diff --git a/data_structures/disjoint_set/union_find.py b/data_structures/disjoint_set/union_find.py
new file mode 100644
index 000000000000..12e2c83fe942
--- /dev/null
+++ b/data_structures/disjoint_set/union_find.py
@@ -0,0 +1,83 @@
+"""
+Union-Find (Disjoint Set Union) with Path Compression and Union by Rank
+
+Use Case:
+- Efficient structure to manage disjoint sets
+- Useful in network connectivity, Kruskal's MST, and clustering
+
+Time Complexity:
+- Nearly constant: O(α(n)) where α is the inverse Ackermann function
+
+Author: Michael Alexander Montoya
+"""
+
+
+class UnionFind:
+ def __init__(self, size: int) -> None:
+ """
+ Initializes a Union-Find data structure with `size` elements.
+
+ >>> uf = UnionFind(5)
+ >>> uf.find(0)
+ 0
+ """
+ self.parent = list(range(size))
+ self.rank = [0] * size
+
+ def find(self, node: int) -> int:
+ """
+ Finds the representative/root of the set that `node` belongs to.
+
+ >>> uf = UnionFind(5)
+ >>> uf.find(3)
+ 3
+ """
+ if self.parent[node] != node:
+ self.parent[node] = self.find(self.parent[node]) # Path compression
+ return self.parent[node]
+
+ def union(self, node_a: int, node_b: int) -> bool:
+ """
+ Unites the sets that contain elements `node_a` and `node_b`.
+
+ >>> uf = UnionFind(5)
+ >>> uf.union(0, 1)
+ True
+ >>> uf.find(1) == uf.find(0)
+ True
+ >>> uf.union(0, 1)
+ False
+ """
+ root_a = self.find(node_a)
+ root_b = self.find(node_b)
+
+ if root_a == root_b:
+ return False # Already connected
+
+ if self.rank[root_a] < self.rank[root_b]:
+ self.parent[root_a] = root_b
+ elif self.rank[root_a] > self.rank[root_b]:
+ self.parent[root_b] = root_a
+ else:
+ self.parent[root_b] = root_a
+ self.rank[root_a] += 1
+
+ return True
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()
+
+ uf = UnionFind(10)
+ uf.union(1, 2)
+ uf.union(2, 3)
+ uf.union(4, 5)
+
+ print("1 and 3 connected:", uf.find(1) == uf.find(3)) # True
+ print("1 and 5 connected:", uf.find(1) == uf.find(5)) # False
+
+ uf.union(3, 5)
+
+ print("1 and 5 connected after union:", uf.find(1) == uf.find(5)) # True
diff --git a/searches/exponential_search.py b/searches/exponential_search.py
index ed09b14e101c..79e3e80ed059 100644
--- a/searches/exponential_search.py
+++ b/searches/exponential_search.py
@@ -1,113 +1,48 @@
-#!/usr/bin/env python3
-
"""
-Pure Python implementation of exponential search algorithm
+Exponential Search Algorithm
-For more information, see the Wikipedia page:
-https://en.wikipedia.org/wiki/Exponential_search
+Time Complexity:
+- Best Case: O(1)
+- Average/Worst Case: O(log i), where i is the index of the first element >= target
-For doctests run the following command:
-python3 -m doctest -v exponential_search.py
+Use Case:
+Efficient for searching in sorted arrays where the target is near the beginning.
-For manual testing run:
-python3 exponential_search.py
+Author: Michael Alexander Montoya
"""
-from __future__ import annotations
-
-
-def binary_search_by_recursion(
- sorted_collection: list[int], item: int, left: int = 0, right: int = -1
-) -> int:
- """Pure implementation of binary search algorithm in Python using recursion
-
- Be careful: the collection must be ascending sorted otherwise, the result will be
- unpredictable.
- :param sorted_collection: some ascending sorted collection with comparable items
- :param item: item value to search
- :param left: starting index for the search
- :param right: ending index for the search
- :return: index of the found item or -1 if the item is not found
-
- Examples:
- >>> binary_search_by_recursion([0, 5, 7, 10, 15], 0, 0, 4)
- 0
- >>> binary_search_by_recursion([0, 5, 7, 10, 15], 15, 0, 4)
- 4
- >>> binary_search_by_recursion([0, 5, 7, 10, 15], 5, 0, 4)
- 1
- >>> binary_search_by_recursion([0, 5, 7, 10, 15], 6, 0, 4)
- -1
- """
- if right < 0:
- right = len(sorted_collection) - 1
- if list(sorted_collection) != sorted(sorted_collection):
- raise ValueError("sorted_collection must be sorted in ascending order")
- if right < left:
+def exponential_search(arr, target):
+ if len(arr) == 0:
return -1
- midpoint = left + (right - left) // 2
-
- if sorted_collection[midpoint] == item:
- return midpoint
- elif sorted_collection[midpoint] > item:
- return binary_search_by_recursion(sorted_collection, item, left, midpoint - 1)
- else:
- return binary_search_by_recursion(sorted_collection, item, midpoint + 1, right)
-
-
-def exponential_search(sorted_collection: list[int], item: int) -> int:
- """
- Pure implementation of an exponential search algorithm in Python.
- For more information, refer to:
- https://en.wikipedia.org/wiki/Exponential_search
-
- Be careful: the collection must be ascending sorted, otherwise the result will be
- unpredictable.
-
- :param sorted_collection: some ascending sorted collection with comparable items
- :param item: item value to search
- :return: index of the found item or -1 if the item is not found
-
- The time complexity of this algorithm is O(log i) where i is the index of the item.
-
- Examples:
- >>> exponential_search([0, 5, 7, 10, 15], 0)
- 0
- >>> exponential_search([0, 5, 7, 10, 15], 15)
- 4
- >>> exponential_search([0, 5, 7, 10, 15], 5)
- 1
- >>> exponential_search([0, 5, 7, 10, 15], 6)
- -1
- """
- if list(sorted_collection) != sorted(sorted_collection):
- raise ValueError("sorted_collection must be sorted in ascending order")
-
- if sorted_collection[0] == item:
+ if arr[0] == target:
return 0
- bound = 1
- while bound < len(sorted_collection) and sorted_collection[bound] < item:
- bound *= 2
+ # Find range for binary search by repeated doubling
+ index = 1
+ while index < len(arr) and arr[index] <= target:
+ index *= 2
- left = bound // 2
- right = min(bound, len(sorted_collection) - 1)
- return binary_search_by_recursion(sorted_collection, item, left, right)
+ # Perform binary search in the found range
+ return binary_search(arr, target, index // 2, min(index, len(arr) - 1))
-if __name__ == "__main__":
- import doctest
+def binary_search(arr, target, left, right):
+ while left <= right:
+ mid = (left + right) // 2
+ if arr[mid] == target:
+ return mid
+ elif arr[mid] < target:
+ left = mid + 1
+ else:
+ right = mid - 1
+ return -1
- doctest.testmod()
- # Manual testing
- user_input = input("Enter numbers separated by commas: ").strip()
- collection = sorted(int(item) for item in user_input.split(","))
- target = int(input("Enter a number to search for: "))
- result = exponential_search(sorted_collection=collection, item=target)
- if result == -1:
- print(f"{target} was not found in {collection}.")
- else:
- print(f"{target} was found at index {result} in {collection}.")
+# Example usage:
+if __name__ == "__main__":
+ array = [1, 3, 5, 7, 9, 13, 17, 21, 24, 27, 30]
+ target = 13
+ result = exponential_search(array, target)
+ print(f"Target {target} found at index: {result}")
diff --git a/searches/reservoir_sampling.py b/searches/reservoir_sampling.py
new file mode 100644
index 000000000000..e6e6d2c2b0f8
--- /dev/null
+++ b/searches/reservoir_sampling.py
@@ -0,0 +1,54 @@
+"""
+Reservoir Sampling Algorithm
+
+Use Case:
+Efficient for selecting `sample_size` random items from a data stream of unknown size,
+or when the entire dataset cannot fit into memory.
+
+Time Complexity:
+- O(n), where n is the total number of items
+- Space Complexity: O(sample_size)
+
+Author: Michael Alexander Montoya
+"""
+
+import random
+from typing import Iterable
+
+
+def reservoir_sampling(stream: Iterable[int], sample_size: int) -> list[int]:
+ """
+ Performs reservoir sampling on a stream of items.
+
+ Args:
+ stream: An iterable data stream.
+ sample_size: Number of items to sample.
+
+ Returns:
+ A list containing `sample_size` randomly sampled items from the stream.
+
+ >>> result = reservoir_sampling(range(1, 1001), 10)
+ >>> len(result) == 10
+ True
+ """
+ reservoir = []
+
+ for i, item in enumerate(stream):
+ if i < sample_size:
+ reservoir.append(item)
+ else:
+ j = random.randint(0, i)
+ if j < sample_size:
+ reservoir[j] = item
+
+ return reservoir
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()
+
+ stream_data = range(1, 1001)
+ sample = reservoir_sampling(stream_data, 10)
+ print(f"Sampled items: {sample}")