algorithms

Minimal, clean, and well-documented implementations of data structures and algorithms in Python 3.

Each file is self-contained with docstrings, type hints, and complexity notes — designed to be read and learned from.

Quick Start

Install

pip install algorithms

Use

from algorithms.sorting import merge_sort

print(merge_sort([38, 27, 43, 3, 9, 82, 10]))
# [3, 9, 10, 27, 38, 43, 82]

from algorithms.data_structures import BinaryHeap, Trie, BST
from algorithms.graph import dijkstra, bellman_ford
from algorithms.tree import TreeNode

Examples

Graph — Dijkstra's shortest path:

from algorithms.graph import dijkstra

graph = {
    "s": {"a": 2, "b": 1},
    "a": {"s": 3, "b": 4, "c": 8},
    "b": {"s": 4, "a": 2, "d": 2},
    "c": {"a": 2, "d": 7, "t": 4},
    "d": {"b": 1, "c": 11, "t": 5},
    "t": {"c": 3, "d": 5},
}
print(dijkstra(graph, "s", "t"))
# (8, ['s', 'b', 'd', 't'])

Dynamic programming — coin change:

from algorithms.dynamic_programming import coin_change

# Minimum coins to make amount 29 using denominations [1, 5, 10, 25]
print(coin_change([1, 5, 10, 25], 29))
# 7   (25 + 1 + 1 + 1 + 1)

Backtracking — generate permutations:

from algorithms.backtracking import permute

print(permute([1, 2, 3]))
# [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]

Data structures — binary heap:

from algorithms.data_structures import BinaryHeap

heap = BinaryHeap()
for val in [5, 3, 8, 1, 9]:
    heap.insert(val)
print(heap.remove_min())  # 1
print(heap.remove_min())  # 3

Searching — binary search:

from algorithms.searching import binary_search

print(binary_search([1, 3, 5, 7, 9, 11], 7))
# 3   (index of target)

Tree — inorder traversal:

from algorithms.tree import TreeNode
from algorithms.tree import inorder

root = TreeNode(4)
root.left = TreeNode(2)
root.right = TreeNode(6)
root.left.left = TreeNode(1)
root.left.right = TreeNode(3)

print(inorder(root))
# [1, 2, 3, 4, 6]

String — Knuth-Morris-Pratt pattern matching:

from algorithms.string import knuth_morris_pratt

print(knuth_morris_pratt("abxabcabcaby", "abcaby"))
# 6   (starting index of match)

Run Tests

python -m pytest tests/

Project Structure

algorithms/
    data_structures/     # Reusable data structure implementations
    array/               # Array manipulation algorithms
    backtracking/        # Constraint satisfaction & enumeration
    bit_manipulation/    # Bitwise operations & tricks
    compression/         # Encoding & compression schemes
    dynamic_programming/ # Optimal substructure & memoization
    graph/               # Graph algorithms (BFS, DFS, shortest path, flow, ...)
    greedy/              # Greedy strategies
    heap/                # Heap-based algorithms
    linked_list/         # Linked list algorithms
    map/                 # Hash-map-based algorithms
    math/                # Number theory, combinatorics, algebra
    matrix/              # 2D array & linear algebra operations
    queue/               # Queue-based algorithms
    searching/           # Search algorithms (binary, linear, ...)
    set/                 # Set-based algorithms
    sorting/             # Sorting algorithms
    stack/               # Stack-based algorithms
    streaming/           # Streaming & sketching algorithms
    string/              # String matching, manipulation, parsing
    tree/                # Tree algorithms (traversal, BST ops, ...)
tests/                   # One test file per topic

Data Structures

All core data structures live in algorithms/data_structures/:

Data Structure	Module	Key Classes
AVL Tree	avl_tree.py	AvlTree
B-Tree	b_tree.py	BTree
Binary Search Tree	bst.py	BST
Fenwick Tree	fenwick_tree.py	Fenwick_Tree
Graph	graph.py	Node, DirectedEdge, DirectedGraph
Hash Table	hash_table.py	HashTable, ResizableHashTable
Heap	heap.py	BinaryHeap
KD Tree	kd_tree.py	KDTree
Linked List	linked_list.py	SinglyLinkedListNode, DoublyLinkedListNode
Priority Queue	priority_queue.py	PriorityQueue
Queue	queue.py	ArrayQueue, LinkedListQueue
Red-Black Tree	red_black_tree.py	RBTree
Segment Tree	segment_tree.py, iterative_segment_tree.py	SegmentTree
Separate Chaining Hash Table	separate_chaining_hash_table.py	SeparateChainingHashTable
Sqrt Decomposition	sqrt_decomposition.py	SqrtDecomposition
Stack	stack.py	ArrayStack, LinkedListStack
Trie	trie.py	Trie
Union-Find	union_find.py	Union

Algorithms

Array

• delete_nth — keep at most N occurrences of each element
• flatten — recursively flatten nested arrays into a single list
• garage — minimum swaps to rearrange a parking lot
• josephus — eliminate every k-th person in a circular arrangement
• limit — filter elements within min/max bounds
• longest_non_repeat — longest substring without repeating characters
• max_ones_index — find the zero to flip for the longest run of ones
• merge_intervals — combine overlapping intervals
• missing_ranges — find gaps between a low and high bound
• move_zeros — move all zeros to the end, preserving order
• n_sum — find all unique n-tuples that sum to a target
• plus_one — add one to a number represented as a digit array
• remove_duplicates — remove duplicate elements preserving order
• rotate — rotate an array right by k positions
• summarize_ranges — summarize consecutive integers as range tuples
• three_sum — find all unique triplets that sum to zero
• top_1 — find the most frequently occurring values
• trimmean — compute mean after trimming extreme values
• two_sum — find two indices whose values sum to a target

Backtracking

• add_operators — insert +, -, * between digits to reach a target
• anagram — check if two strings are anagrams
• array_sum_combinations — find three-element combos from arrays that hit a target sum
• combination_sum — find combinations (with reuse) that sum to a target
• factor_combinations — generate all factor combinations of a number
• find_words — find words on a letter board via trie-based search
• generate_abbreviations — generate all possible abbreviations of a word
• generate_parenthesis — generate all valid parenthesis combinations
• letter_combination — phone keypad digit-to-letter combinations
• palindrome_partitioning — partition a string into palindromic substrings
• pattern_match — match a string to a pattern via bijection mapping
• permute — generate all permutations of distinct elements
• permute_unique — generate unique permutations when duplicates exist
• subsets — generate all subsets (power set)
• minimax — game-tree search with alpha-beta pruning
• subsets_unique — generate unique subsets when duplicates exist

Bit Manipulation

• add_bitwise_operator — add two integers using only bitwise operations
• binary_gap — longest distance between consecutive 1-bits
• bit_operation — get, set, clear, and update individual bits
• bytes_int_conversion — convert between integers and byte sequences
• count_flips_to_convert — count bit flips needed to convert one integer to another
• count_ones — count the number of 1-bits (Hamming weight)
• find_difference — find the added character between two strings using XOR
• find_missing_number — find a missing number in a sequence using XOR
• flip_bit_longest_sequence — longest run of 1s after flipping a single 0
• gray_code — generate Gray code sequences and convert between Gray and binary
• has_alternative_bit — check if binary representation has alternating bits
• insert_bit — insert bits at a specific position in an integer
• power_of_two — check if an integer is a power of two
• remove_bit — remove a bit at a given position
• reverse_bits — reverse all 32 bits of an unsigned integer
• single_number — find the element appearing once (others appear twice) via XOR
• single_number2 — find the element appearing once (others appear three times)
• single_number3 — find two unique elements (others appear twice)
• subsets — generate all subsets using bitmask enumeration
• swap_pair — swap adjacent bit pairs in an integer

Compression

• elias — Elias gamma and delta universal integer coding
• huffman_coding — variable-length prefix codes for lossless compression
• rle_compression — run-length encoding for consecutive character compression

Dynamic Programming

• bitmask — travelling salesman problem via bitmask dynamic programming
• buy_sell_stock — maximize profit from a stock price array
• climbing_stairs — count ways to climb stairs taking 1 or 2 steps
• coin_change — minimum coins to make a given amount
• combination_sum — count combinations that sum to a target (with reuse)
• count_paths_dp — count paths in a grid using recursion, memoization, and bottom-up DP
• edit_distance — minimum edits to transform one string into another
• egg_drop — minimize trials to find the critical floor
• fibonacci — compute Fibonacci numbers with memoization
• hosoya_triangle — generate the Hosoya triangle of Fibonacci-like numbers
• house_robber — maximize loot from non-adjacent houses
• int_divide — count the number of integer partitions
• job_scheduling — maximize profit from weighted job scheduling
• k_factor — find the k-factor of a string pattern
• knapsack — maximize value under a weight constraint
• longest_common_subsequence — find the longest common subsequence of two strings
• longest_increasing — find the longest increasing subsequence
• matrix_chain_order — minimize scalar multiplications for matrix chain
• [max_product_subar