Mastering Hash Functions: Understanding Key % 1000 Indices

For the hash function key % 1000, what is the range of possible indices?

• A. 0 to 500
• B. 0 to 999
• C. 1 to 1000
• D. 1 to 999

Answer: (B)

The range of possible indices for the hash function key % 1000 is from 0 to 999. This is because the modulus operation effectively maps any integer key into a confined range between 0 and one less than the divisor, which, in this case, is 1000. When you perform the operation `key % 1000`, you are computing the remainder of the division of `key` by 1000. Since the remainder can take any value from 0 up to (but not including) 1000, it includes all integers from 0 to 999. Therefore, the set of all possible outcomes of this hash function is precisely 1000 unique values: 0, 1, 2, ..., 998, and 999, making the correct range 0 to 999. Other ranges listed, such as from 0 to 500 or 1 to 1000, do not encompass the complete set of values that the modulus operation can yield for the divisor of 1000, highlighting why they are not correct in this context. Similarly, the range from 1 to 999 excludes the number 0, which is also a valid output of the modulus operation when the key is

Understanding the workings of hash functions can feel like trying to navigate a maze blindfolded—unless someone hands you a map. If you’re gearing up for the Western Governors University ICSC2100 C949 Data Structures and Algorithms I exam, you'll want to be crystal clear on concepts like the modulus operation. So, let’s dissect the hash function key % 1000 and explore its range of possible indices. Spoiler alert: It’s 0 to 999!

First things first—what the heck is the modulus operation? Easy! It’s a fancy way of asking, "What’s left over after I divide this number by another?" When you run the operation key % 1000, you're essentially figuring out the remainder when the key is divided by 1000. Simple, right? The intriguing part is how this operation confines our results.

Picture it: every integer key we throw into the modulus operation gets mapped into a neat little box—specifically, it can yield any value from 0 to one less than the divisor (which is 1000 in our case). So the possible outcomes are all integers from 0 all the way up to 999. Now, if you tally those up, that's a grand total of 1000 unique values: 0, 1, 2… all the way through 998, and of course, 999.

Just to clarify, other options like 0 to 500 or even 1 to 1000? Nah, they don’t cut it. The range of 0 to 500 is far too narrow. It ignores a whopping half of our possible values! And that other contender, 1 to 1000, misses out on the very crucial number—0. It’s like throwing a pizza party and forgetting the pizza! Always remember that with the modulus operation, zero is as valid as any other number.

Now, think about how this basic yet powerful concept of hash functions relates to everyday programming—and even to life! In programming, hash functions help keep our data organized, letting us retrieve information quickly, much like finding your favorite pizza topping in a fully stocked kitchen. The quicker we can access that data is essential, mainly if you’re managing databases or working on maintaining an efficient application.

Plus, understanding hash functions and modulus operations better prepares you not just for your exams, but also for real-world coding challenges. From searching algorithms to data retrieval methods, a solid grasp helps make your programming life a breeze.

So, when you tackle questions like, “What is the range of possible indices for the hash function key % 1000?” remember: it’s all about the numbers being mapped neatly into that range of 0 to 999. That lightbulb moment of clarity can do wonders for your confidence heading into your next exam question.

Keep practicing, stay curious, and approach those data structures with the same zest you'd bring to an exciting programming project! Happy coding!