diff --git a/DIRECTORY.md b/DIRECTORY.md
index d6ceb04a62eb..4657985d5324 100644
--- a/DIRECTORY.md
+++ b/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)
@@ -104,10 +105,14 @@
   * [Reverse Bits](bit_manipulation/reverse_bits.py)
   * [Rotate Bits](bit_manipulation/rotate_bits.py)
   * [Single Bit Manipulation Operations](bit_manipulation/single_bit_manipulation_operations.py)
+  * [Single Number](bit_manipulation/single_number.py)
   * [Swap All Odd And Even Bits](bit_manipulation/swap_all_odd_and_even_bits.py)
 
 ## [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 +171,7 @@
   * [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 +186,7 @@
   * [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)
@@ -198,6 +205,9 @@
 ## [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)
@@ -205,6 +215,7 @@
   * [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)
@@ -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)
@@ -712,15 +724,18 @@
   * [Loss Functions](machine_learning/loss_functions.py)
   * Lstm
     * [Lstm Prediction](machine_learning/lstm/lstm_prediction.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)
   * [Random Forest Classifier](machine_learning/random_forest_classifier.py)
   * [Random Forest Regressor](machine_learning/random_forest_regressor.py)
+  * [Rmsprop](machine_learning/rmsprop.py)
   * [Scoring Functions](machine_learning/scoring_functions.py)
   * [Self Organizing Map](machine_learning/self_organizing_map.py)
   * [Sequential Minimum Optimization](machine_learning/sequential_minimum_optimization.py)
@@ -737,6 +752,7 @@
   * [Arc Length](maths/arc_length.py)
   * [Area](maths/area.py)
   * [Area Under Curve](maths/area_under_curve.py)
+  * [Autocorrelation](maths/autocorrelation.py)
   * [Average Absolute Deviation](maths/average_absolute_deviation.py)
   * [Average Mean](maths/average_mean.py)
   * [Average Median](maths/average_median.py)
@@ -782,6 +798,7 @@
   * [Fibonacci](maths/fibonacci.py)
   * [Find Max](maths/find_max.py)
   * [Find Min](maths/find_min.py)
+  * [First Fundamental Form](maths/first_fundamental_form.py)
   * [Floor](maths/floor.py)
   * [Gamma](maths/gamma.py)
   * [Gaussian](maths/gaussian.py)
@@ -844,6 +861,7 @@
     * [Square Root](maths/numerical_analysis/square_root.py)
     * [Weierstrass Method](maths/numerical_analysis/weierstrass_method.py)
   * [Odd Sieve](maths/odd_sieve.py)
+  * [Padovan Sequence](maths/padovan_sequence.py)
   * [Pell Number](maths/pell_number.py)
   * [Perfect Cube](maths/perfect_cube.py)
   * [Perfect Number](maths/perfect_number.py)
@@ -873,6 +891,8 @@
   * [Reverse Factorial Recursive](maths/reverse_factorial_recursive.py)
   * [Segmented Sieve](maths/segmented_sieve.py)
   * Series
+    * [Alternate Harmonic Series](maths/series/alternate_harmonic_series.py)
+    * [Alternating Harmonic Series](maths/series/alternating_harmonic_series.py)
     * [Arithmetic](maths/series/arithmetic.py)
     * [Geometric](maths/series/geometric.py)
     * [Geometric Series](maths/series/geometric_series.py)
@@ -912,6 +932,7 @@
     * [Polygonal Numbers](maths/special_numbers/polygonal_numbers.py)
     * [Pronic Number](maths/special_numbers/pronic_number.py)
     * [Proth Number](maths/special_numbers/proth_number.py)
+    * [Spy Number](maths/special_numbers/spy_number.py)
     * [Triangular Numbers](maths/special_numbers/triangular_numbers.py)
     * [Trimorphic Number](maths/special_numbers/trimorphic_number.py)
     * [Ugly Numbers](maths/special_numbers/ugly_numbers.py)
diff --git a/bit_manipulation/single_number.py b/bit_manipulation/single_number.py
new file mode 100644
index 000000000000..0a59adb2d7b1
--- /dev/null
+++ b/bit_manipulation/single_number.py
@@ -0,0 +1,30 @@
+def single_number(nums: list[int]) -> int:
+    """
+    Find the single number in an array where every other number appears twice.
+
+    Args:
+        nums: List of integers where every integer appears twice except for one.
+
+    Returns:
+        The single integer that appears once.
+
+    Example:
+    >>> single_number([4, 1, 2, 1, 2])
+    4
+    >>> single_number([2, 2, 1])
+    1
+    >>> single_number([1])
+    1
+    """
+    result = 0
+    for num in nums:
+        result ^= num  # Applying XOR operation
+    return result
+
+
+if __name__ == "__main__":
+    # Test cases
+    print(single_number([4, 1, 2, 1, 2]))  # Output: 4
+    print(single_number([2, 2, 1]))  # Output: 1
+    print(single_number([1]))  # Output: 1
+    print(single_number([5, 3, 5, 7, 3]))  # Output: 7