week07

Functions

Question 1

Write a function called power that takes a required integer parameter as number and an optional integer parameter as n. The default value for n should be 2. The function should return the nth power of number.

Input	Output
5	25
3 2	9
4 3	64

Question 2

Write a function which takes a number and prints the first 6 powers of the number using power() function from previous question.

Input	Output
2	2 4 8 16 32 64
3	3 9 27 81 243 729

Question 3

An abundant number or excessive number is a number that is smaller than the sum of its proper divisors.

Write a function which takes two integers and finds the abundant numbers between those numbers (including them). If there are abundant numbers in the range, the function prints these numbers; otherwise, prints no abundant number.

Example: The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. The amount by which the sum exceeds the number is the abundance.

Input	Output
20 35	20 24 30
10 40	12 18 20 24 30 36 40
3 10	no abundant number

Question 4 - Elementary Number Theory

Question 4a - Modulus

Using only addition, subtraction and a while loop, write a function that takes two numbers A, B and returns A % B.

Input	Output
17 3	2
27 5	2
11 17	11

Question 4b - GCD

The greatest common divisor or GCD of two integers is the largest number that divides both integers.

Write a function which takes two positive integers and returns their GCD.

Hint: Implement Euler's method.

Input	Output
2 5	1
12 8	4
8 9	1
15 30	15

Question 4c - LCM

The lowest common multiple or LCM of two integers is the smallest number that is a multiple of both numbers

Write a function which takes two positive integers and returns their LCM.

Hint: GCD(a,b) * LCM(a,b) = a*b

Input	Output
2 5	10
12 8	24
8 9	72
15 30	30

Question 5 - Think

Write a function that takes an integer and thinks that much. Default value is 1.

Input	Output
think()	hm
think(2)	hmm
think(5)	hmmmmm

Question 6 - You're a Square!

When you multiply a number by itself, the result is a square number.

Write a function that takes an integer and determines whether it is a square number or not.

Input	Output
25	True
23	False
0	True
-1	False

Question 7

Write a floor function. If the input is anything other than integer or float, print a warning to the console that the input is invalid.

PARAMETER	RETURN
123	123
123.7	123
Hi!	Invalid input: Hi!

Hint: You can use type(var) function to get the type of var

Question 8 - Points

Question 8a - Distance

Write a function distance which takes the coordinates of two points (x1, y1, x2, y2) and returns Euclidian distance between these points.

Input	Output
3, 0, 0, 4	5.0
5, 8, 10, 20	13.0

Question 8b - Closest

Write a function which takes the coordinates of two points (x1, y1, x2, y2) and returns the point closest to the origin. Use the distance function.

Input	Output
3, 0, 0, 4	3, 0
11, 7, 6, 8	6, 8

Question 8c - Valid Triangle

Write a function that takes three vertices of a triangle (x1, y1, x2, y2, x3, y3), and returns True if it is a valid triangle, False otherwise. If the distance between any two points is zero, raise ZeroDivisionError.

Input	Output
3, 0, 0, 4, 1, 1	True
11, 7, 6, 8, 11, 7	ZeroDivisionError
0, 0, 0, 1, 0, 2	False

Question 8d - Perimeter

Write a function that takes three vertices of a triangle (x1, y1, x2, y2, x3, y3), and returns the perimeter (sum of edges). If the distance between any two points is zero, raise ZeroDivisionError. If the triangle is invalid, raise ValueError.

Input	Output
3, 0, 0, 4, 1, 1	10.39834563766817
11, 7, 6, 8, 11, 7	ZeroDivisionError
0, 0, 0, 1, 0, 2	ValueError

Question 8e - Area

Write a function that takes three vertices of a triangle (x1, y1, x2, y2, x3, y3), and returns the area. If the distance between any two points is zero, return -1. If the triangle is invalid, return 0.

Input	Output
3, 0, 0, 4, 1, 1	2.5
11, 7, 6, 8, 11, 7	-1
0, 0, 0, 1, 0, 2	0

Question 8f - Point in Triangle

Write a function that takes three vertices of a triangle (x1, y1, x2, y2, x3, y3), and coordinates of a point. Return True if the point is inside the triangle, False otherwise.

Input	Output
-3, 5, 9, 1, -6, -7, -2, 0	True
-3, 5, 9, 1, -6, -7, 9, 1	True
-3, 5, 9, 1, -6, -7, 12, 1	False