Added Chakravala method to solve pell's equation

DIRECTORY.md

@@ -9,6 +9,7 @@
  * [Newton Forward Interpolation](arithmetic_analysis/newton_forward_interpolation.py)
  * [Newton Method](arithmetic_analysis/newton_method.py)
  * [Newton Raphson](arithmetic_analysis/newton_raphson.py)
+ * [Newton Raphson New](arithmetic_analysis/newton_raphson_new.py)
  * [Secant Method](arithmetic_analysis/secant_method.py)
 
 ## Audio Filters
@@ -107,6 +108,7 @@
  * [Lempel Ziv](compression/lempel_ziv.py)
  * [Lempel Ziv Decompress](compression/lempel_ziv_decompress.py)
  * [Peak Signal To Noise Ratio](compression/peak_signal_to_noise_ratio.py)
+ * [Run Length Encoding](compression/run_length_encoding.py)
 
 ## Computer Vision
  * [Cnn Classification](computer_vision/cnn_classification.py)
@@ -474,6 +476,7 @@
  * [Binomial Distribution](maths/binomial_distribution.py)
  * [Bisection](maths/bisection.py)
  * [Ceil](maths/ceil.py)
+ * [Chakravala](maths/chakravala.py)
  * [Check Polygon](maths/check_polygon.py)
  * [Chudnovsky Algorithm](maths/chudnovsky_algorithm.py)
  * [Collatz Sequence](maths/collatz_sequence.py)
@@ -621,6 +624,7 @@
  * [Linear Congruential Generator](other/linear_congruential_generator.py)
  * [Lru Cache](other/lru_cache.py)
  * [Magicdiamondpattern](other/magicdiamondpattern.py)
+ * [Maximum Subarray](other/maximum_subarray.py)
  * [Nested Brackets](other/nested_brackets.py)
  * [Password Generator](other/password_generator.py)
  * [Scoring Algorithm](other/scoring_algorithm.py)
@@ -1053,6 +1057,7 @@
  * [Fetch Bbc News](web_programming/fetch_bbc_news.py)
  * [Fetch Github Info](web_programming/fetch_github_info.py)
  * [Fetch Jobs](web_programming/fetch_jobs.py)
+ * [Fetch Quotes](web_programming/fetch_quotes.py)
  * [Fetch Well Rx Price](web_programming/fetch_well_rx_price.py)
  * [Get Imdb Top 250 Movies Csv](web_programming/get_imdb_top_250_movies_csv.py)
  * [Get Imdbtop](web_programming/get_imdbtop.py)

maths/chakravala.py

@@ -0,0 +1,120 @@
+"""
+Implementing Chakravala method using python
+
+https://en.wikipedia.org/wiki/Chakravala_method
+https://kappadath-gopal.blogspot.com/2013/04/ancient-medieval-indian-mathematics.html
+
+The chakravala method is a cyclic algorithm to solve indeterminate quadratic equations,
+including Pell's equation.
+
+"""
+
+import math
+
+
+def is_perfect_square(num: int) -> bool:
+ """
+ Check if a number is perfect square number or not
+ :param num: the number to be checked
+ :return: True if number is square number, otherwise False
+
+ >>> is_perfect_square(9)
+ True
+ >>> is_perfect_square(16)
+ True
+ >>> is_perfect_square(1)
+ True
+ >>> is_perfect_square(0)
+ True
+ >>> is_perfect_square(10)
+ False
+ """
+
+ sr = int(math.sqrt(num))
+ return sr * sr == num
+
+
+def chakravala_method(num: int) -> (tuple[int, int] | tuple):
+ """
+ This method takes in the value of N in the equation
+
+ x^2 = N*y^2 + 1
+ :param num: the number N equals to
+ :return: empty tuple if N is perfect square else tuple(x,y)
+
+ >>> chakravala_method(1)
+ ()
+ >>> chakravala_method(2)
+ (3, 2)
+ >>> chakravala_method(4)
+ ()
+ >>> chakravala_method(5)
+ (9, 4)
+ >>> chakravala_method(7)
+ (8, 3)
+
+ """
+
+ if is_perfect_square(num):
+ return ()
+
+ # Takes b = 1 and finds a and k accordingly, refer to algorithm link
+ # variable naming is used as same as algorithm, (a,b,k,m) except N = num
+
+ b = 1
+
+ min_diff = num
+ a = 0
+ while True:
+ diff = abs(num - (a + 1) ** 2)
+ if min_diff > diff:
+ min_diff = diff
+ a += 1
+ continue
+ break
+
+ k = a**2 - num
+
+ while True:
+
+ kabs = abs(k)
+
+ if k == 1:
+ return (a, b)
+
+ if k == -1 or kabs == 2 or (kabs == 4 and (a % 2 == 0 or b % 2 == 0)):
+ return (abs((a**2 + num * b**2) // k), abs(2 * a * b // k))
+
+ min_diff = num
+ n = 1 # loop variable
+ n2 = n # stores the correct value of n
+ while True:
+ if kabs * n <= a:
+ n += 1
+ continue
+ if (kabs * n - a) % b == 0:
+ m = (kabs * n - a) // b
+ else:
+ n += 1
+ continue
+
+ diff = abs(m**2 - num)
+ if min_diff > diff:
+ min_diff = diff
+ n2 = n
+ n += 1
+ continue
+ break
+ m = (kabs * n2 - a) // b
+
+ a, b = abs((a * m + num * b) // k), abs((a + b * m) // k)
+ k = (m**2 - num) // k
+
+
+if __name__ == "__main__":
+
+ import doctest
+
+ doctest.testmod()
+
+ print("X and Y for the equation X^2 - 13Y^2 = 1 is: ", chakravala_method(13))

DIRECTORY.md

@@ -9,6 +9,7 @@
  * [Newton Forward Interpolation](arithmetic_analysis/newton_forward_interpolation.py)
  * [Newton Method](arithmetic_analysis/newton_method.py)
  * [Newton Raphson](arithmetic_analysis/newton_raphson.py)
+ * [Newton Raphson New](arithmetic_analysis/newton_raphson_new.py)
  * [Secant Method](arithmetic_analysis/secant_method.py)
 
 ## Audio Filters
@@ -107,6 +108,7 @@
  * [Lempel Ziv](compression/lempel_ziv.py)
  * [Lempel Ziv Decompress](compression/lempel_ziv_decompress.py)
  * [Peak Signal To Noise Ratio](compression/peak_signal_to_noise_ratio.py)
+ * [Run Length Encoding](compression/run_length_encoding.py)
 
 ## Computer Vision
  * [Cnn Classification](computer_vision/cnn_classification.py)
@@ -474,6 +476,7 @@
  * [Binomial Distribution](maths/binomial_distribution.py)
  * [Bisection](maths/bisection.py)
  * [Ceil](maths/ceil.py)
+ * [Chakravala](maths/chakravala.py)
  * [Check Polygon](maths/check_polygon.py)
  * [Chudnovsky Algorithm](maths/chudnovsky_algorithm.py)
  * [Collatz Sequence](maths/collatz_sequence.py)
@@ -621,6 +624,7 @@
  * [Linear Congruential Generator](other/linear_congruential_generator.py)
  * [Lru Cache](other/lru_cache.py)
  * [Magicdiamondpattern](other/magicdiamondpattern.py)
+ * [Maximum Subarray](other/maximum_subarray.py)
  * [Nested Brackets](other/nested_brackets.py)
  * [Password Generator](other/password_generator.py)
  * [Scoring Algorithm](other/scoring_algorithm.py)
@@ -1053,6 +1057,7 @@
  * [Fetch Bbc News](web_programming/fetch_bbc_news.py)
  * [Fetch Github Info](web_programming/fetch_github_info.py)
  * [Fetch Jobs](web_programming/fetch_jobs.py)
+ * [Fetch Quotes](web_programming/fetch_quotes.py)
  * [Fetch Well Rx Price](web_programming/fetch_well_rx_price.py)
  * [Get Imdb Top 250 Movies Csv](web_programming/get_imdb_top_250_movies_csv.py)
  * [Get Imdbtop](web_programming/get_imdbtop.py)

maths/chakravala.py

@@ -0,0 +1,120 @@
+"""
+Implementing Chakravala method using python
+
+https://en.wikipedia.org/wiki/Chakravala_method
+https://kappadath-gopal.blogspot.com/2013/04/ancient-medieval-indian-mathematics.html
+
+The chakravala method is a cyclic algorithm to solve indeterminate quadratic equations,
+including Pell's equation.
+
+"""
+
+import math
+
+
+def is_perfect_square(num: int) -> bool:
+ """
+ Check if a number is perfect square number or not
+ :param num: the number to be checked
+ :return: True if number is square number, otherwise False
+
+ >>> is_perfect_square(9)
+ True
+ >>> is_perfect_square(16)
+ True
+ >>> is_perfect_square(1)
+ True
+ >>> is_perfect_square(0)
+ True
+ >>> is_perfect_square(10)
+ False
+ """
+
+ sr = int(math.sqrt(num))
+ return sr * sr == num
+
+
+def chakravala_method(num: int) -> (tuple[int, int] | tuple):
+ """
+ This method takes in the value of N in the equation
+
+ x^2 = N*y^2 + 1
+ :param num: the number N equals to
+ :return: empty tuple if N is perfect square else tuple(x,y)
+
+ >>> chakravala_method(1)
+ ()
+ >>> chakravala_method(2)
+ (3, 2)
+ >>> chakravala_method(4)
+ ()
+ >>> chakravala_method(5)
+ (9, 4)
+ >>> chakravala_method(7)
+ (8, 3)
+
+ """
+
+ if is_perfect_square(num):
+ return ()
+
+ # Takes b = 1 and finds a and k accordingly, refer to algorithm link
+ # variable naming is used as same as algorithm, (a,b,k,m) except N = num
+
+ b = 1
+
+ min_diff = num
+ a = 0
+ while True:
+ diff = abs(num - (a + 1) ** 2)
+ if min_diff > diff:
+ min_diff = diff
+ a += 1
+ continue
+ break
+
+ k = a**2 - num
+
+ while True:
+
+ kabs = abs(k)
+
+ if k == 1:
+ return (a, b)
+
+ if k == -1 or kabs == 2 or (kabs == 4 and (a % 2 == 0 or b % 2 == 0)):
+ return (abs((a**2 + num * b**2) // k), abs(2 * a * b // k))
+
+ min_diff = num
+ n = 1 # loop variable
+ n2 = n # stores the correct value of n
+ while True:
+ if kabs * n <= a:
+ n += 1
+ continue
+ if (kabs * n - a) % b == 0:
+ m = (kabs * n - a) // b
+ else:
+ n += 1
+ continue
+
+ diff = abs(m**2 - num)
+ if min_diff > diff:
+ min_diff = diff
+ n2 = n
+ n += 1
+ continue
+ break
+ m = (kabs * n2 - a) // b
+
+ a, b = abs((a * m + num * b) // k), abs((a + b * m) // k)
+ k = (m**2 - num) // k
+
+
+if __name__ == "__main__":
+
+ import doctest
+
+ doctest.testmod()
+
+ print("X and Y for the equation X^2 - 13Y^2 = 1 is: ", chakravala_method(13))

DIRECTORY.md

@@ -9,6 +9,7 @@
  * [Newton Forward Interpolation](arithmetic_analysis/newton_forward_interpolation.py)
  * [Newton Method](arithmetic_analysis/newton_method.py)
  * [Newton Raphson](arithmetic_analysis/newton_raphson.py)
+ * [Newton Raphson New](arithmetic_analysis/newton_raphson_new.py)
  * [Secant Method](arithmetic_analysis/secant_method.py)
 
 ## Audio Filters
@@ -107,6 +108,7 @@
  * [Lempel Ziv](compression/lempel_ziv.py)
  * [Lempel Ziv Decompress](compression/lempel_ziv_decompress.py)
  * [Peak Signal To Noise Ratio](compression/peak_signal_to_noise_ratio.py)
+ * [Run Length Encoding](compression/run_length_encoding.py)
 
 ## Computer Vision
  * [Cnn Classification](computer_vision/cnn_classification.py)
@@ -474,6 +476,7 @@
  * [Binomial Distribution](maths/binomial_distribution.py)
  * [Bisection](maths/bisection.py)
  * [Ceil](maths/ceil.py)
+ * [Chakravala](maths/chakravala.py)
  * [Check Polygon](maths/check_polygon.py)
  * [Chudnovsky Algorithm](maths/chudnovsky_algorithm.py)
  * [Collatz Sequence](maths/collatz_sequence.py)
@@ -621,6 +624,7 @@
  * [Linear Congruential Generator](other/linear_congruential_generator.py)
  * [Lru Cache](other/lru_cache.py)
  * [Magicdiamondpattern](other/magicdiamondpattern.py)
+ * [Maximum Subarray](other/maximum_subarray.py)
  * [Nested Brackets](other/nested_brackets.py)
  * [Password Generator](other/password_generator.py)
  * [Scoring Algorithm](other/scoring_algorithm.py)
@@ -1053,6 +1057,7 @@
  * [Fetch Bbc News](web_programming/fetch_bbc_news.py)
  * [Fetch Github Info](web_programming/fetch_github_info.py)
  * [Fetch Jobs](web_programming/fetch_jobs.py)
+ * [Fetch Quotes](web_programming/fetch_quotes.py)
  * [Fetch Well Rx Price](web_programming/fetch_well_rx_price.py)
  * [Get Imdb Top 250 Movies Csv](web_programming/get_imdb_top_250_movies_csv.py)
  * [Get Imdbtop](web_programming/get_imdbtop.py)

maths/chakravala.py

@@ -0,0 +1,120 @@
+"""
+Implementing Chakravala method using python
+
+https://en.wikipedia.org/wiki/Chakravala_method
+https://kappadath-gopal.blogspot.com/2013/04/ancient-medieval-indian-mathematics.html
+
+The chakravala method is a cyclic algorithm to solve indeterminate quadratic equations,
+including Pell's equation.
+
+"""
+
+import math
+
+
+def is_perfect_square(num: int) -> bool:
+ """
+ Check if a number is perfect square number or not
+ :param num: the number to be checked
+ :return: True if number is square number, otherwise False
+
+ >>> is_perfect_square(9)
+ True
+ >>> is_perfect_square(16)
+ True
+ >>> is_perfect_square(1)
+ True
+ >>> is_perfect_square(0)
+ True
+ >>> is_perfect_square(10)
+ False
+ """
+
+ sr = int(math.sqrt(num))
+ return sr * sr == num
+
+
+def chakravala_method(num: int) -> (tuple[int, int] | tuple):
+ """
+ This method takes in the value of N in the equation
+
+ x^2 = N*y^2 + 1
+ :param num: the number N equals to
+ :return: empty tuple if N is perfect square else tuple(x,y)
+
+ >>> chakravala_method(1)
+ ()
+ >>> chakravala_method(2)
+ (3, 2)
+ >>> chakravala_method(4)
+ ()
+ >>> chakravala_method(5)
+ (9, 4)
+ >>> chakravala_method(7)
+ (8, 3)
+
+ """
+
+ if is_perfect_square(num):
+ return ()
+
+ # Takes b = 1 and finds a and k accordingly, refer to algorithm link
+ # variable naming is used as same as algorithm, (a,b,k,m) except N = num
+
+ b = 1
+
+ min_diff = num
+ a = 0
+ while True:
+ diff = abs(num - (a + 1) ** 2)
+ if min_diff > diff:
+ min_diff = diff
+ a += 1
+ continue
+ break
+
+ k = a**2 - num
+
+ while True:
+
+ kabs = abs(k)
+
+ if k == 1:
+ return (a, b)
+
+ if k == -1 or kabs == 2 or (kabs == 4 and (a % 2 == 0 or b % 2 == 0)):
+ return (abs((a**2 + num * b**2) // k), abs(2 * a * b // k))
+
+ min_diff = num
+ n = 1 # loop variable
+ n2 = n # stores the correct value of n
+ while True:
+ if kabs * n <= a:
+ n += 1
+ continue
+ if (kabs * n - a) % b == 0:
+ m = (kabs * n - a) // b
+ else:
+ n += 1
+ continue
+
+ diff = abs(m**2 - num)
+ if min_diff > diff:
+ min_diff = diff
+ n2 = n
+ n += 1
+ continue
+ break
+ m = (kabs * n2 - a) // b
+
+ a, b = abs((a * m + num * b) // k), abs((a + b * m) // k)
+ k = (m**2 - num) // k
+
+
+if __name__ == "__main__":
+
+ import doctest
+
+ doctest.testmod()
+
+ print("X and Y for the equation X^2 - 13Y^2 = 1 is: ", chakravala_method(13))

DIRECTORY.md

@@ -9,6 +9,7 @@
  * [Newton Forward Interpolation](arithmetic_analysis/newton_forward_interpolation.py)
  * [Newton Method](arithmetic_analysis/newton_method.py)
  * [Newton Raphson](arithmetic_analysis/newton_raphson.py)
+ * [Newton Raphson New](arithmetic_analysis/newton_raphson_new.py)
  * [Secant Method](arithmetic_analysis/secant_method.py)
 
 ## Audio Filters
@@ -107,6 +108,7 @@
  * [Lempel Ziv](compression/lempel_ziv.py)
  * [Lempel Ziv Decompress](compression/lempel_ziv_decompress.py)
  * [Peak Signal To Noise Ratio](compression/peak_signal_to_noise_ratio.py)
+ * [Run Length Encoding](compression/run_length_encoding.py)
 
 ## Computer Vision
  * [Cnn Classification](computer_vision/cnn_classification.py)
@@ -474,6 +476,7 @@
  * [Binomial Distribution](maths/binomial_distribution.py)
  * [Bisection](maths/bisection.py)
  * [Ceil](maths/ceil.py)
+ * [Chakravala](maths/chakravala.py)
  * [Check Polygon](maths/check_polygon.py)
  * [Chudnovsky Algorithm](maths/chudnovsky_algorithm.py)
  * [Collatz Sequence](maths/collatz_sequence.py)
@@ -621,6 +624,7 @@
  * [Linear Congruential Generator](other/linear_congruential_generator.py)
  * [Lru Cache](other/lru_cache.py)
  * [Magicdiamondpattern](other/magicdiamondpattern.py)
+ * [Maximum Subarray](other/maximum_subarray.py)
  * [Nested Brackets](other/nested_brackets.py)
  * [Password Generator](other/password_generator.py)
  * [Scoring Algorithm](other/scoring_algorithm.py)
@@ -1053,6 +1057,7 @@
  * [Fetch Bbc News](web_programming/fetch_bbc_news.py)
  * [Fetch Github Info](web_programming/fetch_github_info.py)
  * [Fetch Jobs](web_programming/fetch_jobs.py)
+ * [Fetch Quotes](web_programming/fetch_quotes.py)
  * [Fetch Well Rx Price](web_programming/fetch_well_rx_price.py)
  * [Get Imdb Top 250 Movies Csv](web_programming/get_imdb_top_250_movies_csv.py)
  * [Get Imdbtop](web_programming/get_imdbtop.py)

maths/chakravala.py

@@ -0,0 +1,120 @@
+"""
+Implementing Chakravala method using python
+
+https://en.wikipedia.org/wiki/Chakravala_method
+https://kappadath-gopal.blogspot.com/2013/04/ancient-medieval-indian-mathematics.html
+
+The chakravala method is a cyclic algorithm to solve indeterminate quadratic equations,
+including Pell's equation.
+
+"""
+
+import math
+
+
+def is_perfect_square(num: int) -> bool:
+ """
+ Check if a number is perfect square number or not
+ :param num: the number to be checked
+ :return: True if number is square number, otherwise False
+
+ >>> is_perfect_square(9)
+ True
+ >>> is_perfect_square(16)
+ True
+ >>> is_perfect_square(1)
+ True
+ >>> is_perfect_square(0)
+ True
+ >>> is_perfect_square(10)
+ False
+ """
+
+ sr = int(math.sqrt(num))
+ return sr * sr == num
+
+
+def chakravala_method(num: int) -> (tuple[int, int] | tuple):
+ """
+ This method takes in the value of N in the equation
+
+ x^2 = N*y^2 + 1
+ :param num: the number N equals to
+ :return: empty tuple if N is perfect square else tuple(x,y)
+
+ >>> chakravala_method(1)
+ ()
+ >>> chakravala_method(2)
+ (3, 2)
+ >>> chakravala_method(4)
+ ()
+ >>> chakravala_method(5)
+ (9, 4)
+ >>> chakravala_method(7)
+ (8, 3)
+
+ """
+
+ if is_perfect_square(num):
+ return ()
+
+ # Takes b = 1 and finds a and k accordingly, refer to algorithm link
+ # variable naming is used as same as algorithm, (a,b,k,m) except N = num
+
+ b = 1
+
+ min_diff = num
+ a = 0
+ while True:
+ diff = abs(num - (a + 1) ** 2)
+ if min_diff > diff:
+ min_diff = diff
+ a += 1
+ continue
+ break
+
+ k = a**2 - num
+
+ while True:
+
+ kabs = abs(k)
+
+ if k == 1:
+ return (a, b)
+
+ if k == -1 or kabs == 2 or (kabs == 4 and (a % 2 == 0 or b % 2 == 0)):
+ return (abs((a**2 + num * b**2) // k), abs(2 * a * b // k))
+
+ min_diff = num
+ n = 1 # loop variable
+ n2 = n # stores the correct value of n
+ while True:
+ if kabs * n <= a:
+ n += 1
+ continue
+ if (kabs * n - a) % b == 0:
+ m = (kabs * n - a) // b
+ else:
+ n += 1
+ continue
+
+ diff = abs(m**2 - num)
+ if min_diff > diff:
+ min_diff = diff
+ n2 = n
+ n += 1
+ continue
+ break
+ m = (kabs * n2 - a) // b
+
+ a, b = abs((a * m + num * b) // k), abs((a + b * m) // k)
+ k = (m**2 - num) // k
+
+
+if __name__ == "__main__":
+
+ import doctest
+
+ doctest.testmod()
+
+ print("X and Y for the equation X^2 - 13Y^2 = 1 is: ", chakravala_method(13))

DIRECTORY.md

@@ -9,6 +9,7 @@
  * [Newton Forward Interpolation](arithmetic_analysis/newton_forward_interpolation.py)
  * [Newton Method](arithmetic_analysis/newton_method.py)
  * [Newton Raphson](arithmetic_analysis/newton_raphson.py)
+ * [Newton Raphson New](arithmetic_analysis/newton_raphson_new.py)
  * [Secant Method](arithmetic_analysis/secant_method.py)
 
 ## Audio Filters
@@ -107,6 +108,7 @@
  * [Lempel Ziv](compression/lempel_ziv.py)
  * [Lempel Ziv Decompress](compression/lempel_ziv_decompress.py)
  * [Peak Signal To Noise Ratio](compression/peak_signal_to_noise_ratio.py)
+ * [Run Length Encoding](compression/run_length_encoding.py)
 
 ## Computer Vision
  * [Cnn Classification](computer_vision/cnn_classification.py)
@@ -474,6 +476,7 @@
  * [Binomial Distribution](maths/binomial_distribution.py)
  * [Bisection](maths/bisection.py)
  * [Ceil](maths/ceil.py)
+ * [Chakravala](maths/chakravala.py)
  * [Check Polygon](maths/check_polygon.py)
  * [Chudnovsky Algorithm](maths/chudnovsky_algorithm.py)
  * [Collatz Sequence](maths/collatz_sequence.py)
@@ -621,6 +624,7 @@
  * [Linear Congruential Generator](other/linear_congruential_generator.py)
  * [Lru Cache](other/lru_cache.py)
  * [Magicdiamondpattern](other/magicdiamondpattern.py)
+ * [Maximum Subarray](other/maximum_subarray.py)
  * [Nested Brackets](other/nested_brackets.py)
  * [Password Generator](other/password_generator.py)
  * [Scoring Algorithm](other/scoring_algorithm.py)
@@ -1053,6 +1057,7 @@
  * [Fetch Bbc News](web_programming/fetch_bbc_news.py)
  * [Fetch Github Info](web_programming/fetch_github_info.py)
  * [Fetch Jobs](web_programming/fetch_jobs.py)
+ * [Fetch Quotes](web_programming/fetch_quotes.py)
  * [Fetch Well Rx Price](web_programming/fetch_well_rx_price.py)
  * [Get Imdb Top 250 Movies Csv](web_programming/get_imdb_top_250_movies_csv.py)
  * [Get Imdbtop](web_programming/get_imdbtop.py)

maths/chakravala.py

@@ -0,0 +1,120 @@
+"""
+Implementing Chakravala method using python
+
+https://en.wikipedia.org/wiki/Chakravala_method
+https://kappadath-gopal.blogspot.com/2013/04/ancient-medieval-indian-mathematics.html
+
+The chakravala method is a cyclic algorithm to solve indeterminate quadratic equations,
+including Pell's equation.
+
+"""
+
+import math
+
+
+def is_perfect_square(num: int) -> bool:
+ """
+ Check if a number is perfect square number or not
+ :param num: the number to be checked
+ :return: True if number is square number, otherwise False
+
+ >>> is_perfect_square(9)
+ True
+ >>> is_perfect_square(16)
+ True
+ >>> is_perfect_square(1)
+ True
+ >>> is_perfect_square(0)
+ True
+ >>> is_perfect_square(10)
+ False
+ """
+
+ sr = int(math.sqrt(num))
+ return sr * sr == num
+
+
+def chakravala_method(num: int) -> (tuple[int, int] | tuple):
+ """
+ This method takes in the value of N in the equation
+
+ x^2 = N*y^2 + 1
+ :param num: the number N equals to
+ :return: empty tuple if N is perfect square else tuple(x,y)
+
+ >>> chakravala_method(1)
+ ()
+ >>> chakravala_method(2)
+ (3, 2)
+ >>> chakravala_method(4)
+ ()
+ >>> chakravala_method(5)
+ (9, 4)
+ >>> chakravala_method(7)
+ (8, 3)
+
+ """
+
+ if is_perfect_square(num):
+ return ()
+
+ # Takes b = 1 and finds a and k accordingly, refer to algorithm link
+ # variable naming is used as same as algorithm, (a,b,k,m) except N = num
+
+ b = 1
+
+ min_diff = num
+ a = 0
+ while True:
+ diff = abs(num - (a + 1) ** 2)
+ if min_diff > diff:
+ min_diff = diff
+ a += 1
+ continue
+ break
+
+ k = a**2 - num
+
+ while True:
+
+ kabs = abs(k)
+
+ if k == 1:
+ return (a, b)
+
+ if k == -1 or kabs == 2 or (kabs == 4 and (a % 2 == 0 or b % 2 == 0)):
+ return (abs((a**2 + num * b**2) // k), abs(2 * a * b // k))
+
+ min_diff = num
+ n = 1 # loop variable
+ n2 = n # stores the correct value of n
+ while True:
+ if kabs * n <= a:
+ n += 1
+ continue
+ if (kabs * n - a) % b == 0:
+ m = (kabs * n - a) // b
+ else:
+ n += 1
+ continue
+
+ diff = abs(m**2 - num)
+ if min_diff > diff:
+ min_diff = diff
+ n2 = n
+ n += 1
+ continue
+ break
+ m = (kabs * n2 - a) // b
+
+ a, b = abs((a * m + num * b) // k), abs((a + b * m) // k)
+ k = (m**2 - num) // k
+
+
+if __name__ == "__main__":
+
+ import doctest
+
+ doctest.testmod()
+
+ print("X and Y for the equation X^2 - 13Y^2 = 1 is: ", chakravala_method(13))

DIRECTORY.md

@@ -9,6 +9,7 @@
  * [Newton Forward Interpolation](arithmetic_analysis/newton_forward_interpolation.py)
  * [Newton Method](arithmetic_analysis/newton_method.py)
  * [Newton Raphson](arithmetic_analysis/newton_raphson.py)
+ * [Newton Raphson New](arithmetic_analysis/newton_raphson_new.py)
  * [Secant Method](arithmetic_analysis/secant_method.py)
 
 ## Audio Filters
@@ -107,6 +108,7 @@
  * [Lempel Ziv](compression/lempel_ziv.py)
  * [Lempel Ziv Decompress](compression/lempel_ziv_decompress.py)
  * [Peak Signal To Noise Ratio](compression/peak_signal_to_noise_ratio.py)
+ * [Run Length Encoding](compression/run_length_encoding.py)
 
 ## Computer Vision
  * [Cnn Classification](computer_vision/cnn_classification.py)
@@ -474,6 +476,7 @@
  * [Binomial Distribution](maths/binomial_distribution.py)
  * [Bisection](maths/bisection.py)
  * [Ceil](maths/ceil.py)
+ * [Chakravala](maths/chakravala.py)
  * [Check Polygon](maths/check_polygon.py)
  * [Chudnovsky Algorithm](maths/chudnovsky_algorithm.py)
  * [Collatz Sequence](maths/collatz_sequence.py)
@@ -621,6 +624,7 @@
  * [Linear Congruential Generator](other/linear_congruential_generator.py)
  * [Lru Cache](other/lru_cache.py)
  * [Magicdiamondpattern](other/magicdiamondpattern.py)
+ * [Maximum Subarray](other/maximum_subarray.py)
  * [Nested Brackets](other/nested_brackets.py)
  * [Password Generator](other/password_generator.py)
  * [Scoring Algorithm](other/scoring_algorithm.py)
@@ -1053,6 +1057,7 @@
  * [Fetch Bbc News](web_programming/fetch_bbc_news.py)
  * [Fetch Github Info](web_programming/fetch_github_info.py)
  * [Fetch Jobs](web_programming/fetch_jobs.py)
+ * [Fetch Quotes](web_programming/fetch_quotes.py)
  * [Fetch Well Rx Price](web_programming/fetch_well_rx_price.py)
  * [Get Imdb Top 250 Movies Csv](web_programming/get_imdb_top_250_movies_csv.py)
  * [Get Imdbtop](web_programming/get_imdbtop.py)

maths/chakravala.py

@@ -0,0 +1,120 @@
+"""
+Implementing Chakravala method using python
+
+https://en.wikipedia.org/wiki/Chakravala_method
+https://kappadath-gopal.blogspot.com/2013/04/ancient-medieval-indian-mathematics.html
+
+The chakravala method is a cyclic algorithm to solve indeterminate quadratic equations,
+including Pell's equation.
+
+"""
+
+import math
+
+
+def is_perfect_square(num: int) -> bool:
+ """
+ Check if a number is perfect square number or not
+ :param num: the number to be checked
+ :return: True if number is square number, otherwise False
+
+ >>> is_perfect_square(9)
+ True
+ >>> is_perfect_square(16)
+ True
+ >>> is_perfect_square(1)
+ True
+ >>> is_perfect_square(0)
+ True
+ >>> is_perfect_square(10)
+ False
+ """
+
+ sr = int(math.sqrt(num))
+ return sr * sr == num
+
+
+def chakravala_method(num: int) -> (tuple[int, int] | tuple):
+ """
+ This method takes in the value of N in the equation
+
+ x^2 = N*y^2 + 1
+ :param num: the number N equals to
+ :return: empty tuple if N is perfect square else tuple(x,y)
+
+ >>> chakravala_method(1)
+ ()
+ >>> chakravala_method(2)
+ (3, 2)
+ >>> chakravala_method(4)
+ ()
+ >>> chakravala_method(5)
+ (9, 4)
+ >>> chakravala_method(7)
+ (8, 3)
+
+ """
+
+ if is_perfect_square(num):
+ return ()
+
+ # Takes b = 1 and finds a and k accordingly, refer to algorithm link
+ # variable naming is used as same as algorithm, (a,b,k,m) except N = num
+
+ b = 1
+
+ min_diff = num
+ a = 0
+ while True:
+ diff = abs(num - (a + 1) ** 2)
+ if min_diff > diff:
+ min_diff = diff
+ a += 1
+ continue
+ break
+
+ k = a**2 - num
+
+ while True:
+
+ kabs = abs(k)
+
+ if k == 1:
+ return (a, b)
+
+ if k == -1 or kabs == 2 or (kabs == 4 and (a % 2 == 0 or b % 2 == 0)):
+ return (abs((a**2 + num * b**2) // k), abs(2 * a * b // k))
+
+ min_diff = num
+ n = 1 # loop variable
+ n2 = n # stores the correct value of n
+ while True:
+ if kabs * n <= a:
+ n += 1
+ continue
+ if (kabs * n - a) % b == 0:
+ m = (kabs * n - a) // b
+ else:
+ n += 1
+ continue
+
+ diff = abs(m**2 - num)
+ if min_diff > diff:
+ min_diff = diff
+ n2 = n
+ n += 1
+ continue
+ break
+ m = (kabs * n2 - a) // b
+
+ a, b = abs((a * m + num * b) // k), abs((a + b * m) // k)
+ k = (m**2 - num) // k
+
+
+if __name__ == "__main__":
+
+ import doctest
+
+ doctest.testmod()
+
+ print("X and Y for the equation X^2 - 13Y^2 = 1 is: ", chakravala_method(13))

DIRECTORY.md

@@ -9,6 +9,7 @@
  * [Newton Forward Interpolation](arithmetic_analysis/newton_forward_interpolation.py)
  * [Newton Method](arithmetic_analysis/newton_method.py)
  * [Newton Raphson](arithmetic_analysis/newton_raphson.py)
+ * [Newton Raphson New](arithmetic_analysis/newton_raphson_new.py)
  * [Secant Method](arithmetic_analysis/secant_method.py)
 
 ## Audio Filters
@@ -107,6 +108,7 @@
  * [Lempel Ziv](compression/lempel_ziv.py)
  * [Lempel Ziv Decompress](compression/lempel_ziv_decompress.py)
  * [Peak Signal To Noise Ratio](compression/peak_signal_to_noise_ratio.py)
+ * [Run Length Encoding](compression/run_length_encoding.py)
 
 ## Computer Vision
  * [Cnn Classification](computer_vision/cnn_classification.py)
@@ -474,6 +476,7 @@
  * [Binomial Distribution](maths/binomial_distribution.py)
  * [Bisection](maths/bisection.py)
  * [Ceil](maths/ceil.py)
+ * [Chakravala](maths/chakravala.py)
  * [Check Polygon](maths/check_polygon.py)
  * [Chudnovsky Algorithm](maths/chudnovsky_algorithm.py)
  * [Collatz Sequence](maths/collatz_sequence.py)
@@ -621,6 +624,7 @@
  * [Linear Congruential Generator](other/linear_congruential_generator.py)
  * [Lru Cache](other/lru_cache.py)
  * [Magicdiamondpattern](other/magicdiamondpattern.py)
+ * [Maximum Subarray](other/maximum_subarray.py)
  * [Nested Brackets](other/nested_brackets.py)
  * [Password Generator](other/password_generator.py)
  * [Scoring Algorithm](other/scoring_algorithm.py)
@@ -1053,6 +1057,7 @@
  * [Fetch Bbc News](web_programming/fetch_bbc_news.py)
  * [Fetch Github Info](web_programming/fetch_github_info.py)
  * [Fetch Jobs](web_programming/fetch_jobs.py)
+ * [Fetch Quotes](web_programming/fetch_quotes.py)
  * [Fetch Well Rx Price](web_programming/fetch_well_rx_price.py)
  * [Get Imdb Top 250 Movies Csv](web_programming/get_imdb_top_250_movies_csv.py)
  * [Get Imdbtop](web_programming/get_imdbtop.py)

maths/chakravala.py

@@ -0,0 +1,120 @@
+"""
+Implementing Chakravala method using python
+
+https://en.wikipedia.org/wiki/Chakravala_method
+https://kappadath-gopal.blogspot.com/2013/04/ancient-medieval-indian-mathematics.html
+
+The chakravala method is a cyclic algorithm to solve indeterminate quadratic equations,
+including Pell's equation.
+
+"""
+
+import math
+
+
+def is_perfect_square(num: int) -> bool:
+ """
+ Check if a number is perfect square number or not
+ :param num: the number to be checked
+ :return: True if number is square number, otherwise False
+
+ >>> is_perfect_square(9)
+ True
+ >>> is_perfect_square(16)
+ True
+ >>> is_perfect_square(1)
+ True
+ >>> is_perfect_square(0)
+ True
+ >>> is_perfect_square(10)
+ False
+ """
+
+ sr = int(math.sqrt(num))
+ return sr * sr == num
+
+
+def chakravala_method(num: int) -> (tuple[int, int] | tuple):
+ """
+ This method takes in the value of N in the equation
+
+ x^2 = N*y^2 + 1
+ :param num: the number N equals to
+ :return: empty tuple if N is perfect square else tuple(x,y)
+
+ >>> chakravala_method(1)
+ ()
+ >>> chakravala_method(2)
+ (3, 2)
+ >>> chakravala_method(4)
+ ()
+ >>> chakravala_method(5)
+ (9, 4)
+ >>> chakravala_method(7)
+ (8, 3)
+
+ """
+
+ if is_perfect_square(num):
+ return ()
+
+ # Takes b = 1 and finds a and k accordingly, refer to algorithm link
+ # variable naming is used as same as algorithm, (a,b,k,m) except N = num
+
+ b = 1
+
+ min_diff = num
+ a = 0
+ while True:
+ diff = abs(num - (a + 1) ** 2)
+ if min_diff > diff:
+ min_diff = diff
+ a += 1
+ continue
+ break
+
+ k = a**2 - num
+
+ while True:
+
+ kabs = abs(k)
+
+ if k == 1:
+ return (a, b)
+
+ if k == -1 or kabs == 2 or (kabs == 4 and (a % 2 == 0 or b % 2 == 0)):
+ return (abs((a**2 + num * b**2) // k), abs(2 * a * b // k))
+
+ min_diff = num
+ n = 1 # loop variable
+ n2 = n # stores the correct value of n
+ while True:
+ if kabs * n <= a:
+ n += 1
+ continue
+ if (kabs * n - a) % b == 0:
+ m = (kabs * n - a) // b
+ else:
+ n += 1
+ continue
+
+ diff = abs(m**2 - num)
+ if min_diff > diff:
+ min_diff = diff
+ n2 = n
+ n += 1
+ continue
+ break
+ m = (kabs * n2 - a) // b
+
+ a, b = abs((a * m + num * b) // k), abs((a + b * m) // k)
+ k = (m**2 - num) // k
+
+
+if __name__ == "__main__":
+
+ import doctest
+
+ doctest.testmod()
+
+ print("X and Y for the equation X^2 - 13Y^2 = 1 is: ", chakravala_method(13))

DIRECTORY.md

@@ -9,6 +9,7 @@
  * [Newton Forward Interpolation](arithmetic_analysis/newton_forward_interpolation.py)
  * [Newton Method](arithmetic_analysis/newton_method.py)
  * [Newton Raphson](arithmetic_analysis/newton_raphson.py)
+ * [Newton Raphson New](arithmetic_analysis/newton_raphson_new.py)
  * [Secant Method](arithmetic_analysis/secant_method.py)
 
 ## Audio Filters
@@ -107,6 +108,7 @@
  * [Lempel Ziv](compression/lempel_ziv.py)
  * [Lempel Ziv Decompress](compression/lempel_ziv_decompress.py)
  * [Peak Signal To Noise Ratio](compression/peak_signal_to_noise_ratio.py)
+ * [Run Length Encoding](compression/run_length_encoding.py)
 
 ## Computer Vision
  * [Cnn Classification](computer_vision/cnn_classification.py)
@@ -474,6 +476,7 @@
  * [Binomial Distribution](maths/binomial_distribution.py)
  * [Bisection](maths/bisection.py)
  * [Ceil](maths/ceil.py)
+ * [Chakravala](maths/chakravala.py)
  * [Check Polygon](maths/check_polygon.py)
  * [Chudnovsky Algorithm](maths/chudnovsky_algorithm.py)
  * [Collatz Sequence](maths/collatz_sequence.py)
@@ -621,6 +624,7 @@
  * [Linear Congruential Generator](other/linear_congruential_generator.py)
  * [Lru Cache](other/lru_cache.py)
  * [Magicdiamondpattern](other/magicdiamondpattern.py)
+ * [Maximum Subarray](other/maximum_subarray.py)
  * [Nested Brackets](other/nested_brackets.py)
  * [Password Generator](other/password_generator.py)
  * [Scoring Algorithm](other/scoring_algorithm.py)
@@ -1053,6 +1057,7 @@
  * [Fetch Bbc News](web_programming/fetch_bbc_news.py)
  * [Fetch Github Info](web_programming/fetch_github_info.py)
  * [Fetch Jobs](web_programming/fetch_jobs.py)
+ * [Fetch Quotes](web_programming/fetch_quotes.py)
  * [Fetch Well Rx Price](web_programming/fetch_well_rx_price.py)
  * [Get Imdb Top 250 Movies Csv](web_programming/get_imdb_top_250_movies_csv.py)
  * [Get Imdbtop](web_programming/get_imdbtop.py)

maths/chakravala.py

@@ -0,0 +1,120 @@
+"""
+Implementing Chakravala method using python
+
+https://en.wikipedia.org/wiki/Chakravala_method
+https://kappadath-gopal.blogspot.com/2013/04/ancient-medieval-indian-mathematics.html
+
+The chakravala method is a cyclic algorithm to solve indeterminate quadratic equations,
+including Pell's equation.
+
+"""
+
+import math
+
+
+def is_perfect_square(num: int) -> bool:
+ """
+ Check if a number is perfect square number or not
+ :param num: the number to be checked
+ :return: True if number is square number, otherwise False
+
+ >>> is_perfect_square(9)
+ True
+ >>> is_perfect_square(16)
+ True
+ >>> is_perfect_square(1)
+ True
+ >>> is_perfect_square(0)
+ True
+ >>> is_perfect_square(10)
+ False
+ """
+
+ sr = int(math.sqrt(num))
+ return sr * sr == num
+
+
+def chakravala_method(num: int) -> (tuple[int, int] | tuple):
+ """
+ This method takes in the value of N in the equation
+
+ x^2 = N*y^2 + 1
+ :param num: the number N equals to
+ :return: empty tuple if N is perfect square else tuple(x,y)
+
+ >>> chakravala_method(1)
+ ()
+ >>> chakravala_method(2)
+ (3, 2)
+ >>> chakravala_method(4)
+ ()
+ >>> chakravala_method(5)
+ (9, 4)
+ >>> chakravala_method(7)
+ (8, 3)
+
+ """
+
+ if is_perfect_square(num):
+ return ()
+
+ # Takes b = 1 and finds a and k accordingly, refer to algorithm link
+ # variable naming is used as same as algorithm, (a,b,k,m) except N = num
+
+ b = 1
+
+ min_diff = num
+ a = 0
+ while True:
+ diff = abs(num - (a + 1) ** 2)
+ if min_diff > diff:
+ min_diff = diff
+ a += 1
+ continue
+ break
+
+ k = a**2 - num
+
+ while True:
+
+ kabs = abs(k)
+
+ if k == 1:
+ return (a, b)
+
+ if k == -1 or kabs == 2 or (kabs == 4 and (a % 2 == 0 or b % 2 == 0)):
+ return (abs((a**2 + num * b**2) // k), abs(2 * a * b // k))
+
+ min_diff = num
+ n = 1 # loop variable
+ n2 = n # stores the correct value of n
+ while True:
+ if kabs * n <= a:
+ n += 1
+ continue
+ if (kabs * n - a) % b == 0:
+ m = (kabs * n - a) // b
+ else:
+ n += 1
+ continue
+
+ diff = abs(m**2 - num)
+ if min_diff > diff:
+ min_diff = diff
+ n2 = n
+ n += 1
+ continue
+ break
+ m = (kabs * n2 - a) // b
+
+ a, b = abs((a * m + num * b) // k), abs((a + b * m) // k)
+ k = (m**2 - num) // k
+
+
+if __name__ == "__main__":
+
+ import doctest
+
+ doctest.testmod()
+
+ print("X and Y for the equation X^2 - 13Y^2 = 1 is: ", chakravala_method(13))