Merge branch 'TheAlgorithms:master' into terminal_velocity

Author: pluto-tofu

Diff for: .github/ISSUE_TEMPLATE/feature_request.yml

@@ -6,14 +6,14 @@ body:
     attributes:
       value: >
         Before requesting please search [existing issues](https://github.com/TheAlgorithms/Python/labels/enhancement).
+        Do not create issues to implement new algorithms as these will be closed.
         Usage questions such as "How do I...?"  belong on the
         [Discord](https://discord.gg/c7MnfGFGa6) and will be closed.
 
   - type: textarea
     attributes:
       label: "Feature description"
       description: >
-        This could be new algorithms, data structures or improving any existing
-        implementations.
+        This could include new topics or improving any existing implementations.
     validations:
       required: true

Diff for: .pre-commit-config.yaml

@@ -46,7 +46,7 @@ repos:
         pass_filenames: false
 
   - repo: https://github.com/abravalheri/validate-pyproject
-    rev: v0.14
+    rev: v0.15
     hooks:
       - id: validate-pyproject
 

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)
 
@@ -174,10 +176,13 @@
 ## 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)
+    * [Sparse Table](data_structures/arrays/sparse_table.py)
   * Binary Tree
     * [Avl Tree](data_structures/binary_tree/avl_tree.py)
     * [Basic Binary Tree](data_structures/binary_tree/basic_binary_tree.py)
@@ -187,10 +192,12 @@
     * [Binary Tree Node Sum](data_structures/binary_tree/binary_tree_node_sum.py)
     * [Binary Tree Path Sum](data_structures/binary_tree/binary_tree_path_sum.py)
     * [Binary Tree Traversals](data_structures/binary_tree/binary_tree_traversals.py)
+    * [Diameter Of Binary Tree](data_structures/binary_tree/diameter_of_binary_tree.py)
     * [Diff Views Of Binary Tree](data_structures/binary_tree/diff_views_of_binary_tree.py)
     * [Distribute Coins](data_structures/binary_tree/distribute_coins.py)
     * [Fenwick Tree](data_structures/binary_tree/fenwick_tree.py)
     * [Flatten Binarytree To Linkedlist](data_structures/binary_tree/flatten_binarytree_to_linkedlist.py)
+    * [Floor And Ceiling](data_structures/binary_tree/floor_and_ceiling.py)
     * [Inorder Tree Traversal 2022](data_structures/binary_tree/inorder_tree_traversal_2022.py)
     * [Is Bst](data_structures/binary_tree/is_bst.py)
     * [Lazy Segment Tree](data_structures/binary_tree/lazy_segment_tree.py)
@@ -261,6 +268,7 @@
     * [Postfix Evaluation](data_structures/stacks/postfix_evaluation.py)
     * [Prefix Evaluation](data_structures/stacks/prefix_evaluation.py)
     * [Stack](data_structures/stacks/stack.py)
+    * [Stack Using Two Queues](data_structures/stacks/stack_using_two_queues.py)
     * [Stack With Doubly Linked List](data_structures/stacks/stack_with_doubly_linked_list.py)
     * [Stack With Singly Linked List](data_structures/stacks/stack_with_singly_linked_list.py)
     * [Stock Span Problem](data_structures/stacks/stock_span_problem.py)
@@ -334,7 +342,7 @@
   * [Longest Increasing Subsequence](dynamic_programming/longest_increasing_subsequence.py)
   * [Longest Increasing Subsequence O(Nlogn)](dynamic_programming/longest_increasing_subsequence_o(nlogn).py)
   * [Longest Palindromic Subsequence](dynamic_programming/longest_palindromic_subsequence.py)
-  * [Longest Sub Array](dynamic_programming/longest_sub_array.py)
+  * [Matrix Chain Multiplication](dynamic_programming/matrix_chain_multiplication.py)
   * [Matrix Chain Order](dynamic_programming/matrix_chain_order.py)
   * [Max Non Adjacent Sum](dynamic_programming/max_non_adjacent_sum.py)
   * [Max Product Subarray](dynamic_programming/max_product_subarray.py)
@@ -357,18 +365,21 @@
   * [Trapped Water](dynamic_programming/trapped_water.py)
   * [Tribonacci](dynamic_programming/tribonacci.py)
   * [Viterbi](dynamic_programming/viterbi.py)
+  * [Wildcard Matching](dynamic_programming/wildcard_matching.py)
   * [Word Break](dynamic_programming/word_break.py)
 
 ## Electronics
   * [Apparent Power](electronics/apparent_power.py)
   * [Builtin Voltage](electronics/builtin_voltage.py)
   * [Carrier Concentration](electronics/carrier_concentration.py)
   * [Charging Capacitor](electronics/charging_capacitor.py)
+  * [Charging Inductor](electronics/charging_inductor.py)
   * [Circular Convolution](electronics/circular_convolution.py)
   * [Coulombs Law](electronics/coulombs_law.py)
   * [Electric Conductivity](electronics/electric_conductivity.py)
   * [Electric Power](electronics/electric_power.py)
   * [Electrical Impedance](electronics/electrical_impedance.py)
+  * [Ic 555 Timer](electronics/ic_555_timer.py)
   * [Ind Reactance](electronics/ind_reactance.py)
   * [Ohms Law](electronics/ohms_law.py)
   * [Real And Reactive Power](electronics/real_and_reactive_power.py)
@@ -385,6 +396,7 @@
 
 ## 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)
@@ -475,6 +487,7 @@
   * [Fractional Knapsack](greedy_methods/fractional_knapsack.py)
   * [Fractional Knapsack 2](greedy_methods/fractional_knapsack_2.py)
   * [Gas Station](greedy_methods/gas_station.py)
+  * [Minimum Coin Change](greedy_methods/minimum_coin_change.py)
   * [Minimum Waiting Time](greedy_methods/minimum_waiting_time.py)
   * [Optimal Merge Pattern](greedy_methods/optimal_merge_pattern.py)
 
@@ -516,6 +529,7 @@
   * [Simplex](linear_programming/simplex.py)
 
 ## Machine Learning
+  * [Apriori Algorithm](machine_learning/apriori_algorithm.py)
   * [Astar](machine_learning/astar.py)
   * [Data Transformations](machine_learning/data_transformations.py)
   * [Decision Tree](machine_learning/decision_tree.py)
@@ -606,7 +620,6 @@
   * [Gcd Of N Numbers](maths/gcd_of_n_numbers.py)
   * [Germain Primes](maths/germain_primes.py)
   * [Greatest Common Divisor](maths/greatest_common_divisor.py)
-  * [Greedy Coin Change](maths/greedy_coin_change.py)
   * [Hamming Numbers](maths/hamming_numbers.py)
   * [Hardy Ramanujanalgo](maths/hardy_ramanujanalgo.py)
   * [Harshad Numbers](maths/harshad_numbers.py)
@@ -617,6 +630,7 @@
   * [Is Ip V4 Address Valid](maths/is_ip_v4_address_valid.py)
   * [Is Square Free](maths/is_square_free.py)
   * [Jaccard Similarity](maths/jaccard_similarity.py)
+  * [Joint Probability Distribution](maths/joint_probability_distribution.py)
   * [Juggler Sequence](maths/juggler_sequence.py)
   * [Karatsuba](maths/karatsuba.py)
   * [Krishnamurthy Number](maths/krishnamurthy_number.py)
@@ -671,6 +685,7 @@
   * [Radix2 Fft](maths/radix2_fft.py)
   * [Remove Digit](maths/remove_digit.py)
   * [Runge Kutta](maths/runge_kutta.py)
+  * [Runge Kutta Fehlberg 45](maths/runge_kutta_fehlberg_45.py)
   * [Segmented Sieve](maths/segmented_sieve.py)
   * Series
     * [Arithmetic](maths/series/arithmetic.py)
@@ -688,6 +703,7 @@
   * [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 +744,7 @@
   * [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)
@@ -781,7 +798,7 @@
 
 ## Physics
   * [Altitude Pressure](physics/altitude_pressure.py)
-  * [Archimedes Principle](physics/archimedes_principle.py)
+  * [Archimedes Principle Of Buoyant Force](physics/archimedes_principle_of_buoyant_force.py)
   * [Basic Orbital Capture](physics/basic_orbital_capture.py)
   * [Casimir Effect](physics/casimir_effect.py)
   * [Centripetal Force](physics/centripetal_force.py)
@@ -803,6 +820,7 @@
   * [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 +1124,7 @@
 ## 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 +1212,7 @@
   * [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 +1245,7 @@
   * [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: arithmetic_analysis/lu_decomposition.py

@@ -88,15 +88,19 @@ def lower_upper_decomposition(table: np.ndarray) -> tuple[np.ndarray, np.ndarray
 
     lower = np.zeros((rows, columns))
     upper = np.zeros((rows, columns))
+
+    # in 'total', the necessary data is extracted through slices
+    # and the sum of the products is obtained.
+
     for i in range(columns):
         for j in range(i):
-            total = sum(lower[i][k] * upper[k][j] for k in range(j))
+            total = np.sum(lower[i, :i] * upper[:i, j])
             if upper[j][j] == 0:
                 raise ArithmeticError("No LU decomposition exists")
             lower[i][j] = (table[i][j] - total) / upper[j][j]
         lower[i][i] = 1
         for j in range(i, columns):
-            total = sum(lower[i][k] * upper[k][j] for k in range(j))
+            total = np.sum(lower[i, :i] * upper[:i, j])
             upper[i][j] = table[i][j] - total
     return lower, upper
 

Diff for: backtracking/all_combinations.py

@@ -1,15 +1,40 @@
 """
         In this problem, we want to determine all possible combinations of k
         numbers out of 1 ... n. We use backtracking to solve this problem.
-        Time complexity: O(C(n,k)) which is O(n choose k) = O((n!/(k! * (n - k)!)))
+
+        Time complexity: O(C(n,k)) which is O(n choose k) = O((n!/(k! * (n - k)!))),
 """
 from __future__ import annotations
 
+from itertools import combinations
+
+
+def combination_lists(n: int, k: int) -> list[list[int]]:
+    """
+    >>> combination_lists(n=4, k=2)
+    [[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]
+    """
+    return [list(x) for x in combinations(range(1, n + 1), k)]
+
 
 def generate_all_combinations(n: int, k: int) -> list[list[int]]:
     """
     >>> generate_all_combinations(n=4, k=2)
     [[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]
+    >>> generate_all_combinations(n=0, k=0)
+    [[]]
+    >>> generate_all_combinations(n=10, k=-1)
+    Traceback (most recent call last):
+        ...
+    RecursionError: maximum recursion depth exceeded
+    >>> generate_all_combinations(n=-1, k=10)
+    []
+    >>> generate_all_combinations(n=5, k=4)
+    [[1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 4, 5], [1, 3, 4, 5], [2, 3, 4, 5]]
+    >>> from itertools import combinations
+    >>> all(generate_all_combinations(n, k) == combination_lists(n, k)
+    ...     for n in range(1, 6) for k in range(1, 6))
+    True
     """
 
     result: list[list[int]] = []
@@ -34,13 +59,17 @@ def create_all_state(
         current_list.pop()
 
 
-def print_all_state(total_list: list[list[int]]) -> None:
-    for i in total_list:
-        print(*i)
+if __name__ == "__main__":
+    from doctest import testmod
 
+    testmod()
+    print(generate_all_combinations(n=4, k=2))
+    tests = ((n, k) for n in range(1, 5) for k in range(1, 5))
+    for n, k in tests:
+        print(n, k, generate_all_combinations(n, k) == combination_lists(n, k))
 
-if __name__ == "__main__":
-    n = 4
-    k = 2
-    total_list = generate_all_combinations(n, k)
-    print_all_state(total_list)
+    print("Benchmark:")
+    from timeit import timeit
+
+    for func in ("combination_lists", "generate_all_combinations"):
+        print(f"{func:>25}(): {timeit(f'{func}(n=4, k = 2)', globals=globals())}")

Diff for: backtracking/power_sum.py

@@ -6,8 +6,6 @@
 The only solution is 2^2+3^2. Constraints: 1<=X<=1000, 2<=N<=10.
 """
 
-from math import pow
-
 
 def backtrack(
     needed_sum: int,
@@ -19,25 +17,25 @@ def backtrack(
     """
     >>> backtrack(13, 2, 1, 0, 0)
     (0, 1)
-    >>> backtrack(100, 2, 1, 0, 0)
-    (0, 3)
-    >>> backtrack(100, 3, 1, 0, 0)
+    >>> backtrack(10, 2, 1, 0, 0)
+    (0, 1)
+    >>> backtrack(10, 3, 1, 0, 0)
+    (0, 0)
+    >>> backtrack(20, 2, 1, 0, 0)
     (0, 1)
-    >>> backtrack(800, 2, 1, 0, 0)
-    (0, 561)
-    >>> backtrack(1000, 10, 1, 0, 0)
+    >>> backtrack(15, 10, 1, 0, 0)
     (0, 0)
-    >>> backtrack(400, 2, 1, 0, 0)
-    (0, 55)
-    >>> backtrack(50, 1, 1, 0, 0)
-    (0, 3658)
+    >>> backtrack(16, 2, 1, 0, 0)
+    (0, 1)
+    >>> backtrack(20, 1, 1, 0, 0)
+    (0, 64)
     """
     if current_sum == needed_sum:
         # If the sum of the powers is equal to needed_sum, then we have a solution.
         solutions_count += 1
         return current_sum, solutions_count
 
-    i_to_n = int(pow(current_number, power))
+    i_to_n = current_number**power
     if current_sum + i_to_n <= needed_sum:
         # If the sum of the powers is less than needed_sum, then continue adding powers.
         current_sum += i_to_n
@@ -57,17 +55,17 @@ def solve(needed_sum: int, power: int) -> int:
     """
     >>> solve(13, 2)
     1
-    >>> solve(100, 2)
-    3
-    >>> solve(100, 3)
+    >>> solve(10, 2)
     1
-    >>> solve(800, 2)
-    561
-    >>> solve(1000, 10)
+    >>> solve(10, 3)
     0
-    >>> solve(400, 2)
-    55
-    >>> solve(50, 1)
+    >>> solve(20, 2)
+    1
+    >>> solve(15, 10)
+    0
+    >>> solve(16, 2)
+    1
+    >>> solve(20, 1)
     Traceback (most recent call last):
         ...
     ValueError: Invalid input