add prefix sum (#7959)

* add prefix sum

* updating DIRECTORY.md

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DIRECTORY.md

@@ -162,6 +162,7 @@
 ## Data Structures
   * Arrays
     * [Permutations](data_structures/arrays/permutations.py)
+    * [Prefix Sum](data_structures/arrays/prefix_sum.py)
   * Binary Tree
     * [Avl Tree](data_structures/binary_tree/avl_tree.py)
     * [Basic Binary Tree](data_structures/binary_tree/basic_binary_tree.py)
@@ -174,6 +175,7 @@
     * [Diff Views Of Binary Tree](data_structures/binary_tree/diff_views_of_binary_tree.py)
     * [Fenwick Tree](data_structures/binary_tree/fenwick_tree.py)
     * [Inorder Tree Traversal 2022](data_structures/binary_tree/inorder_tree_traversal_2022.py)
+    * [Is Bst](data_structures/binary_tree/is_bst.py)
     * [Lazy Segment Tree](data_structures/binary_tree/lazy_segment_tree.py)
     * [Lowest Common Ancestor](data_structures/binary_tree/lowest_common_ancestor.py)
     * [Maximum Fenwick Tree](data_structures/binary_tree/maximum_fenwick_tree.py)

data_structures/arrays/prefix_sum.py

@@ -0,0 +1,78 @@
+"""
+Author  : Alexander Pantyukhin
+Date    : November 3, 2022
+
+Implement the class of prefix sum with useful functions based on it.
+
+"""
+
+
+class PrefixSum:
+    def __init__(self, array: list[int]) -> None:
+        len_array = len(array)
+        self.prefix_sum = [0] * len_array
+
+        if len_array > 0:
+            self.prefix_sum[0] = array[0]
+
+        for i in range(1, len_array):
+            self.prefix_sum[i] = self.prefix_sum[i - 1] + array[i]
+
+    def get_sum(self, start: int, end: int) -> int:
+        """
+        The function returns the sum of array from the start to the end indexes.
+        Runtime : O(1)
+        Space: O(1)
+
+        >>> PrefixSum([1,2,3]).get_sum(0, 2)
+        6
+        >>> PrefixSum([1,2,3]).get_sum(1, 2)
+        5
+        >>> PrefixSum([1,2,3]).get_sum(2, 2)
+        3
+        >>> PrefixSum([1,2,3]).get_sum(2, 3)
+        Traceback (most recent call last):
+        ...
+        IndexError: list index out of range
+        """
+        if start == 0:
+            return self.prefix_sum[end]
+
+        return self.prefix_sum[end] - self.prefix_sum[start - 1]
+
+    def contains_sum(self, target_sum: int) -> bool:
+        """
+        The function returns True if array contains the target_sum,
+        False otherwise.
+
+        Runtime : O(n)
+        Space: O(n)
+
+        >>> PrefixSum([1,2,3]).contains_sum(6)
+        True
+        >>> PrefixSum([1,2,3]).contains_sum(5)
+        True
+        >>> PrefixSum([1,2,3]).contains_sum(3)
+        True
+        >>> PrefixSum([1,2,3]).contains_sum(4)
+        False
+        >>> PrefixSum([1,2,3]).contains_sum(7)
+        False
+        >>> PrefixSum([1,-2,3]).contains_sum(2)
+        True
+        """
+
+        sums = {0}
+        for sum_item in self.prefix_sum:
+            if sum_item - target_sum in sums:
+                return True
+
+            sums.add(sum_item)
+
+        return False
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()