Move files for special numbers to own directory (#10714)

maths/special_numbers/armstrong_numbers.py

@@ -1,98 +1,98 @@
-"""
+"""
-An Armstrong number is equal to the sum of its own digits each raised to the
+An Armstrong number is equal to the sum of its own digits each raised to the
-power of the number of digits.
+power of the number of digits.
-
+
-For example, 370 is an Armstrong number because 3*3*3 + 7*7*7 + 0*0*0 = 370.
+For example, 370 is an Armstrong number because 3*3*3 + 7*7*7 + 0*0*0 = 370.
-
+
-Armstrong numbers are also called Narcissistic numbers and Pluperfect numbers.
+Armstrong numbers are also called Narcissistic numbers and Pluperfect numbers.
-
+
-On-Line Encyclopedia of Integer Sequences entry: https://oeis.org/A005188
+On-Line Encyclopedia of Integer Sequences entry: https://oeis.org/A005188
-"""
+"""
-PASSING = (1, 153, 370, 371, 1634, 24678051, 115132219018763992565095597973971522401)
+PASSING = (1, 153, 370, 371, 1634, 24678051, 115132219018763992565095597973971522401)
-FAILING: tuple = (-153, -1, 0, 1.2, 200, "A", [], {}, None)
+FAILING: tuple = (-153, -1, 0, 1.2, 200, "A", [], {}, None)
-
+
-
+
-def armstrong_number(n: int) -> bool:
+def armstrong_number(n: int) -> bool:
-    """
+    """
-    Return True if n is an Armstrong number or False if it is not.
+    Return True if n is an Armstrong number or False if it is not.
-
+
-    >>> all(armstrong_number(n) for n in PASSING)
+    >>> all(armstrong_number(n) for n in PASSING)
-    True
+    True
-    >>> any(armstrong_number(n) for n in FAILING)
+    >>> any(armstrong_number(n) for n in FAILING)
-    False
+    False
-    """
+    """
-    if not isinstance(n, int) or n < 1:
+    if not isinstance(n, int) or n < 1:
-        return False
+        return False
-
+
-    # Initialization of sum and number of digits.
+    # Initialization of sum and number of digits.
-    total = 0
+    total = 0
-    number_of_digits = 0
+    number_of_digits = 0
-    temp = n
+    temp = n
-    # Calculation of digits of the number
+    # Calculation of digits of the number
-    number_of_digits = len(str(n))
+    number_of_digits = len(str(n))
-    # Dividing number into separate digits and find Armstrong number
+    # Dividing number into separate digits and find Armstrong number
-    temp = n
+    temp = n
-    while temp > 0:
+    while temp > 0:
-        rem = temp % 10
+        rem = temp % 10
-        total += rem**number_of_digits
+        total += rem**number_of_digits
-        temp //= 10
+        temp //= 10
-    return n == total
+    return n == total
-
+
-
+
-def pluperfect_number(n: int) -> bool:
+def pluperfect_number(n: int) -> bool:
-    """Return True if n is a pluperfect number or False if it is not
+    """Return True if n is a pluperfect number or False if it is not
-
+
-    >>> all(armstrong_number(n) for n in PASSING)
+    >>> all(armstrong_number(n) for n in PASSING)
-    True
+    True
-    >>> any(armstrong_number(n) for n in FAILING)
+    >>> any(armstrong_number(n) for n in FAILING)
-    False
+    False
-    """
+    """
-    if not isinstance(n, int) or n < 1:
+    if not isinstance(n, int) or n < 1:
-        return False
+        return False
-
+
-    # Init a "histogram" of the digits
+    # Init a "histogram" of the digits
-    digit_histogram = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
+    digit_histogram = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
-    digit_total = 0
+    digit_total = 0
-    total = 0
+    total = 0
-    temp = n
+    temp = n
-    while temp > 0:
+    while temp > 0:
-        temp, rem = divmod(temp, 10)
+        temp, rem = divmod(temp, 10)
-        digit_histogram[rem] += 1
+        digit_histogram[rem] += 1
-        digit_total += 1
+        digit_total += 1
-
+
-    for cnt, i in zip(digit_histogram, range(len(digit_histogram))):
+    for cnt, i in zip(digit_histogram, range(len(digit_histogram))):
-        total += cnt * i**digit_total
+        total += cnt * i**digit_total
-
+
-    return n == total
+    return n == total
-
+
-
+
-def narcissistic_number(n: int) -> bool:
+def narcissistic_number(n: int) -> bool:
-    """Return True if n is a narcissistic number or False if it is not.
+    """Return True if n is a narcissistic number or False if it is not.
-
+
-    >>> all(armstrong_number(n) for n in PASSING)
+    >>> all(armstrong_number(n) for n in PASSING)
-    True
+    True
-    >>> any(armstrong_number(n) for n in FAILING)
+    >>> any(armstrong_number(n) for n in FAILING)
-    False
+    False
-    """
+    """
-    if not isinstance(n, int) or n < 1:
+    if not isinstance(n, int) or n < 1:
-        return False
+        return False
-    expo = len(str(n))  # the power that all digits will be raised to
+    expo = len(str(n))  # the power that all digits will be raised to
-    # check if sum of each digit multiplied expo times is equal to number
+    # check if sum of each digit multiplied expo times is equal to number
-    return n == sum(int(i) ** expo for i in str(n))
+    return n == sum(int(i) ** expo for i in str(n))
-
+
-
+
-def main():
+def main():
-    """
+    """
-    Request that user input an integer and tell them if it is Armstrong number.
+    Request that user input an integer and tell them if it is Armstrong number.
-    """
+    """
-    num = int(input("Enter an integer to see if it is an Armstrong number: ").strip())
+    num = int(input("Enter an integer to see if it is an Armstrong number: ").strip())
-    print(f"{num} is {'' if armstrong_number(num) else 'not '}an Armstrong number.")
+    print(f"{num} is {'' if armstrong_number(num) else 'not '}an Armstrong number.")
-    print(f"{num} is {'' if narcissistic_number(num) else 'not '}an Armstrong number.")
+    print(f"{num} is {'' if narcissistic_number(num) else 'not '}an Armstrong number.")
-    print(f"{num} is {'' if pluperfect_number(num) else 'not '}an Armstrong number.")
+    print(f"{num} is {'' if pluperfect_number(num) else 'not '}an Armstrong number.")
-
+
-
+
-if __name__ == "__main__":
+if __name__ == "__main__":
-    import doctest
+    import doctest
-
+
-    doctest.testmod()
+    doctest.testmod()
-    main()
+    main()

maths/special_numbers/harshad_numbers.py

@@ -1,158 +1,158 @@
-"""
+"""
-A harshad number (or more specifically an n-harshad number) is a number that's
+A harshad number (or more specifically an n-harshad number) is a number that's
-divisible by the sum of its digits in some given base n.
+divisible by the sum of its digits in some given base n.
-Reference: https://en.wikipedia.org/wiki/Harshad_number
+Reference: https://en.wikipedia.org/wiki/Harshad_number
-"""
+"""
-
+
-
+
-def int_to_base(number: int, base: int) -> str:
+def int_to_base(number: int, base: int) -> str:
-    """
+    """
-    Convert a given positive decimal integer to base 'base'.
+    Convert a given positive decimal integer to base 'base'.
-    Where 'base' ranges from 2 to 36.
+    Where 'base' ranges from 2 to 36.
-
+
-    Examples:
+    Examples:
-    >>> int_to_base(23, 2)
+    >>> int_to_base(23, 2)
-    '10111'
+    '10111'
-    >>> int_to_base(58, 5)
+    >>> int_to_base(58, 5)
-    '213'
+    '213'
-    >>> int_to_base(167, 16)
+    >>> int_to_base(167, 16)
-    'A7'
+    'A7'
-    >>> # bases below 2 and beyond 36 will error
+    >>> # bases below 2 and beyond 36 will error
-    >>> int_to_base(98, 1)
+    >>> int_to_base(98, 1)
-    Traceback (most recent call last):
+    Traceback (most recent call last):
-        ...
+        ...
-    ValueError: 'base' must be between 2 and 36 inclusive
+    ValueError: 'base' must be between 2 and 36 inclusive
-    >>> int_to_base(98, 37)
+    >>> int_to_base(98, 37)
-    Traceback (most recent call last):
+    Traceback (most recent call last):
-        ...
+        ...
-    ValueError: 'base' must be between 2 and 36 inclusive
+    ValueError: 'base' must be between 2 and 36 inclusive
-    """
+    """
-
+
-    if base < 2 or base > 36:
+    if base < 2 or base > 36:
-        raise ValueError("'base' must be between 2 and 36 inclusive")
+        raise ValueError("'base' must be between 2 and 36 inclusive")
-
+
-    digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
+    digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
-    result = ""
+    result = ""
-
+
-    if number < 0:
+    if number < 0:
-        raise ValueError("number must be a positive integer")
+        raise ValueError("number must be a positive integer")
-
+
-    while number > 0:
+    while number > 0:
-        number, remainder = divmod(number, base)
+        number, remainder = divmod(number, base)
-        result = digits[remainder] + result
+        result = digits[remainder] + result
-
+
-    if result == "":
+    if result == "":
-        result = "0"
+        result = "0"
-
+
-    return result
+    return result
-
+
-
+
-def sum_of_digits(num: int, base: int) -> str:
+def sum_of_digits(num: int, base: int) -> str:
-    """
+    """
-    Calculate the sum of digit values in a positive integer
+    Calculate the sum of digit values in a positive integer
-    converted to the given 'base'.
+    converted to the given 'base'.
-    Where 'base' ranges from 2 to 36.
+    Where 'base' ranges from 2 to 36.
-
+
-    Examples:
+    Examples:
-    >>> sum_of_digits(103, 12)
+    >>> sum_of_digits(103, 12)
-    '13'
+    '13'
-    >>> sum_of_digits(1275, 4)
+    >>> sum_of_digits(1275, 4)
-    '30'
+    '30'
-    >>> sum_of_digits(6645, 2)
+    >>> sum_of_digits(6645, 2)
-    '1001'
+    '1001'
-    >>> # bases below 2 and beyond 36 will error
+    >>> # bases below 2 and beyond 36 will error
-    >>> sum_of_digits(543, 1)
+    >>> sum_of_digits(543, 1)
-    Traceback (most recent call last):
+    Traceback (most recent call last):
-        ...
+        ...
-    ValueError: 'base' must be between 2 and 36 inclusive
+    ValueError: 'base' must be between 2 and 36 inclusive
-    >>> sum_of_digits(543, 37)
+    >>> sum_of_digits(543, 37)
-    Traceback (most recent call last):
+    Traceback (most recent call last):
-        ...
+        ...
-    ValueError: 'base' must be between 2 and 36 inclusive
+    ValueError: 'base' must be between 2 and 36 inclusive
-    """
+    """
-
+
-    if base < 2 or base > 36:
+    if base < 2 or base > 36:
-        raise ValueError("'base' must be between 2 and 36 inclusive")
+        raise ValueError("'base' must be between 2 and 36 inclusive")
-
+
-    num_str = int_to_base(num, base)
+    num_str = int_to_base(num, base)
-    res = sum(int(char, base) for char in num_str)
+    res = sum(int(char, base) for char in num_str)
-    res_str = int_to_base(res, base)
+    res_str = int_to_base(res, base)
-    return res_str
+    return res_str
-
+
-
+
-def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
+def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
-    """
+    """
-    Finds all Harshad numbers smaller than num in base 'base'.
+    Finds all Harshad numbers smaller than num in base 'base'.
-    Where 'base' ranges from 2 to 36.
+    Where 'base' ranges from 2 to 36.
-
+
-    Examples:
+    Examples:
-    >>> harshad_numbers_in_base(15, 2)
+    >>> harshad_numbers_in_base(15, 2)
-    ['1', '10', '100', '110', '1000', '1010', '1100']
+    ['1', '10', '100', '110', '1000', '1010', '1100']
-    >>> harshad_numbers_in_base(12, 34)
+    >>> harshad_numbers_in_base(12, 34)
-    ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B']
+    ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B']
-    >>> harshad_numbers_in_base(12, 4)
+    >>> harshad_numbers_in_base(12, 4)
-    ['1', '2', '3', '10', '12', '20', '21']
+    ['1', '2', '3', '10', '12', '20', '21']
-    >>> # bases below 2 and beyond 36 will error
+    >>> # bases below 2 and beyond 36 will error
-    >>> harshad_numbers_in_base(234, 37)
+    >>> harshad_numbers_in_base(234, 37)
-    Traceback (most recent call last):
+    Traceback (most recent call last):
-        ...
+        ...
-    ValueError: 'base' must be between 2 and 36 inclusive
+    ValueError: 'base' must be between 2 and 36 inclusive
-    >>> harshad_numbers_in_base(234, 1)
+    >>> harshad_numbers_in_base(234, 1)
-    Traceback (most recent call last):
+    Traceback (most recent call last):
-        ...
+        ...
-    ValueError: 'base' must be between 2 and 36 inclusive
+    ValueError: 'base' must be between 2 and 36 inclusive
-    """
+    """
-
+
-    if base < 2 or base > 36:
+    if base < 2 or base > 36:
-        raise ValueError("'base' must be between 2 and 36 inclusive")
+        raise ValueError("'base' must be between 2 and 36 inclusive")
-
+
-    if limit < 0:
+    if limit < 0:
-        return []
+        return []
-
+
-    numbers = [
+    numbers = [
-        int_to_base(i, base)
+        int_to_base(i, base)
-        for i in range(1, limit)
+        for i in range(1, limit)
-        if i % int(sum_of_digits(i, base), base) == 0
+        if i % int(sum_of_digits(i, base), base) == 0
-    ]
+    ]
-
+
-    return numbers
+    return numbers
-
+
-
+
-def is_harshad_number_in_base(num: int, base: int) -> bool:
+def is_harshad_number_in_base(num: int, base: int) -> bool:
-    """
+    """
-    Determines whether n in base 'base' is a harshad number.
+    Determines whether n in base 'base' is a harshad number.
-    Where 'base' ranges from 2 to 36.
+    Where 'base' ranges from 2 to 36.
-
+
-    Examples:
+    Examples:
-    >>> is_harshad_number_in_base(18, 10)
+    >>> is_harshad_number_in_base(18, 10)
-    True
+    True
-    >>> is_harshad_number_in_base(21, 10)
+    >>> is_harshad_number_in_base(21, 10)
-    True
+    True
-    >>> is_harshad_number_in_base(-21, 5)
+    >>> is_harshad_number_in_base(-21, 5)
-    False
+    False
-    >>> # bases below 2 and beyond 36 will error
+    >>> # bases below 2 and beyond 36 will error
-    >>> is_harshad_number_in_base(45, 37)
+    >>> is_harshad_number_in_base(45, 37)
-    Traceback (most recent call last):
+    Traceback (most recent call last):
-        ...
+        ...
-    ValueError: 'base' must be between 2 and 36 inclusive
+    ValueError: 'base' must be between 2 and 36 inclusive
-    >>> is_harshad_number_in_base(45, 1)
+    >>> is_harshad_number_in_base(45, 1)
-    Traceback (most recent call last):
+    Traceback (most recent call last):
-        ...
+        ...
-    ValueError: 'base' must be between 2 and 36 inclusive
+    ValueError: 'base' must be between 2 and 36 inclusive
-    """
+    """
-
+
-    if base < 2 or base > 36:
+    if base < 2 or base > 36:
-        raise ValueError("'base' must be between 2 and 36 inclusive")
+        raise ValueError("'base' must be between 2 and 36 inclusive")
-
+
-    if num < 0:
+    if num < 0:
-        return False
+        return False
-
+
-    n = int_to_base(num, base)
+    n = int_to_base(num, base)
-    d = sum_of_digits(num, base)
+    d = sum_of_digits(num, base)
-    return int(n, base) % int(d, base) == 0
+    return int(n, base) % int(d, base) == 0
-
+
-
+
-if __name__ == "__main__":
+if __name__ == "__main__":
-    import doctest
+    import doctest
-
+
-    doctest.testmod()
+    doctest.testmod()

maths/special_numbers/ugly_numbers.py

@@ -1,54 +1,54 @@
-"""
+"""
-Ugly numbers are numbers whose only prime factors are 2, 3 or 5. The sequence
+Ugly numbers are numbers whose only prime factors are 2, 3 or 5. The sequence
-1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, … shows the first 11 ugly numbers. By convention,
+1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, … shows the first 11 ugly numbers. By convention,
-1 is included.
+1 is included.
-Given an integer n, we have to find the nth ugly number.
+Given an integer n, we have to find the nth ugly number.
-
+
-For more details, refer this article
+For more details, refer this article
-https://www.geeksforgeeks.org/ugly-numbers/
+https://www.geeksforgeeks.org/ugly-numbers/
-"""
+"""
-
+
-
+
-def ugly_numbers(n: int) -> int:
+def ugly_numbers(n: int) -> int:
-    """
+    """
-    Returns the nth ugly number.
+    Returns the nth ugly number.
-    >>> ugly_numbers(100)
+    >>> ugly_numbers(100)
-    1536
+    1536
-    >>> ugly_numbers(0)
+    >>> ugly_numbers(0)
-    1
+    1
-    >>> ugly_numbers(20)
+    >>> ugly_numbers(20)
-    36
+    36
-    >>> ugly_numbers(-5)
+    >>> ugly_numbers(-5)
-    1
+    1
-    >>> ugly_numbers(-5.5)
+    >>> ugly_numbers(-5.5)
-    Traceback (most recent call last):
+    Traceback (most recent call last):
-        ...
+        ...
-    TypeError: 'float' object cannot be interpreted as an integer
+    TypeError: 'float' object cannot be interpreted as an integer
-    """
+    """
-    ugly_nums = [1]
+    ugly_nums = [1]
-
+
-    i2, i3, i5 = 0, 0, 0
+    i2, i3, i5 = 0, 0, 0
-    next_2 = ugly_nums[i2] * 2
+    next_2 = ugly_nums[i2] * 2
-    next_3 = ugly_nums[i3] * 3
+    next_3 = ugly_nums[i3] * 3
-    next_5 = ugly_nums[i5] * 5
+    next_5 = ugly_nums[i5] * 5
-
+
-    for _ in range(1, n):
+    for _ in range(1, n):
-        next_num = min(next_2, next_3, next_5)
+        next_num = min(next_2, next_3, next_5)
-        ugly_nums.append(next_num)
+        ugly_nums.append(next_num)
-        if next_num == next_2:
+        if next_num == next_2:
-            i2 += 1
+            i2 += 1
-            next_2 = ugly_nums[i2] * 2
+            next_2 = ugly_nums[i2] * 2
-        if next_num == next_3:
+        if next_num == next_3:
-            i3 += 1
+            i3 += 1
-            next_3 = ugly_nums[i3] * 3
+            next_3 = ugly_nums[i3] * 3
-        if next_num == next_5:
+        if next_num == next_5:
-            i5 += 1
+            i5 += 1
-            next_5 = ugly_nums[i5] * 5
+            next_5 = ugly_nums[i5] * 5
-    return ugly_nums[-1]
+    return ugly_nums[-1]
-
+
-
+
-if __name__ == "__main__":
+if __name__ == "__main__":
-    from doctest import testmod
+    from doctest import testmod
-
+
-    testmod(verbose=True)
+    testmod(verbose=True)
-    print(f"{ugly_numbers(200) = }")
+    print(f"{ugly_numbers(200) = }")