BRAIN YU: When you're loading words into your dictionary and when you're checking to see if a word is spelled correctly or not, you're going to need to call on your hash function, a function that's going to take a word and return which index into your hash table you should use in order to find that word or insert the word into your data structure. So what is the hash function? Well, the hash function is going to take a char star or a string as input representing the word that you're going to hash. And it's going to return an unsigned integer, an integer that won't be negative, representing which index into the hash table you should use that corresponds to that particular word. 

So what does your hash function need to do? Well, it needs to take as input a word, and that word is going to have alphabetical characters, and it may have apostrophes in it as well. And the output of your hash function is going to be a numerical index between 0 and N minus 1 inclusive. Recall that N is defined at the top of the file and is the total number of buckets in your hash table, in other words, the length of that array of linked lists. We've, by default, set N equal to 1. But you can and should set N to be some larger number so that you have more buckets in your hash table and, therefore, can spread your data out a little bit more making for faster search times. 

And importantly, your hash function should be deterministic. If I give it the same input again and again, I should get the same output, such that when I'm loading a word like apple into the dictionary, I'll be able to calculate the hash value of the word apple and insert apple into that index into the hash table. And then when I'm checking to see if the word apple is spelled correctly or not, I should be able to call the hash function on the word apple, get the same value as before, and then check only that particular linked list in the hash table to see if the word apple is there or not. 

So you'll need to decide on a value of N, the number of buckets that your hash table is going to have, in other words, the length of your array, and also the possible values that your hash function can return. A larger N value means you have more buckets and your hash table and, therefore, data is spread apart more and could potentially mean faster search times. But you'll need to make sure that the output of your hash function is some value between 0 and n minus 1 inclusive because those will be the only valid indices into your hash table. 

If your function were to end up with a value greater than N you could always take that value mod N or the remainder when you divide by N, in other words, to get a value that's in the appropriate range. Now what are some examples of some hash functions? Well, a very simple hash function might just take the first letter of the word. If the first letter of the word is A, then the hash value is going to be 0. If the first letter of the word is B, the hash value is 1, so on and so forth. If the first letter of the word is Z, the hash value might be 25. 

In this case, your value of N is 26 because you'd have 26 different buckets, one for every letter of the alphabet. Of course, 26 isn't very many buckets, especially considering the fact that the large dictionary that we're going to give you contains more than 143,000 words. So you might consider using other hash functions, like looking at the first two or three or more letters or doing some sort of math using all of the individual values of the letters. 

But once you've completed the hash function, you'll now have the ability to take a word and determine which of the linked lists inside of your hash table it should correspond to.