:
+        if right_element < a or left_element > b:
             return -math.inf
-        if l >= a and r <= b:  # noqa: E741
+        if left_element >= a and right_element <= b:
             return self.st[idx]
-        mid = (l + r) // 2
-        q1 = self.query(self.left(idx), l, mid, a, b)
-        q2 = self.query(self.right(idx), mid + 1, r, a, b)
+        mid = (left_element + right_element) // 2
+        q1 = self.query(self.left(idx), left_element, mid, a, b)
+        q2 = self.query(self.right(idx), mid + 1, right_element, a, b)
         return max(q1, q2)
 
-    def showData(self):
+    def show_data(self) -> None:
         showList = []
         for i in range(1, N + 1):
             showList += [self.query(1, 1, self.N, i, i)]
@@ -96,4 +131,4 @@ def showData(self):
     segt.update(1, 1, N, 1, 3, 111)
     print(segt.query(1, 1, N, 1, 15))
     segt.update(1, 1, N, 7, 8, 235)
-    segt.showData()
+    segt.show_data()

data_structures/binary_tree/lowest_common_ancestor.py

@@ -2,17 +2,29 @@
 # https://en.wikipedia.org/wiki/Breadth-first_search
 
 import queue
+from typing import Dict, List, Tuple
 
 
-def swap(a, b):
+def swap(a: int, b: int) -> Tuple[int, int]:
+    """
+    Return a tuple (b, a) when given two integers a and b
+    >>> swap(2,3)
+    (3, 2)
+    >>> swap(3,4)
+    (4, 3)
+    >>> swap(67, 12)
+    (12, 67)
+    """
     a ^= b
     b ^= a
     a ^= b
     return a, b
 
 
-# creating sparse table which saves each nodes 2^i-th parent
-def creatSparse(max_node, parent):
+def create_sparse(max_node: int, parent: List[List[int]]) -> List[List[int]]:
+    """
+    creating sparse table which saves each nodes 2^i-th parent
+    """
     j = 1
     while (1 << j) < max_node:
         for i in range(1, max_node + 1):
@@ -22,7 +34,9 @@ def creatSparse(max_node, parent):
 
 
 # returns lca of node u,v
-def LCA(u, v, level, parent):
+def lowest_common_ancestor(
+    u: int, v: int, level: List[int], parent: List[List[int]]
+) -> List[List[int]]:
     # u must be deeper in the tree than v
     if level[u] < level[v]:
         u, v = swap(u, v)
@@ -42,10 +56,18 @@ def LCA(u, v, level, parent):
 
 
 # runs a breadth first search from root node of the tree
-# sets every nodes direct parent
-# parent of root node is set to 0
-# calculates depth of each node from root node
-def bfs(level, parent, max_node, graph, root=1):
+def breadth_first_search(
+    level: List[int],
+    parent: List[List[int]],
+    max_node: int,
+    graph: Dict[int, int],
+    root=1,
+) -> Tuple[List[int], List[List[int]]]:
+    """
+    sets every nodes direct parent
+    parent of root node is set to 0
+    calculates depth of each node from root node
+    """
     level[root] = 0
     q = queue.Queue(maxsize=max_node)
     q.put(root)
@@ -59,7 +81,7 @@ def bfs(level, parent, max_node, graph, root=1):
     return level, parent
 
 
-def main():
+def main() -> None:
     max_node = 13
     # initializing with 0
     parent = [[0 for _ in range(max_node + 10)] for _ in range(20)]
@@ -80,14 +102,14 @@ def main():
         12: [],
         13: [],
     }
-    level, parent = bfs(level, parent, max_node, graph, 1)
-    parent = creatSparse(max_node, parent)
-    print("LCA of node 1 and 3 is: ", LCA(1, 3, level, parent))
-    print("LCA of node 5 and 6 is: ", LCA(5, 6, level, parent))
-    print("LCA of node 7 and 11 is: ", LCA(7, 11, level, parent))
-    print("LCA of node 6 and 7 is: ", LCA(6, 7, level, parent))
-    print("LCA of node 4 and 12 is: ", LCA(4, 12, level, parent))
-    print("LCA of node 8 and 8 is: ", LCA(8, 8, level, parent))
+    level, parent = breadth_first_search(level, parent, max_node, graph, 1)
+    parent = create_sparse(max_node, parent)
+    print("LCA of node 1 and 3 is: ", lowest_common_ancestor(1, 3, level, parent))
+    print("LCA of node 5 and 6 is: ", lowest_common_ancestor(5, 6, level, parent))
+    print("LCA of node 7 and 11 is: ", lowest_common_ancestor(7, 11, level, parent))
+    print("LCA of node 6 and 7 is: ", lowest_common_ancestor(6, 7, level, parent))
+    print("LCA of node 4 and 12 is: ", lowest_common_ancestor(4, 12, level, parent))
+    print("LCA of node 8 and 8 is: ", lowest_common_ancestor(8, 8, level, parent))
 
 
 if __name__ == "__main__":