How to do an analysis in 5 steps

Doing mathematical analysis can be intimidating. However, what you are really doing is simply explaining a thought process. This can be done in a fairly consistent step by step manner. This section looks at the steps you should take to do this and break down how to approach an analysis.

Step 0: It is good to start by putting your code in.

unsigned int factorial (unsigned int n){
    unsigned int rc = 1;
    //multiplying 1*1 gives 1 so we don't start from 1
    for (unsigned int i=2;i<=n;i++){
        rc=rc*i;
    }
    return rc;
}

If you are copying code into a markdown wiki page, you can use surround the code block with ``` to do a block quote.

To format according to a language provide the name of the language after the third tick that precedes the block. For example:

```cpp

put your code here.  code will be c++ syntax formatted

```

Step 1: Establish variables and functions (mathematical ones):

Step 2: Count your operations

Put the operation count in a comment beside each line of the code blurb. The loop runs n-1 times (i goes from 2 to n inclusive). Thus any operations that occur in the loop is counted as n-1.

unsigned int factorial (unsigned int n){
    unsigned int rc = 1;                    // 1
    //multiplying 1*1 gives 1 so we don't start from 1
    for (unsigned int i=2;i<=n;i++){        //1 + (n-1) + (n-1)
        rc=rc*i;                            //2(n-1)
    }
    return rc;                              //1
}

Step 3: Establish the Mathematical Expression for T(n)

We add up the operation counts in the comments

Step 4: Simplify your Equation

\begin{align*} T(n) &=1 + 1 + (n-1) + (n-1) + 2(n-1) + 1 \\ &= 4(n-1) +3 \\ &= 4n-4 +3 \\ &=4n -1 \end{align*}

Step 5: State your final result.

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