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Assignment #1 - due date: Mar 29, 2024

What to turn in: a single .fsx script that contains your solutions to every problem. Be sure to add comments with the exercise numbers and any other details you think will help evaluating your code.

Numbers, sequences/lists, mapping, filtering, folding (15 points)

  1. Given a list of integers, return a new list with each element squared. (1 point)

  2. Write a function that filters out all odd numbers from a given list of integers, returning a list of only the even numbers. (1 point)

  3. Write a function that takes a list of numbers and returns the sum of all positive numbers in the list. (1 point)

  4. Given a list of names (strings), return a new list with each name capitalized. (1 point)

  5. Write a function that takes a list of strings and an integer n, returning a list of strings where each string has a length greater than n. (1 point)

  6. Write a function that takes a list of integers and an divisor, and returns the count of numbers which are divisible by it. (2 points)

  7. Create a function that takes a list and an element, and returns all the indices of the list where this element can be found. (2 points)

  8. Given a list of strings, write a function that concatenates only those strings that are longer than a given length n. (2 points)

  9. Assuming a list of tuples where each tuple contains an (id, value), write a function to find the tuple with the maximum value. (2 points)

  10. Given a list of elements that could repeat, write a function that returns a list of tuples, each containing an element from the input list and the number of times it appears. (2 points)

Discriminated unions (10 points)

  1. Define a DU for a traffic light (Red, Yellow, Green). Write a function that takes a traffic light state and returns the next state. (2 points)

  2. Create a DU for basic arithmetic operations (Add, Subtract, Multiply, Divide). Implement a function that takes two numbers and an operation, then performs the operation on the numbers. (2 points)

  3. Define a DU for different shapes (e.g., Circle, Rectangle, Square, etc.) Write a function that calculates the area of the given shape. (2 points)

  4. Define a DU for temperature scales (Celsius, Fahrenheit). Write a function that converts temperatures between the scales. (1 points)

  5. Create a DU to represent a simplified JSON value. Include cases for JsonObject, JsonArray, JsonString, JsonNumber, and JsonBoolean. Write a function that takes such a JSON value and pretty-prints it to a string. (3 points)

Functions, recursion (15 points)

  1. Write a recursive function to compute the nth Fibonacci number. (3 points)

  2. Implement a recursive binary search algorithm that searches for a given element within a sorted array. (3 points)

  3. Write a recursive function to sort a list of integers using the merge sort algorithm. (3 points)

  4. Given a binary tree (as a nested structure of nodes), write a recursive function to compute the depth of the tree. (3 points)

  5. Create a recursive function to check whether a given string is a palindrome (reads the same backward as forward). (3 points)

Extra credit

You can turn in the first assignment from 2022 for extra credit.