Module 5: Sequences Without End

Practice Tasks

Complete these tasks to reinforce what you learned in this module.

Task 1: Fibonacci without an end

Write an infinite Fibonacci iterator starting 0, 1, 1, 2, 3 — then print the first ten values on one line, separated by single spaces.

Expected Output:

`0 1 1 2 3 5 8 13 21 34`

Hint: while (true) with yield return a;, then shuffle a and b forward. Main already has the Take(10) and the join.

Starter Code:

task.cs

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static IEnumerable<long> Fibonacci()
    {
        // Never-ending: 0, 1, 1, 2, 3, 5, ...
        yield break;
    }

    static void Main()
    {
        Console.WriteLine(string.Join(" ", Fibonacci().Take(10)));
    }
}

Task 2: The first multiple that is big enough

From an infinite sequence of natural numbers, find the first multiple of 7 whose square is greater than 1000, and print that square.

Expected Output:

`1225`

Hint: Naturals().Where(n => n % 7 == 0).Select(n => n * n).First(n => n > 1000).

Starter Code:

task.cs

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static IEnumerable<int> Naturals()
    {
        for (int i = 1; ; i++)
        {
            yield return i;
        }
    }

    static void Main()
    {
        // Squares of multiples of 7 — print the first one over 1000
    }
}

Task 3: Count what was actually produced

Find the first natural number divisible by 13, then print how many values the infinite sequence produced in total. Have the iterator count each value it hands out.

Expected Output:

13, then 13 — the sequence stopped the moment the answer was found.

Hint: Increment the counter just before each yield return. First stops asking as soon as its condition holds.

Starter Code:

task.cs

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static int _produced;

    static IEnumerable<int> Naturals()
    {
        for (int i = 1; ; i++)
        {
            // Count this value, then hand it back
            yield return i;
        }
    }

    static void Main()
    {
        var first = Naturals().First(n => n % 13 == 0);

        Console.WriteLine(first);
        Console.WriteLine(_produced);
    }
}

using System; using System.Collections.Generic; using System.Linq; class Program { static IEnumerable<long> Fibonacci() { // Never-ending: 0, 1, 1, 2, 3, 5, ... yield break; } static void Main() { Console.WriteLine(string.Join(" ", Fibonacci().Take(10))); } }

using System; using System.Collections.Generic; using System.Linq; class Program { static IEnumerable<int> Naturals() { for (int i = 1; ; i++) { yield return i; } } static void Main() { // Squares of multiples of 7 — print the first one over 1000 } }

using System; using System.Collections.Generic; using System.Linq; class Program { static int _produced; static IEnumerable<int> Naturals() { for (int i = 1; ; i++) { // Count this value, then hand it back yield return i; } } static void Main() { var first = Naturals().First(n => n % 13 == 0); Console.WriteLine(first); Console.WriteLine(_produced); } }