Design.md

Project-Euler

Problem 1: Multiples of 3 and 5

1. multiples(limit, factors, union = True, intersection = False)

   Returns a list of multiples under limit of any/all numbers in factors.

   union (default : True): If true, returns list of all multiples of any of numbers in factors.

   intersection (default : False): If true, returns list of multiples of all of numbers in factors.

   If both intersection and union are simultaneously:

   a. False, then list of list of all multiples of each factor in factors is returned

   b. True, then throws an exception.

   Note: Even though, multiples() appears to show similar functionalities to filter_seq(), it is not so as we pass only a single parameter to the condition function while filtering which is not the case with multiples as we take multiple inputs in is_multiple().

2. is_multiple(n, factors, all = true)

   Returns whether n is a multiple of all/any of numbers in factors

   all (default : True):

   • If true, returns True if n is a multiple of all numbers in factors

   • Else if false, returns True if n is a multiple of any number in factors

3. sum_seq(seq) Returns the sum of all numbers in seq

Problem 2: Even Fibonacci Numbers

1. generate_seq(n, until = True, length = False, seq_type = "natural_no")

   Returns a sequence of type seq_type of length n or until the value n is approached

   until (default : True): If true returns sequence until the no. n is reached.

   length (default : False): If true returns first n numbers in the seq.

   seq_type (default : "natural_no"): Defines the type of the sequence required. Takes values:

   • "fibonacci"
   • "natural_no"
   • "triangular"
   • "collatz"
   • "prime"
   • "even"
   • "palindrome"
   • "odd"

   If both until and length are False, first n Fibonacci numbers are returned.

   If both until and length are True, method throws an exception.

2. filter_seq(seq, condition = None, custom = None falsy = False)

   Returns a list of values from seq obeying the given condition

   condition (str): Can take values:

   • even
   • palindrome
   • prime

   falsy (bool): If true returns a list of values from seq not obeying the condition

   custom: Pass a custom method which checks a condition. filter_seq() then returns a list of values which obey the condition in the custom method

3. even(n)

   Returns true if n is even.

Problem 3: Largest Prime Factor

1. factors(nums, proper = True, separate = True, union = False, intersection = False)

   Returns the factors of all numbers in nums.

   union (default : True): If true, returns list of all factors of any of numbers in nums.

   intersection (default : False): If true, returns list of factors of all of numbers in nums.

   If both intersection and union are simultaneously:

   a. False, then list of list of all factor of each no. in nums is returned

   b. True, then throws an exception.

   proper (default : True): If true, returns all proper factors (all factors including 1 and n) of n else return improper factors.

2. prime(n)

   Returns True if n is prime else returns False

3. max_value(seq)

   Returns the maximum value in a sequence seq.

Problem 4: Largest Palindrome Product

1. products(multipliers, num_of_multipliers = 2)

   Returns the list of products of numbers from multipliers taken num_of_multipliers at a time.

2. palindrome(n)

   Checks whether n is a palindrome or not.

Problem 5: Smallest Multiple

1. least_common_multiple(nums)

   Returns the LCM of all numbers in nums.

2. greatest_common_divisor(nums)

   Returns the GCD of all numbers in nums.

Problem 6: Sum square difference

1. power_num(n, power)

   Returns the value of n to the power power.

2. power_seq(seq, power)

   Returns the list of all numbers in the seq raised to the power power

Problem 7: 10001th Prime

1. nth_number(n, num_type = "natural", custom_type = None)

   Returns the nth num_type number

   num_type (default : "natural"): Type of nth number needed. Takes the values: "prime", "even", "odd", "palidrome"

   custom_type (default : None): pass a function to check the type of number. nth_number() then returns the nth number of type whose custom type is checked.

Problem 10: Summation of Primes

Uses the functions documented above

Problem 11: Largest product in a grid

1. columns(grid)

   Returns the columns of a grid.

2. rows(grid)

   Returns the rows of a grid.

3. diagonals(grid)

   Returns the elements along slants of a grid.

Problem 12: Highly divisible triangular number

1. no_of_factors_seq(seq)

   Returns the list of no. of factors of each value in a sequence.

Problem 13: Large sum

1. first_n_digits(num, n)

   Returns the list of the first n digits of a number num

Problem 14: Longest Collatz sequence

1. size_seq(limits, type = "natural_nos")

   Returns a list of sizes of all sequences having their limit in limits.

   type (default : "natural_nos"): Defines type of a seq. Can take the values:

   • "fibonacci"
   • "natural_no"
   • "triangular"
   • "collatz"
   • "prime"
   • "even"
   • "palindrome"
   • "odd"