static void Main(string[] args)
{
Console.WriteLine("Hello, fox. We have some Problems to take care of, and we're (probably) going to do them out of order.");
Console.WriteLine("First, let's create an array...");
// We're going to do Problem 3 first - an algorithm with
// time complexity of O(n^2). We're going to create an
// Arbitrarily Big Array.
Random random = new Random();
int lemgth = random.Next(10, 20);
int max = 0;
// The "starting numbers" for our algorithm.
Chain <int> chain = new Chain <int>(max);
// I imported my ChainCore library for the purpose.
Console.WriteLine("We are getting " + lemgth.ToString() + " numbers.");
for (int i = 0; i < lemgth; i++)
{ // For "lemgth" times...
max = random.Next((max + 1), (max + 10));
// This lets us be sure that each number is bigger than the last.
chain.Add(max);
// And then we add it.
}
// End of "outer" for loop
int[] array = Chain <int> .Array(chain);
Console.WriteLine("Chain array completed! Here it is:\n");
for (int i = 0; i < array.Length; i++)
{
Console.WriteLine("Index " + i.ToString() + ": " + array[i].ToString());
}
/*
* This algorithm ends up being O(n^2) because of the way the Chain class works.
*
* For one thing, because of the way the Chain class works,
* to add a new item it has to first iterate through the whole
* list to find the "end". This means that the steps to just add
* to it scales up with the size of the list. Moving them to the array
* is similar, because it has to go through the whole chain to find each number.
* ChainCore may be very memory efficient, but it is *not* efficient
* in time complexity.
*
* And that's fine. I suppose. I don't know. You can't really see it from
* here without being familiar with ChainCore to begin with. I hope there's
* not a lot of people like that using it.
*/
int sum = 0;
foreach (int number in array)
{
sum += number;
}
// End of foreach
Console.WriteLine("As it happens, the total sum is " + sum.ToString() + "!");
/* Here we do the summation problem. Not including the steps to get
* the array to begin with, the best we can get here is O(n) - we have to count
* every number, and there's not really any good way to "cheat" on that since
* we don't know ahead of time what those numbers are.
*/
Console.WriteLine("Now, we're going to find a random number in it with a binary search.");
int target = random.Next(array[0], array[array.Length - 1]);
Console.WriteLine("We're searching for " + target.ToString() + ".");
// It *might* not exist. That's fine, and on purpose.
bool search = true;
int index = 0;
int top = array.Length;
int bottom = 0;
int range = top - bottom;
int current = top / 2;
while (search)
{ // Until we've found the closest number...
Console.WriteLine("- Checking Index " + current.ToString());
if (array[current] == target || range <= 1)
{ // If this is the number OR there's only one number left...
Console.WriteLine("- FOUND IT!");
index = current;
search = false;
}
else if (array[current] < target)
{ // If we're "too high"...
Console.WriteLine("- " + array[current].ToString() + " is too low!");
bottom = current;
}
else if (array[current] > target)
{ // If we're "too low"...
Console.WriteLine("- " + array[current].ToString() + " is too high!");
top = current;
}
// End of Else If statement
range = top - bottom;
// Find the new range
current = (range / 2) + bottom;
// Get the next index
}
// End of While loop
Console.WriteLine("The closest number is at index " + index.ToString() + " and happens to be " + array[index].ToString());
/* And that concludes our binary search! As was explained in class,
* the binary search is O(log n) because each step we add doubles the size
* of the list we can search effectively.
*/
}