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--- notes:discrete:fall2023:projects:mor0 [2023/10/29 21:21] – created wedge
+++ notes:discrete:fall2023:projects:mor0 [2023/11/16 01:24] (current) – [Matrix] cfoster8
@@ Line 3: / Line 3: @@
 =====Matrix=====
+A matrix is simply data stored within a grid. It can be thought of as a multi-dimensional array, or "an array of arrays". For example, a 2D array may also be referred to as a matrix (a table of rows and columns).
+And the initialization would look something like this
+<code C>
+int matrix[2][3] = { { 1, 7 }, { 2, 9, 6 } };
+</code>
+When accessing data within a matrix imagine the matrix as a coordinate grid, and the numbers you give the matrix is the coordinate point of that data within the matrix.
+Like arrays, Matrices are fixed in size. You allocate the memory for it when created and it cannot be changed.
+In theory, a matrix can have as many dimensions as you want. As many times as you can nest an array in an array, a matrix of that many dimensions can be created. Because that's all a matrix is, at least this type of matrix, an array of arrays to the nth degree.
 =====Recursion=====
+The concept of recursion is actually simple but implementing it is more challenging than you might think. Recursion works by creating a function that calls itself until it hits a base case to end/breakout of the recursion function. Along with the base case, it has another case that slowly leads to the base case.
+A simple implementation of this can be seen with a function that gets the factorial value given a certain number.
+Here is what that function looks like:
+<code C>
+// Factorial function using recursion
+int factorial(int n)
+{
+    // Base case for when the number given is 0
+    if (n == 0)
+    {
+        return 1;
+    }
+    // Takes the given value and multiplies it by the previous factorial value
+    else
+    {
+        // Function calls itself (calls n-1) until it reaches the base case (0)
+        return n * factorial(n - 1);
+    }
+}
+</code>
+As you can see the function starts with the base case and then actually implements the logic for the function. Let's give n a value of 3. First, we are going to check if n is 0 and when it fails that check it will return 3*factorial(2), and then it will evaluate when n is 2. This pattern will continue until it evaluates n being 0. Now that the function has not been called again it returns 1 because n is 0. Now factorial(1) can complete its return, then factorial(2), and finally factorial(3). The result of factorial(3) is 6.
+====Properties of Recursion====
+Recursion can cause issues when not handled properly. The easiest way for this to happen is to cause a **stack overflow**.
+A stack overflow occurs when a recursive function is never properly broken and repeats indefinitely until memory (the stack) is used up. This happens when the base case condition check is faulty or nonexistent.
+====Why Use Recursion Instead of a Loop?====
+There are several differences between loops and recursion. A couple of them being:
+  * Loop uses repetition to go over sequential data, while recursion uses a selection structure.
+  * Loops are less memory and processor intensive than recursive functions.
+Recursion does have its advantages over loops though.
+  * The code is easier to understand and is generally shorter.
+  * Recursion can solve some problems that normal loops can not.

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