Merge branch 'TheAlgorithms:master' into patch-sparse

Author: hollowcrust

Diff for: DIRECTORY.md

@@ -63,7 +63,9 @@
 
 ## Boolean Algebra
   * [And Gate](boolean_algebra/and_gate.py)
+  * [Imply Gate](boolean_algebra/imply_gate.py)
   * [Nand Gate](boolean_algebra/nand_gate.py)
+  * [Nimply Gate](boolean_algebra/nimply_gate.py)
   * [Nor Gate](boolean_algebra/nor_gate.py)
   * [Not Gate](boolean_algebra/not_gate.py)
   * [Or Gate](boolean_algebra/or_gate.py)
@@ -119,9 +121,9 @@
   * [Shuffled Shift Cipher](ciphers/shuffled_shift_cipher.py)
   * [Simple Keyword Cypher](ciphers/simple_keyword_cypher.py)
   * [Simple Substitution Cipher](ciphers/simple_substitution_cipher.py)
-  * [Trafid Cipher](ciphers/trafid_cipher.py)
   * [Transposition Cipher](ciphers/transposition_cipher.py)
   * [Transposition Cipher Encrypt Decrypt File](ciphers/transposition_cipher_encrypt_decrypt_file.py)
+  * [Trifid Cipher](ciphers/trifid_cipher.py)
   * [Vigenere Cipher](ciphers/vigenere_cipher.py)
   * [Xor Cipher](ciphers/xor_cipher.py)
 
@@ -174,7 +176,9 @@
 ## Data Structures
   * Arrays
     * [Equilibrium Index In Array](data_structures/arrays/equilibrium_index_in_array.py)
+    * [Find Triplets With 0 Sum](data_structures/arrays/find_triplets_with_0_sum.py)
     * [Median Two Array](data_structures/arrays/median_two_array.py)
+    * [Pairs With Given Sum](data_structures/arrays/pairs_with_given_sum.py)
     * [Permutations](data_structures/arrays/permutations.py)
     * [Prefix Sum](data_structures/arrays/prefix_sum.py)
     * [Product Sum](data_structures/arrays/product_sum.py)
@@ -385,6 +389,7 @@
 
 ## Financial
   * [Equated Monthly Installments](financial/equated_monthly_installments.py)
+  * [Exponential Moving Average](financial/exponential_moving_average.py)
   * [Interest](financial/interest.py)
   * [Present Value](financial/present_value.py)
   * [Price Plus Tax](financial/price_plus_tax.py)
@@ -670,6 +675,7 @@
   * [Radians](maths/radians.py)
   * [Radix2 Fft](maths/radix2_fft.py)
   * [Remove Digit](maths/remove_digit.py)
+  * [Rkf45](maths/rkf45.py)
   * [Runge Kutta](maths/runge_kutta.py)
   * [Segmented Sieve](maths/segmented_sieve.py)
   * Series
@@ -688,6 +694,7 @@
   * [Sin](maths/sin.py)
   * [Sock Merchant](maths/sock_merchant.py)
   * [Softmax](maths/softmax.py)
+  * [Solovay Strassen Primality Test](maths/solovay_strassen_primality_test.py)
   * [Square Root](maths/square_root.py)
   * [Sum Of Arithmetic Series](maths/sum_of_arithmetic_series.py)
   * [Sum Of Digits](maths/sum_of_digits.py)
@@ -728,6 +735,7 @@
   * [Spiral Print](matrix/spiral_print.py)
   * Tests
     * [Test Matrix Operation](matrix/tests/test_matrix_operation.py)
+  * [Validate Sudoku Board](matrix/validate_sudoku_board.py)
 
 ## Networking Flow
   * [Ford Fulkerson](networking_flow/ford_fulkerson.py)
@@ -803,6 +811,7 @@
   * [Rms Speed Of Molecule](physics/rms_speed_of_molecule.py)
   * [Shear Stress](physics/shear_stress.py)
   * [Speed Of Sound](physics/speed_of_sound.py)
+  * [Speeds Of Gas Molecules](physics/speeds_of_gas_molecules.py)
 
 ## Project Euler
   * Problem 001
@@ -1106,6 +1115,7 @@
 ## Scheduling
   * [First Come First Served](scheduling/first_come_first_served.py)
   * [Highest Response Ratio Next](scheduling/highest_response_ratio_next.py)
+  * [Job Sequence With Deadline](scheduling/job_sequence_with_deadline.py)
   * [Job Sequencing With Deadline](scheduling/job_sequencing_with_deadline.py)
   * [Multi Level Feedback Queue](scheduling/multi_level_feedback_queue.py)
   * [Non Preemptive Shortest Job First](scheduling/non_preemptive_shortest_job_first.py)
@@ -1193,6 +1203,7 @@
   * [Capitalize](strings/capitalize.py)
   * [Check Anagrams](strings/check_anagrams.py)
   * [Credit Card Validator](strings/credit_card_validator.py)
+  * [Damerau Levenshtein Distance](strings/damerau_levenshtein_distance.py)
   * [Detecting English Programmatically](strings/detecting_english_programmatically.py)
   * [Dna](strings/dna.py)
   * [Frequency Finder](strings/frequency_finder.py)
@@ -1225,6 +1236,7 @@
   * [String Switch Case](strings/string_switch_case.py)
   * [Strip](strings/strip.py)
   * [Text Justification](strings/text_justification.py)
+  * [Title](strings/title.py)
   * [Top K Frequent Words](strings/top_k_frequent_words.py)
   * [Upper](strings/upper.py)
   * [Wave](strings/wave.py)

Diff for: bit_manipulation/missing_number.py

@@ -11,11 +11,18 @@ def find_missing_number(nums: list[int]) -> int:
     Example:
         >>> find_missing_number([0, 1, 3, 4])
         2
+        >>> find_missing_number([1, 3, 4, 5, 6])
+        2
+        >>> find_missing_number([6, 5, 4, 2, 1])
+        3
+        >>> find_missing_number([6, 1, 5, 3, 4])
+        2
     """
-    n = len(nums)
-    missing_number = n
+    low = min(nums)
+    high = max(nums)
+    missing_number = high
 
-    for i in range(n):
-        missing_number ^= i ^ nums[i]
+    for i in range(low, high):
+        missing_number ^= i ^ nums[i - low]
 
     return missing_number

Diff for: ciphers/trafid_cipher.py renamed to ciphers/trifid_cipher.py

@@ -0,0 +1,75 @@
+from __future__ import annotations
+
+"""
+    Calculate the frequency and/or duty cycle of an astable 555 timer.
+    * https://en.wikipedia.org/wiki/555_timer_IC#Astable
+
+    These functions take in the value of the external resistances (in ohms)
+    and capacitance (in Microfarad), and calculates the following:
+
+    -------------------------------------
+    | Freq = 1.44 /[( R1+ 2 x R2) x C1] |               ... in Hz
+    -------------------------------------
+    where Freq is the frequency,
+          R1 is the first resistance in ohms,
+          R2 is the second resistance in ohms,
+          C1 is the capacitance in Microfarads.
+
+    ------------------------------------------------
+    | Duty Cycle = (R1 + R2) / (R1 + 2 x R2) x 100 |    ... in %
+    ------------------------------------------------
+    where R1 is the first resistance in ohms,
+          R2 is the second resistance in ohms.
+"""
+
+
+def astable_frequency(
+    resistance_1: float, resistance_2: float, capacitance: float
+) -> float:
+    """
+    Usage examples:
+    >>> astable_frequency(resistance_1=45, resistance_2=45, capacitance=7)
+    1523.8095238095239
+    >>> astable_frequency(resistance_1=356, resistance_2=234, capacitance=976)
+    1.7905459175553078
+    >>> astable_frequency(resistance_1=2, resistance_2=-1, capacitance=2)
+    Traceback (most recent call last):
+        ...
+    ValueError: All values must be positive
+    >>> astable_frequency(resistance_1=45, resistance_2=45, capacitance=0)
+    Traceback (most recent call last):
+        ...
+    ValueError: All values must be positive
+    """
+
+    if resistance_1 <= 0 or resistance_2 <= 0 or capacitance <= 0:
+        raise ValueError("All values must be positive")
+    return (1.44 / ((resistance_1 + 2 * resistance_2) * capacitance)) * 10**6
+
+
+def astable_duty_cycle(resistance_1: float, resistance_2: float) -> float:
+    """
+    Usage examples:
+    >>> astable_duty_cycle(resistance_1=45, resistance_2=45)
+    66.66666666666666
+    >>> astable_duty_cycle(resistance_1=356, resistance_2=234)
+    71.60194174757282
+    >>> astable_duty_cycle(resistance_1=2, resistance_2=-1)
+    Traceback (most recent call last):
+        ...
+    ValueError: All values must be positive
+    >>> astable_duty_cycle(resistance_1=0, resistance_2=0)
+    Traceback (most recent call last):
+        ...
+    ValueError: All values must be positive
+    """
+
+    if resistance_1 <= 0 or resistance_2 <= 0:
+        raise ValueError("All values must be positive")
+    return (resistance_1 + resistance_2) / (resistance_1 + 2 * resistance_2) * 100
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

Diff for: electronics/ic_555_timer.py

@@ -0,0 +1,124 @@
+"""
+Calculate joint probability distribution
+https://en.wikipedia.org/wiki/Joint_probability_distribution
+"""
+
+
+def joint_probability_distribution(
+    x_values: list[int],
+    y_values: list[int],
+    x_probabilities: list[float],
+    y_probabilities: list[float],
+) -> dict:
+    """
+    >>> joint_distribution =  joint_probability_distribution(
+    ...     [1, 2], [-2, 5, 8], [0.7, 0.3], [0.3, 0.5, 0.2]
+    ... )
+    >>> from math import isclose
+    >>> isclose(joint_distribution.pop((1, 8)), 0.14)
+    True
+    >>> joint_distribution
+    {(1, -2): 0.21, (1, 5): 0.35, (2, -2): 0.09, (2, 5): 0.15, (2, 8): 0.06}
+    """
+    return {
+        (x, y): x_prob * y_prob
+        for x, x_prob in zip(x_values, x_probabilities)
+        for y, y_prob in zip(y_values, y_probabilities)
+    }
+
+
+# Function to calculate the expectation (mean)
+def expectation(values: list, probabilities: list) -> float:
+    """
+    >>> from math import isclose
+    >>> isclose(expectation([1, 2], [0.7, 0.3]), 1.3)
+    True
+    """
+    return sum(x * p for x, p in zip(values, probabilities))
+
+
+# Function to calculate the variance
+def variance(values: list[int], probabilities: list[float]) -> float:
+    """
+    >>> from math import isclose
+    >>> isclose(variance([1,2],[0.7,0.3]), 0.21)
+    True
+    """
+    mean = expectation(values, probabilities)
+    return sum((x - mean) ** 2 * p for x, p in zip(values, probabilities))
+
+
+# Function to calculate the covariance
+def covariance(
+    x_values: list[int],
+    y_values: list[int],
+    x_probabilities: list[float],
+    y_probabilities: list[float],
+) -> float:
+    """
+    >>> covariance([1, 2], [-2, 5, 8], [0.7, 0.3], [0.3, 0.5, 0.2])
+    -2.7755575615628914e-17
+    """
+    mean_x = expectation(x_values, x_probabilities)
+    mean_y = expectation(y_values, y_probabilities)
+    return sum(
+        (x - mean_x) * (y - mean_y) * px * py
+        for x, px in zip(x_values, x_probabilities)
+        for y, py in zip(y_values, y_probabilities)
+    )
+
+
+# Function to calculate the standard deviation
+def standard_deviation(variance: float) -> float:
+    """
+    >>> standard_deviation(0.21)
+    0.458257569495584
+    """
+    return variance**0.5
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()
+    # Input values for X and Y
+    x_vals = input("Enter values of X separated by spaces: ").split()
+    y_vals = input("Enter values of Y separated by spaces: ").split()
+
+    # Convert input values to integers
+    x_values = [int(x) for x in x_vals]
+    y_values = [int(y) for y in y_vals]
+
+    # Input probabilities for X and Y
+    x_probs = input("Enter probabilities for X separated by spaces: ").split()
+    y_probs = input("Enter probabilities for Y separated by spaces: ").split()
+    assert len(x_values) == len(x_probs)
+    assert len(y_values) == len(y_probs)
+
+    # Convert input probabilities to floats
+    x_probabilities = [float(p) for p in x_probs]
+    y_probabilities = [float(p) for p in y_probs]
+
+    # Calculate the joint probability distribution
+    jpd = joint_probability_distribution(
+        x_values, y_values, x_probabilities, y_probabilities
+    )
+
+    # Print the joint probability distribution
+    print(
+        "\n".join(
+            f"P(X={x}, Y={y}) = {probability}" for (x, y), probability in jpd.items()
+        )
+    )
+    mean_xy = expectation(
+        [x * y for x in x_values for y in y_values],
+        [px * py for px in x_probabilities for py in y_probabilities],
+    )
+    print(f"x mean: {expectation(x_values, x_probabilities) = }")
+    print(f"y mean: {expectation(y_values, y_probabilities) = }")
+    print(f"xy mean: {mean_xy}")
+    print(f"x: {variance(x_values, x_probabilities) = }")
+    print(f"y: {variance(y_values, y_probabilities) = }")
+    print(f"{covariance(x_values, y_values, x_probabilities, y_probabilities) = }")
+    print(f"x: {standard_deviation(variance(x_values, x_probabilities)) = }")
+    print(f"y: {standard_deviation(variance(y_values, y_probabilities)) = }")