K-sorted sequence
Imagine you have a bunch of numbers that are already sorted in order, but someone comes and makes a mess by randomly moving some of the numbers around. This new sequence is called a k-sorted sequence.
But don't worry, it's not too scary! The "k" in k-sorted just means that the numbers are within k positions of where they should be if everything was in order.
For example, if k is 2, then any number in the sequence can be within 2 positions away from where it was originally. So if the number 5 was originally in the third position, it could be moved up to the first position or down to the fifth position and still be considered k-sorted.
The reason we care about k-sorted sequences is that sometimes we need to sort a really big sequence that would take too long to sort all at once. But if we know it's k-sorted, we can sort small chunks of the sequence individually and then merge them together to get the whole sequence sorted.
It's kind of like if you had a bunch of legos that were all mixed up, but you knew that each pile had only a few different colors of legos. You could sort each pile by color and then put them all together to make one big, organized lego creation!
So a k-sorted sequence just means that things are a little bit mixed up, but we can still sort them out by breaking them down into smaller chunks.
But don't worry, it's not too scary! The "k" in k-sorted just means that the numbers are within k positions of where they should be if everything was in order.
For example, if k is 2, then any number in the sequence can be within 2 positions away from where it was originally. So if the number 5 was originally in the third position, it could be moved up to the first position or down to the fifth position and still be considered k-sorted.
The reason we care about k-sorted sequences is that sometimes we need to sort a really big sequence that would take too long to sort all at once. But if we know it's k-sorted, we can sort small chunks of the sequence individually and then merge them together to get the whole sequence sorted.
It's kind of like if you had a bunch of legos that were all mixed up, but you knew that each pile had only a few different colors of legos. You could sort each pile by color and then put them all together to make one big, organized lego creation!
So a k-sorted sequence just means that things are a little bit mixed up, but we can still sort them out by breaking them down into smaller chunks.