Merge branch 'master' into master

Author: cclauss

DIRECTORY.md

@@ -62,6 +62,7 @@
   * [Generate Parentheses Iterative](backtracking/generate_parentheses_iterative.py)
   * [Hamiltonian Cycle](backtracking/hamiltonian_cycle.py)
   * [Knight Tour](backtracking/knight_tour.py)
+  * [M Coloring Problem](backtracking/m_coloring_problem.py)
   * [Match Word Pattern](backtracking/match_word_pattern.py)
   * [Minimax](backtracking/minimax.py)
   * [N Queens](backtracking/n_queens.py)
@@ -108,6 +109,9 @@
 
 ## [Blockchain](blockchain)
   * [Diophantine Equation](blockchain/diophantine_equation.py)
+  * [Merkle Tree](blockchain/merkle_tree.py)
+  * [Simple Blockchain](blockchain/simple_blockchain.py)
+  * [Simple Proof Of Work](blockchain/simple_proof_of_work.py)
 
 ## [Boolean Algebra](boolean_algebra)
   * [And Gate](boolean_algebra/and_gate.py)
@@ -166,6 +170,7 @@
   * [Porta Cipher](ciphers/porta_cipher.py)
   * [Rabin Miller](ciphers/rabin_miller.py)
   * [Rail Fence Cipher](ciphers/rail_fence_cipher.py)
+  * [Rc4](ciphers/rc4.py)
   * [Rot13](ciphers/rot13.py)
   * [Rsa Cipher](ciphers/rsa_cipher.py)
   * [Rsa Factorization](ciphers/rsa_factorization.py)
@@ -180,6 +185,7 @@
   * [Vernam Cipher](ciphers/vernam_cipher.py)
   * [Vigenere Cipher](ciphers/vigenere_cipher.py)
   * [Xor Cipher](ciphers/xor_cipher.py)
+  * [Xtea](ciphers/xtea.py)
 
 ## [Computer Vision](computer_vision)
   * [Cnn Classification](computer_vision/cnn_classification.py)
@@ -198,13 +204,17 @@
 ## [Conversions](conversions)
   * [Astronomical Length Scale Conversion](conversions/astronomical_length_scale_conversion.py)
   * [Binary To Decimal](conversions/binary_to_decimal.py)
+  * [Binary To Excess3](conversions/binary_to_excess3.py)
+  * [Binary To Gray](conversions/binary_to_gray.py)
+  * [Binary To Gray Code](conversions/binary_to_gray_code.py)
   * [Binary To Hexadecimal](conversions/binary_to_hexadecimal.py)
   * [Binary To Octal](conversions/binary_to_octal.py)
   * [Convert Number To Words](conversions/convert_number_to_words.py)
   * [Decimal To Any](conversions/decimal_to_any.py)
   * [Decimal To Binary](conversions/decimal_to_binary.py)
   * [Decimal To Hexadecimal](conversions/decimal_to_hexadecimal.py)
   * [Decimal To Octal](conversions/decimal_to_octal.py)
+  * [Endianness](conversions/endianness.py)
   * [Energy Conversions](conversions/energy_conversions.py)
   * [Excel Title To Column](conversions/excel_title_to_column.py)
   * [Hex To Bin](conversions/hex_to_bin.py)
@@ -540,6 +550,7 @@
 ## [Geodesy](geodesy)
   * [Haversine Distance](geodesy/haversine_distance.py)
   * [Lamberts Ellipsoidal Distance](geodesy/lamberts_ellipsoidal_distance.py)
+  * [Radar Target Calculation](geodesy/radar_target_calculation.py)
 
 ## [Geometry](geometry)
   * [Geometry](geometry/geometry.py)
@@ -689,6 +700,7 @@
   * [Astar](machine_learning/astar.py)
   * [Automatic Differentiation](machine_learning/automatic_differentiation.py)
   * [Data Transformations](machine_learning/data_transformations.py)
+  * [Dbscan](machine_learning/dbscan.py)
   * [Decision Tree](machine_learning/decision_tree.py)
   * [Dimensionality Reduction](machine_learning/dimensionality_reduction.py)
   * [Federated Averaging](machine_learning/federated_averaging.py)
@@ -712,11 +724,13 @@
   * [Loss Functions](machine_learning/loss_functions.py)
   * Lstm
     * [Lstm Prediction](machine_learning/lstm/lstm_prediction.py)
+  * [Mab](machine_learning/mab.py)
   * [Mean Shift](machine_learning/mean_shift.py)
   * [Mfcc](machine_learning/mfcc.py)
   * [Mini Batch Gradient Descent](machine_learning/mini_batch_gradient_descent.py)
   * [Multilayer Perceptron Classifier](machine_learning/multilayer_perceptron_classifier.py)
   * [Naive Bayes Text Classification](machine_learning/naive_bayes_text_classification.py)
+  * [Ordinary Least Squares Regression](machine_learning/ordinary_least_squares_regression.py)
   * [Polynomial Regression](machine_learning/polynomial_regression.py)
   * [Principle Component Analysis](machine_learning/principle_component_analysis.py)
   * [Q Learning](machine_learning/q_learning.py)

backtracking/m_coloring_problem.py

@@ -0,0 +1,86 @@
+def is_safe(
+    node: int,
+    color: int,
+    graph: list[list[int]],
+    num_vertices: int,
+    col: list[int],
+) -> bool:
+    """
+    Check if it is safe to assign a color to a node.
+
+    >>> is_safe(0, 1, [[0,1],[1,0]], 2, [0,1])
+    False
+    >>> is_safe(0, 2, [[0,1],[1,0]], 2, [0,1])
+    True
+    """
+    return all(
+        not (graph[node][k] == 1 and col[k] == color) for k in range(num_vertices)
+    )
+
+
+def solve(
+    node: int,
+    col: list[int],
+    max_colors: int,
+    num_vertices: int,
+    graph: list[list[int]],
+) -> bool:
+    """
+    Recursively try to color the graph using at most max_colors.
+
+    >>> solve(0, [0]*3, 3, 3, [[0,1,0],[1,0,1],[0,1,0]])
+    True
+    >>> solve(0, [0]*3, 2, 3, [[0,1,0],[1,0,1],[0,1,0]])
+    True
+    """
+    if node == num_vertices:
+        return True
+    for c in range(1, max_colors + 1):
+        if is_safe(node, c, graph, num_vertices, col):
+            col[node] = c
+            if solve(node + 1, col, max_colors, num_vertices, graph):
+                return True
+            col[node] = 0
+    return False
+
+
+def graph_coloring(graph: list[list[int]], max_colors: int, num_vertices: int) -> bool:
+    """
+    Determine if the graph can be colored with at most max_colors.
+
+    >>> graph_coloring([[0,1,1],[1,0,1],[1,1,0]], 3, 3)
+    True
+    >>> graph_coloring([[0,1,1],[1,0,1],[1,1,0]], 2, 3)
+    False
+    """
+    col = [0] * num_vertices
+    return solve(0, col, max_colors, num_vertices, graph)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    num_vertices = int(input("Enter vertices: "))
+    num_edges = int(input("Enter edges: "))
+    graph = [[0] * num_vertices for _ in range(num_vertices)]
+
+    print("Enter edges (u v):")
+    for _ in range(num_edges):
+        try:
+            u, v = map(int, input().split())
+            if 0 <= u < num_vertices and 0 <= v < num_vertices:
+                graph[u][v] = 1
+                graph[v][u] = 1
+            else:
+                print("Invalid edge.")
+        except ValueError:
+            print("Invalid input.")
+
+    max_colors = int(input("Enter max colors: "))
+
+    if graph_coloring(graph, max_colors, num_vertices):
+        print("Coloring possible.")
+    else:
+        print("Coloring not possible.")

blockchain/merkle_tree.py

@@ -0,0 +1,107 @@
+"""
+Merkle Tree Construction and Verification
+
+This module implements the construction of a Merkle Tree and
+verification of inclusion proofs for blockchain data integrity.
+
+Each leaf is a SHA-256 hash of a transaction, and internal nodes are
+computed by hashing the concatenation of their child nodes.
+
+References:
+https://en.wikipedia.org/wiki/Merkle_tree
+"""
+
+import hashlib
+
+
+def sha256(data: str) -> str:
+    """
+    Compute the SHA-256 hash of the given string.
+
+    Args:
+        data (str): Input string.
+
+    Returns:
+        str: Hexadecimal SHA-256 hash of the input.
+
+    Example:
+        >>> sha256("abc")
+        'ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad'
+    """
+    return hashlib.sha256(data.encode()).hexdigest()
+
+
+def build_merkle_tree(leaves: list[str]) -> list[list[str]]:
+    """
+    Build a Merkle Tree from the given leaf nodes.
+
+    Args:
+        leaves: List of data strings (transactions).
+
+    Returns:
+        A list of lists representing tree levels,
+        with the last level containing the Merkle root.
+
+    >>> len(build_merkle_tree(["a", "b", "c", "d"])[-1][0])
+    64
+    """
+    if not leaves:
+        raise ValueError("Leaf list cannot be empty.")
+
+    current_level = [sha256(x) for x in leaves]
+    tree = [current_level]
+
+    while len(current_level) > 1:
+        next_level = []
+        for i in range(0, len(current_level), 2):
+            left = current_level[i]
+            right = current_level[i + 1] if i + 1 < len(current_level) else left
+            next_level.append(sha256(left + right))
+        current_level = next_level
+        tree.append(current_level)
+
+    return tree
+
+
+def merkle_root(leaves: list[str]) -> str:
+    """
+    Return the Merkle root hash for a given list of data.
+
+    >>> r = merkle_root(["tx1", "tx2", "tx3"])
+    >>> isinstance(r, str)
+    True
+    """
+    return build_merkle_tree(leaves)[-1][0]
+
+
+def verify_proof(leaf: str, proof: list[str], root: str) -> bool:
+    """
+    Verify inclusion of a leaf using a Merkle proof.
+
+    Args:
+        leaf: Original data string.
+        proof: List of sibling hashes up the path.
+        root: Expected Merkle root hash.
+
+    Returns:
+        True if proof is valid, else False.
+
+    >>> data = ["a", "b", "c", "d"]
+    >>> tree = build_merkle_tree(data)
+    >>> root = tree[-1][0]
+    >>> leaf = "a"
+    >>> proof = [sha256("b"), sha256(sha256("c") + sha256("d"))]
+    >>> verify_proof(leaf, proof, root)
+    True
+    """
+    computed_hash = sha256(leaf)
+    for sibling in proof:
+        combined = sha256(computed_hash + sibling)
+        computed_hash = combined
+    return computed_hash == root
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()