From 6d136036672072a2c4870da7741d4ad3026a7357 Mon Sep 17 00:00:00 2001 From: Vipin Karthic <143083087+vipinkarthic@users.noreply.github.com> Date: Tue, 10 Oct 2023 11:22:37 +0530 Subject: [PATCH] Fixes #9943 Added Doctests to binary_exponentiation_3.py (#10121) * Python mirror_formulae.py is added to the repository * Changes done after reading readme.md * Changes for running doctest on all platforms * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Change 2 for Doctests * Changes for doctest 2 * updating DIRECTORY.md * Doctest whitespace error rectification to mirror_formulae.py * updating DIRECTORY.md * Adding Thermodynamic Work Done Formulae * Work done on/by body in a thermodynamic setting * updating DIRECTORY.md * updating DIRECTORY.md * Doctest adiition to binary_exponentiation_3.py * Change 1 * updating DIRECTORY.md * Rename binary_exponentiation_3.py to binary_exponentiation_2.py * updating DIRECTORY.md * updating DIRECTORY.md * Formatting --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Co-authored-by: Christian Clauss Co-authored-by: Tianyi Zheng --- DIRECTORY.md | 26 +++++++++++++-- maths/binary_exponentiation_2.py | 57 +++++++++++++++++++------------- 2 files changed, 58 insertions(+), 25 deletions(-) diff --git a/DIRECTORY.md b/DIRECTORY.md index b1a23a239..015efb3c7 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -54,13 +54,12 @@ * [Largest Pow Of Two Le Num](bit_manipulation/largest_pow_of_two_le_num.py) * [Missing Number](bit_manipulation/missing_number.py) * [Numbers Different Signs](bit_manipulation/numbers_different_signs.py) + * [Power Of 4](bit_manipulation/power_of_4.py) * [Reverse Bits](bit_manipulation/reverse_bits.py) * [Single Bit Manipulation Operations](bit_manipulation/single_bit_manipulation_operations.py) ## Blockchain - * [Chinese Remainder Theorem](blockchain/chinese_remainder_theorem.py) * [Diophantine Equation](blockchain/diophantine_equation.py) - * [Modular Division](blockchain/modular_division.py) ## Boolean Algebra * [And Gate](boolean_algebra/and_gate.py) @@ -101,11 +100,13 @@ * [Diffie Hellman](ciphers/diffie_hellman.py) * [Elgamal Key Generator](ciphers/elgamal_key_generator.py) * [Enigma Machine2](ciphers/enigma_machine2.py) + * [Fractionated Morse Cipher](ciphers/fractionated_morse_cipher.py) * [Hill Cipher](ciphers/hill_cipher.py) * [Mixed Keyword Cypher](ciphers/mixed_keyword_cypher.py) * [Mono Alphabetic Ciphers](ciphers/mono_alphabetic_ciphers.py) * [Morse Code](ciphers/morse_code.py) * [Onepad Cipher](ciphers/onepad_cipher.py) + * [Permutation Cipher](ciphers/permutation_cipher.py) * [Playfair Cipher](ciphers/playfair_cipher.py) * [Polybius](ciphers/polybius.py) * [Porta Cipher](ciphers/porta_cipher.py) @@ -172,6 +173,7 @@ ## Data Structures * Arrays + * [Equilibrium Index In Array](data_structures/arrays/equilibrium_index_in_array.py) * [Median Two Array](data_structures/arrays/median_two_array.py) * [Permutations](data_structures/arrays/permutations.py) * [Prefix Sum](data_structures/arrays/prefix_sum.py) @@ -352,6 +354,7 @@ * [Smith Waterman](dynamic_programming/smith_waterman.py) * [Subset Generation](dynamic_programming/subset_generation.py) * [Sum Of Subset](dynamic_programming/sum_of_subset.py) + * [Trapped Water](dynamic_programming/trapped_water.py) * [Tribonacci](dynamic_programming/tribonacci.py) * [Viterbi](dynamic_programming/viterbi.py) * [Word Break](dynamic_programming/word_break.py) @@ -360,6 +363,7 @@ * [Apparent Power](electronics/apparent_power.py) * [Builtin Voltage](electronics/builtin_voltage.py) * [Carrier Concentration](electronics/carrier_concentration.py) + * [Charging Capacitor](electronics/charging_capacitor.py) * [Circular Convolution](electronics/circular_convolution.py) * [Coulombs Law](electronics/coulombs_law.py) * [Electric Conductivity](electronics/electric_conductivity.py) @@ -466,6 +470,8 @@ * [Test Min Spanning Tree Prim](graphs/tests/test_min_spanning_tree_prim.py) ## Greedy Methods + * [Best Time To Buy And Sell Stock](greedy_methods/best_time_to_buy_and_sell_stock.py) + * [Fractional Cover Problem](greedy_methods/fractional_cover_problem.py) * [Fractional Knapsack](greedy_methods/fractional_knapsack.py) * [Fractional Knapsack 2](greedy_methods/fractional_knapsack_2.py) * [Gas Station](greedy_methods/gas_station.py) @@ -524,6 +530,10 @@ * Local Weighted Learning * [Local Weighted Learning](machine_learning/local_weighted_learning/local_weighted_learning.py) * [Logistic Regression](machine_learning/logistic_regression.py) + * Loss Functions + * [Binary Cross Entropy](machine_learning/loss_functions/binary_cross_entropy.py) + * [Huber Loss](machine_learning/loss_functions/huber_loss.py) + * [Mean Squared Error](machine_learning/loss_functions/mean_squared_error.py) * [Mfcc](machine_learning/mfcc.py) * [Multilayer Perceptron Classifier](machine_learning/multilayer_perceptron_classifier.py) * [Polynomial Regression](machine_learning/polynomial_regression.py) @@ -564,7 +574,9 @@ * [Carmichael Number](maths/carmichael_number.py) * [Catalan Number](maths/catalan_number.py) * [Ceil](maths/ceil.py) + * [Chebyshev Distance](maths/chebyshev_distance.py) * [Check Polygon](maths/check_polygon.py) + * [Chinese Remainder Theorem](maths/chinese_remainder_theorem.py) * [Chudnovsky Algorithm](maths/chudnovsky_algorithm.py) * [Collatz Sequence](maths/collatz_sequence.py) * [Combinations](maths/combinations.py) @@ -591,6 +603,7 @@ * [Gaussian](maths/gaussian.py) * [Gaussian Error Linear Unit](maths/gaussian_error_linear_unit.py) * [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) @@ -618,7 +631,9 @@ * [Matrix Exponentiation](maths/matrix_exponentiation.py) * [Max Sum Sliding Window](maths/max_sum_sliding_window.py) * [Median Of Two Arrays](maths/median_of_two_arrays.py) + * [Minkowski Distance](maths/minkowski_distance.py) * [Mobius Function](maths/mobius_function.py) + * [Modular Division](maths/modular_division.py) * [Modular Exponential](maths/modular_exponential.py) * [Monte Carlo](maths/monte_carlo.py) * [Monte Carlo Dice](maths/monte_carlo_dice.py) @@ -720,12 +735,16 @@ ## Neural Network * [2 Hidden Layers Neural Network](neural_network/2_hidden_layers_neural_network.py) * Activation Functions + * [Binary Step](neural_network/activation_functions/binary_step.py) * [Exponential Linear Unit](neural_network/activation_functions/exponential_linear_unit.py) * [Leaky Rectified Linear Unit](neural_network/activation_functions/leaky_rectified_linear_unit.py) * [Mish](neural_network/activation_functions/mish.py) * [Rectified Linear Unit](neural_network/activation_functions/rectified_linear_unit.py) * [Scaled Exponential Linear Unit](neural_network/activation_functions/scaled_exponential_linear_unit.py) * [Sigmoid Linear Unit](neural_network/activation_functions/sigmoid_linear_unit.py) + * [Soboleva Modified Hyperbolic Tangent](neural_network/activation_functions/soboleva_modified_hyperbolic_tangent.py) + * [Softplus](neural_network/activation_functions/softplus.py) + * [Squareplus](neural_network/activation_functions/squareplus.py) * [Back Propagation Neural Network](neural_network/back_propagation_neural_network.py) * [Convolution Neural Network](neural_network/convolution_neural_network.py) * [Perceptron](neural_network/perceptron.py) @@ -779,6 +798,7 @@ * [Newtons Second Law Of Motion](physics/newtons_second_law_of_motion.py) * [Photoelectric Effect](physics/photoelectric_effect.py) * [Potential Energy](physics/potential_energy.py) + * [Reynolds Number](physics/reynolds_number.py) * [Rms Speed Of Molecule](physics/rms_speed_of_molecule.py) * [Shear Stress](physics/shear_stress.py) * [Speed Of Sound](physics/speed_of_sound.py) @@ -1101,6 +1121,7 @@ * [Interpolation Search](searches/interpolation_search.py) * [Jump Search](searches/jump_search.py) * [Linear Search](searches/linear_search.py) + * [Median Of Medians](searches/median_of_medians.py) * [Quick Select](searches/quick_select.py) * [Sentinel Linear Search](searches/sentinel_linear_search.py) * [Simple Binary Search](searches/simple_binary_search.py) @@ -1201,6 +1222,7 @@ * [Snake Case To Camel Pascal Case](strings/snake_case_to_camel_pascal_case.py) * [Split](strings/split.py) * [String Switch Case](strings/string_switch_case.py) + * [Strip](strings/strip.py) * [Text Justification](strings/text_justification.py) * [Top K Frequent Words](strings/top_k_frequent_words.py) * [Upper](strings/upper.py) diff --git a/maths/binary_exponentiation_2.py b/maths/binary_exponentiation_2.py index 9cd143e09..edb6b66b2 100644 --- a/maths/binary_exponentiation_2.py +++ b/maths/binary_exponentiation_2.py @@ -1,17 +1,33 @@ """ -* Binary Exponentiation for Powers -* This is a method to find a^b in a time complexity of O(log b) -* This is one of the most commonly used methods of finding powers. -* Also useful in cases where solution to (a^b)%c is required, -* where a,b,c can be numbers over the computers calculation limits. -* Done using iteration, can also be done using recursion +Binary Exponentiation +This is a method to find a^b in O(log b) time complexity +This is one of the most commonly used methods of exponentiation +It's also useful when the solution to (a^b) % c is required because a, b, c may be +over the computer's calculation limits -* @author chinmoy159 -* @version 1.0 dated 10/08/2017 +Let's say you need to calculate a ^ b +- RULE 1 : a ^ b = (a*a) ^ (b/2) ---- example : 4 ^ 4 = (4*4) ^ (4/2) = 16 ^ 2 +- RULE 2 : IF b is odd, then a ^ b = a * (a ^ (b - 1)), where b - 1 is even +Once b is even, repeat the process until b = 1 or b = 0, because a^1 = a and a^0 = 1 + +For modular exponentiation, we use the fact that (a*b) % c = ((a%c) * (b%c)) % c +Now apply RULE 1 or 2 as required + +@author chinmoy159 """ def b_expo(a: int, b: int) -> int: + """ + >>> b_expo(2, 10) + 1024 + >>> b_expo(9, 0) + 1 + >>> b_expo(0, 12) + 0 + >>> b_expo(4, 12) + 16777216 + """ res = 1 while b > 0: if b & 1: @@ -24,6 +40,16 @@ def b_expo(a: int, b: int) -> int: def b_expo_mod(a: int, b: int, c: int) -> int: + """ + >>> b_expo_mod(2, 10, 1000000007) + 1024 + >>> b_expo_mod(11, 13, 19) + 11 + >>> b_expo_mod(0, 19, 20) + 0 + >>> b_expo_mod(15, 5, 4) + 3 + """ res = 1 while b > 0: if b & 1: @@ -33,18 +59,3 @@ def b_expo_mod(a: int, b: int, c: int) -> int: b >>= 1 return res - - -""" -* Wondering how this method works ! -* It's pretty simple. -* Let's say you need to calculate a ^ b -* RULE 1 : a ^ b = (a*a) ^ (b/2) ---- example : 4 ^ 4 = (4*4) ^ (4/2) = 16 ^ 2 -* RULE 2 : IF b is ODD, then ---- a ^ b = a * (a ^ (b - 1)) :: where (b - 1) is even. -* Once b is even, repeat the process to get a ^ b -* Repeat the process till b = 1 OR b = 0, because a^1 = a AND a^0 = 1 -* -* As far as the modulo is concerned, -* the fact : (a*b) % c = ((a%c) * (b%c)) % c -* Now apply RULE 1 OR 2 whichever is required. -"""