SPEAKER: In Caesar, your task is going to be to encipher or encrypt some text by shifting all of the letters in that text by a certain amount. What your program is ultimately going to do is it's first going to get the key-- the amount that we should shift each character by. Then we're going to prompt the user to type in some plain text. Then we're going to encipher that plain text by shifting all the letters by the key. And finally, we're going to print out the resulting cipher text. 

What does this look like? Well, if the key is 2, then for any plaintext character, we're going to shift that character by 2 letters in the alphabet. So if we had a plain text capital A, that would become the ciphertext capital C, because we're shifting it by 2 letters from the alphabet. B would become D. C would become E. So on and so forth up, until X would become Z. 

And then when we get to Y, if we were to shift Y by 2 characters, we would go past the boundary of the alphabet. So what we'll instead want to do is wrap around to the beginning of the alphabet so that Y becomes A when we shift it by 2, and Z becomes B when we shift it by 2. 

What does this mean for how your program should actually work? Well, if we were to run ./caesar and then provide, a command line argument, the number 2-- meaning we'd want to use 2 as the key, shifting everything by 2-- and we were to type in the plain text ABC, then your program should print out the ciphertext CDE-- the same as the plain text, but with every character shifted by 2 letters. 

If we were to instead run ./caesar2 and provide the plain text of "hello," for example, -- then the ciphertext should be this J-G-N-N-Q, which is each of the letters in "hello" shifted by 2 letters. Let's take a look at one last example. 

If I were to run ./caesar with a key of 2 ans input a plaintext of "This is CS50," then the ciphertext should look like this. And there are a couple of things to note here. One is that we're preserving case. 

If a character is an uppercase letter in the plaintext, then it's also an uppercase letter in the ciphertext. And likewise, a character that's a lowercase letter in the plaintext is also a lowercase letter in the ciphertext. And any character that's not an alphabetical character at all-- so things like spaces or numbers or punctuation marks-- those don't change. The spaces stay spaces. The 50 stays 50. The exclamation point stays an exclamation point. Only the alphabetic characters are changing. 

So let's go through each of the steps of the caesar program to figure out how you can actually write the code to do this. The first thing you'll want your program to do is to get the key-- get the amount that we should shift each of the individual letters by. How is your program going to do that? Well, remember that your program is going to take the key as a command line argument, meaning that when the user is running your program, they're going to run your program as something like ./caesar, followed by a number representing the key of how many characters to shift each of the letters by. 

How do you access those command line arguments? Well, recall that in a C program your main function can take arguments. It can take an argument called argc, which is going to represent the argument count-- the number of command line arguments-- and also an array of strings, called argv, representing each of those command line arguments. 

So for example, if I were to run ./caesar2 and then the number 3 as the key, argc would be 2. I typed in two things-- ./caesar2 and 3. And argv is going to be the actual array of strings representing those arguments. And recall that when you have an array, you can access an individual element of that array using square bracket notation. 

So argv[0] is going to be the first string in the argv array-- which, in this case, is ./caesar2-- and argv[1] is going to be the second thing in that argv array-- which, in this case, is the string 3. So that's how we might access the key. 

Now, when we get the key, you'll want to ensure that only a single command line argument is provided, and that that argument contains only digit characters before you actually take that argument and convert it to an integer. What I mean by that is that if the user runs ./caesar, and then 2 and then 8, providing more command line arguments that's expected, your program, rather than doing anything else, should just print out a usage message reminding the user that in order to run the Caesar program, they should run ./caesar2, followed by a key. And you should do this anytime they don't use the correct number of command line arguments. 

But even if they have the correct number of command line arguments, that argument might not be entirely numeric. If the user runs something like ./caesar20x, where the command line argument is not entirely numeric, you should also display a usage message reminding the user that they need to run ./caesar, followed by a valid key. 

How do you check if the key is valid? Well, you'll probably want to take that command line argument and check each of the individual characters in that string to make sure the character is a digit. And you might want to think about what functions might be helpful for checking if an individual character is or is not a digit. 

Once you've checked to make sure that the command line arguments are correct, the last thing you'll need to do here is actually take the command line argument and convert it into an integer. Notice that argv[1] right now, representing the key, is not the number 3, but the string "three." 

Recall that in C, every variable has a type. Some variables are ints, and other variables are strings, for example. And here, argv[1] is the string "three," rather than the integer 3-- which we'll probably want to use in case we need to do some math with that number, for example. 

So what we'll need to do is convert the string into an into an integer. To do this, you can use the A2I function, declared in standard lib.h, that takes a string, like the string 3, and converts it into the number 3, for example. So that function might be helpful for making sure that your key is in fact an integer. 

After you've gotten the key, the next step is to prompt the user to type in the plaintext. To do that, you can use a call to get string, asking the user to type in what plaintext they want to encrypt. Once you've gotten that plaintext, the next step is going to be to encipher that plaintext, shifting all of the letters by the key to get the ciphertext result. 

But before we talk about how to encipher the entire plaintext, let's just talk about how to encipher one particular character. How are we going to do that? Well, there are a couple of cases that we might want to consider. If the character is an alphabetic character, like an uppercase letter or a lowercase letter, for example, then we'll want to shift that plaintext character by the key, making sure to preserve the case. If it was originally an uppercase letter, it should stay in uppercase letter, for example. 

Of course, if the character is not alphabetic-- for example, if it's a space or a punctuation mark or a digit-- then you can leave the character as is. Nothing actually needs to change there. But how do you know if a character is an alphabetic character or an uppercase character or a lowercase character? Well, it turns out, there are a number of functions that you can use that might be helpful here. Functions like is alpha, is upper, and is lower. Is alpha is a function that takes a character and returns a Boolean value, true or false, depending on whether or not that character is alphabetic. And likewise, is upper checks to see if the character is uppercase and is lower checks to see if a character is lowercase. 

If we call is alpha, is upper, and is lower on capital A, for example, is alpha of capital A is true. It is an alphabetic character. Is upper of capital A is also true because capital A is an uppercase letter. And is lower of capital A is false because capital A is not a lowercase letter. And so that can help you to figure out, given a particular character, is it an uppercase character or is it a lowercase character? And every character, uppercase and lowercase, has an ASCII value. 

Recall that ASCII is just a mapping from characters to numbers that represent them, where we've decided that capital A is represented by the number 65, capital B is represented by the number 66, so on and so forth. And lowercase letters have a mapping as well. Lowercase a is represented by the number 97, lowercase b by the number 98, lowercase c by 99, so on and so forth. And you can treat any individual character as equivalent to the number that represents it. 

So what does that mean in code? Well, it means that if I have a character in a variable called c that I set equal to the character A-- capital A-- and I print out that character using %c to mean I want to substitute a character into this string, then what gets printed out, as you might expect, is the character A. But this character A is really just the number 65 inside of my computer, and I can treat this character like the number 65. And like any number, I can do math with it, adding or subtracting numbers from it, for example. 

So I can take capital A and add 1 to it, for example. Capital A is represented by 65. 65 plus 1 is 66. So if I print out the character corresponding to the number 66, what's ultimately going to be printed out is the character B because B in ASCII is represented by the number 66. But what happens if I try to take a character like the character capital Z and shift that by one? If I take the ASCII value corresponding to the letter Z and add 1 to it, I don't get the ASCII value corresponding to capital A. I get something that's outside of the range of all of the capital letters. 

What I'd really like to happen here is that once I try to shift past the letter Z, I want to wrap around back to the beginning of the alphabet, back to the letter A. But how do I do that? Well, to do this, we can take advantage of a formula. And here's the formula that we're going to use to convert the plaintext into the ciphertext. It looks a little bit complicated, but we'll break it down piece by piece. 

c sub i here represents the ith character of the ciphertext. How do we determine what the ith character of the ciphertext is? Well, we're going to start by taking the ith character of the plaintext and we're going to add k to it, where k is the key. And we're going to take that whole result and take it modulo 26. This %26 means we're going to take the remainder when we take this whole value and divide it by 26. 

Why does this work? Well, for sake of example, let's say that a is represented by the number 0, b is represented by the number 1, c is represented by 2, so on and so forth, up until z, represented by the number 25. So how might I go about taking the character z and shifting it by 1, using this formula? Well, here is the formula. And the plaintext character I want to shift is the character z, which is here represented by the number 25. And I want to shift it by the key k, which in this case is 1. 

So I have 25 plus 1, which is the number 26, and 26-- mod 26-- is what's the remainder when I divide 26 by 26? Well, the remainder is just 0, so I'm left with 0, which corresponds to a in the above chart. The result is that I'm able to take a character, shift it by a certain amount. And by using modulo 26, I'm able to get the remainder when I divide it by 26, which allows me to loop back around effectively to the beginning of the alphabet so that z wraps around to a. 

And this mapping of a to 0, b to 1, c to 2, et cetera, you can call an alphabetical index. Where I might say that a's alphabetical index is 0, b's alphabetical index is 1, c's alphabetical index is 2, and so forth. But of course, in our computer, we don't use the alphabetical index to represent each character. We use ASCII, where A is 65 and B is 66 and C is 67, and so we can't directly apply this formula. 

So what do we need to do in order to take an ASCII character and shift it by a certain amount, while still preserving this wrap-around effect of going from the end of the alphabet back to the beginning? Well, here's what we might try to do. We might first convert an ASCII character to its alphabetical index so that capital A becomes the number 0, for example, and capital B becomes the number 1. And you might want to think about what math you could do to make that work. Once you have an alphabetical index, you can shift that alphabetical index using the formula, adding the key and taking the result mod 26 to get the new character's alphabetical index. 

And finally, you can take the resulting alphabetical index and convert that back into ASCII, so that 0 becomes A, 1 becomes B, so on and so forth, being sure to preserve the case-- uppercase letters should remain uppercase, lowercase letters should remain lowercase. And that will allow you to encipher one alphabetic character. If it's alphabetic, you'll want to shift it to its alphabetic index, then shift it using the formula, then convert the result back to ASCII. 

But how, then, instead of enciphering just a single character, do you encipher all of the characters that are in the plaintext? Well, recall that the plaintext is really just a string. And when you have a string, you can access individual characters by using array-like notation, where I can say text[0] will get me the first character of the string text, which in this case is capital T. Likewise, text[1] is lowercase h, text[2] is lowercase i, so on and so forth. And I can use this notation to access any of the characters inside of the string. 

How do I know how many characters are in the string? Well, there's another function called strlen, short for string length, that will take a string and tell you how many characters are in it. In this case, 12. So by combining this, knowing the length of the string, knowing how to access an individual character in the string, and knowing how to encipher an individual character in the string, you should be able to implement this Caesar program by first figuring out what the key is, then getting the plaintext, then enciphering that plaintext by shifting all the alphabetic characters, and printing the result. My name is Brian and this was Caesar.