Corning Community College
CSCS2330 Discrete Structures
Explore and implement a program that implements matrices and uses matrix operations iOR implements algorithmic recursion in some central manner.
You will want to go here to edit and fill in the various sections of the document:
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
int matrix[2][3] = { { 1, 7 }, { 2, 9, 6 } };
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.
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:
// 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); } }
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.
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.
There are several differences between loops and recursion. A couple of them being:
Recursion does have its advantages over loops though.
To be successful in this project, the following criteria (or their equivalent) must be met:
Let's say you have completed work on the project, and are ready to submit, you would do the following:
lab46:~/src/SEMESTER/DESIG/PROJECT$ submit DESIG PROJECT file1 file2 file3 ... fileN
You should get some sort of confirmation indicating successful submission if all went according to plan. If not, check for typos and or locational mismatches.
I'll be evaluating the project based on the following criteria:
208:mor0:final tally of results (208/208) *:mor0:functional program demonstrating concept [104/104] *:mor0:implements and utilizes the concept [104/104]