More Basics#

Solving this set of exercises increases your skills in algorithmic thinking and Python’s syntax. Everything you need has been discussed in the Crash Course chapter. Do not use additional Python features or modules.

Point Inside Rectangle?#

Get two integers from the user and check whether the corresponding point lies inside the rectangle with corners at (-1, -1), (5, -1), (5, 2), (-1, 2). Print a message showing the result.

Solution:

# your solution

Square Numbers#

Get an integer from the user and tell the user whether it’s a square number or not. If you want to compute square roots, use 123 ** 0.5. Print a message if the user gave a negative number.

Hint: Have a look at the output of 16.125 % 1.

Solution:

# your solution

Unique Items#

Write a function no_duplicates which returns True if the passed list contains no duplicates and False if there are duplicates.

Test your function with [1, 4, 5, 6, 3] and [1, 3, 1] (and with [], of course).

Solution:

# your solution

Increasing Subsequence#

Write a function inc_subseq which takes a list of numbers and prints all items except the ones which are smaller than their predecessor.

Test your function (at least) with [1, 3, 2, 3, 4, -2, 9] and [3, 2, 1].

Solution:

# your solution

Area of a Circle#

Get an integer radius of a circle from the user. Calculate and print the circle’s area as well as the edge length of a square with identical area. Check user input for validity. You may use NumPy’s pi constant.

Solution:

# your solution

Quadratic Equations#

Solve the quadratic equation \(a\,x^2+b\,x+c=0\) with user-specified \(a\), \(b\), \(c\) (integers). Give all real solutions.

Solution:

# your solution

Regular Polygons#

Use Matplotlib and NumPy’s sin and cos functions to plot a regular polygon. Ask the user for the number of vertices and check user input for validity.

Hint: For \(n\) vertices the \(k\)th vertex is at \((\cos\varphi,\sin\varphi)\) with \(\varphi=2\,\pi\,\frac{k}{n}\).

Solution:

# your solution

Stars#

Draw a star with user-specified number of outside vertices. Radius for inner vertices is 0.3, for outer vertices it’s 1.

Solution:

# your solution