Shell sort vs Insertion sort
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- Опубліковано 21 тра 2022
- Introduction of Shell sort, and a match with Insertion Sort.
For an introduction of Insertion sort, see:
• Insertion Sort vs Bubb...
Choosing the sequence 9-6-1:
For a list of size 10, the gaps can be any number 1,2,....,9, and the sequence must end with 1.
So each of the gaps 2,3,...,9 can be included in the sequence, or not included. So there's a total of 2^8=256 possible gap sequences. For each we checked the average number of comparisons for all possible 10! permutations.
Here are the 3 best sequences:
9-6-1: 25.512 comparisons
4-1: 25.516 comparisons
6-1: 25.539 comparisons
We could have also checked which has the highest probability of performing less comparisons than insertion sort. Here are the top 3 in this respect:
4-1: prob=0.72
9-4-1: prob=0.704
6-1: prob=0.701
Analyzing Shell sort variants more generally: See it explained in my home page:
www.udiprod.com/shell-sort/#a...
Why did Shell sort lag behind in the second match in comparisons per second? You are welcome to post answers. Or read answer here:
www.udiprod.com/shell-sort/#t...
![[Laser] Firing squad synchronization problem](http://i.ytimg.com/vi/xV1aKUdlljU/mqdefault.jpg)
![[Laser] Firing squad synchronization problem](/img/tr.png)
I like how the robots having to move the full distance between balls approximates the idea of data locality
Everything is smartly thought to approximate all the concepts for everyone to understand, like the robot only being able to compare 2 balls at a time to explain the fact that only humans can roughly compare lots of values (and also the fact that with merge sort the robot had to push the balls when finished sorting...)
I thought this was cool too but what is the real life equivalent of the rocket boosters in the second race?
@@stuartallen2001 clock speed
@@stuartallen2001 Increased cache size.
@@stuartallen2001 memory latency
While this may seem like it's a marginal improvement over insertion sort if you manage to crack the gap code, remember that we are only working with very small lists of 10 items at a time. Once you scale up the list to hundreds or thousands, it becomes a completely different ball game and things like shell sort kick insertion sort to the curb.
And shell sort is among the slower sorts in that tier, too.
Insertion sort is also being handy capped by not using an binary search to find the insertion location. On 10 it would be a rather small reduction of checks, but savings scale up significantly on the hundreds or thousands of element cases.
@@TheFinagle You also need to account for the complexity of actually inserting the value into the array. Binary search makes it faster for you to find the location, but once you do, you still need to shift a bunch of elements over by one position to make room. Insertion sort does that as it is walking the array.
@@TheFinagle Yeah, that's a huge handicap. It would go from O(n^2) comparisons, to O(n*log(n)) comparisons by using a binary search.
@@pseudo_goose Your right, I hadn't though of that.
And if your data type can do easy arbitrary insertion its usually not binary search friendly.
I love that 13 years after the first video you guys are still doing 3d animations with the exact same robot model
me too. it does a good job of keeping the old videos feeling pretty timeless
Hey, if it ain't broke, don't fix it!
for the question at 6:16, I think it's due to shell sort spending more time moving different elements from one place to another on the rack, whereas insertion sort was almost always holding one element and comparing others to it.
I was thinking the same thing. You hit all the points I noticed.
Right! I just added a detailed account here: www.udiprod.com/shell-sort/#timing
But she'll sort had 1 extra comparison
I think that's also why the jet boosts were way more advantageous for Shell Sort. Insertion Sort didn't really utilize the rockets much, but Shell Sort necessarily has to go long distances.
It's been over a decade since his first sorting video yet he is still interested in making sorting videos. Guys, dedicate to your friends and family like this guy dedicate to sorting algorithms.
🥺
😊
Upside: gets into O(nlogn) territory with the right gap sequence
Downside: you need to calculate that gap sequence ahead of time
Shell sort is one of the most interesting sorting algorithms, im glad you’re making videos about it
I really like this lines display. Surely on Quick sort it would show at a glance how the first iteration partitions the set into two non-overlapping subsets.
Yeah, it definitely would, could be a cool addition for quick sort video.
I like these animations. They make the video easy and intuitive to understand.
Having watched a decade of sorting videos as if they were released as a series over the course of a week, the robots getting jet engines is hilarious and a wild plot twist.
Also the whole series is just well made and really shows off the differences in the algorithms.
The fact that this channel is still making these late 1990s-esque animations in the 21st century really keeps me going. Love these robots!
Finally, a new udiprod video! I've been waiting for so long lol
Good that the sorts are back
Insertion is best with actual physical objects, when making room to insert an object in is as simple as shoving everything to the right of it further to the right, rather than with computer memory, moving it over to the next memory address for each and every individual item in memory. With my DVD collection, inserting a movie between positions 23 and 24 out of 50 means shoving all DVD cases 24 through 50 together to the right by .5 inch all at once which can be done in one swift motion of a hand. While in a computer, that means moving the item in slot 50 to slot 51... then moving the item in slot 49 into slot 50, and then moving the item in slot 48 to slot 49... all the way down to then moving the item in slot 24 to slot 25, and then and only then having the space to put the new item into slot 24.
Or if you have a linked-list, but you then need a way to perform the binary search. A linked list is where the computer grabs a random chunk of memory for the new data field, uses pointers to identify that chunk of memory, then has the predecessor and successor items re-point from each other to the new item. After the list is sorted, you then copy the elements from the linked list to the final list.
A linked list is composed of multiple individual data elements, where each data element is composed of the data value, and two pointer values (forward and backward). Element number one has a data value, and two empty pointers. When element number two is added (assuming element number two is supposed to go after element #1), then the 'forward' pointer is reassigned to point at the location of data element number two. Element number two has its backwards pointer to point at element number one.
From there, items number three is analyzed. Item number thre3e is discovered to fit between elements #1 and #2. So another chunk of memory is grabbed, the data value for item #2 is put in that chunk of memory, and then the pointers for element number three are updated. The #3 'forward' pointer is changed to point to element #2, and the backward pointer is changed to point at element #1. Similarly, element #1 has its forward pointer changed to point to element #3, and element #2 has its backwards pointer changed to point at element #3.
(apologies for the words, but I need pretty pictures to better explain it)
I think it'd be better if the balls were numbered because it's hard to tell the difference between some of the shades of red and think about sorting them. would also be better for colorblind people
Commenting to boost this, cus I have red-green color deficiency.
Really? I thought you could differentiate shades of the same color, just not tell the colors apart
Would also help understanding radix sort
@@affegpus4195 it might depend on the specific type of colourblindness, perhaps?
no
Wow, the coolest explanation and visualization of Shell sort I've seen! Thank you so much. So simple, short and clear explanation
Thanks to these videos, I now understand the "sounds of sorting" videos UA-cam keeps recommending me.
The fact that you've used this same visualization for 10+ years with few changes is delightful to me
Babe wake up, new udiprod video just dropped
I love these visual expressions and explanations of algorithms! Please more!
I need more of this. I love coming back here from time to time to watch these guys sort!
Wake up babe, new udiprod video about sorting algorithms just dropped
Boy I can't wait for you guys to explain the absolute magic that is Radix sort. I wish I understood how that thing worked.
Almost 10 years and still making these animations. Kings
new udiprod sorting algo vid dropped?????? why was i not informed immediately. absolutely fantastic
When the world most called for him, he returned
The sort comparisons are back! How about a video highlighting how much the result can be rigged with carefully crafted inputs?
Finally! Another video!
The Return of The King
so glad we are getting another sorting video
STANDINGS:
21 Quicksort
44 Bubble Sort
44 Merge Sort
52 Quicksort
39 Heap Sort
23 Merge Sort
30 Insertion Sort
44 Bubble Sort
36 Bubble Sort
81 Stooge Sort
27 Stooge Sort
605 Bogosort
30 Insertion Sort
31 Shell Sort
Where is Shell(9,6,1) Sort? It's not a proper sort, just a modification of Shell Sort.
I don't get what's going on here
Those are the current standings of all the sorting algorithms featured so far.
Its the same list?
@@affegpus4195 I don't remember.
I have a feeling that this is about to be recommended to everyone
I love that you keep making videos! I really like them, they're quite interesting and relaxing
I love this channel, and what I love the most is that even thought it's been 15 years the art style hasn't changed a bit. Wish you would upload more often
Nothing better than watching these videos at 2:30 AM
I am CS student but I'm bad at math and algorithm
Thank you, now I can understand most of basic understanding
Really awesome to see this channel upload!
Would have been interesting to see binary insertion sort, another optimization to insertion sort
It's always a good thing to see a new Udiprod video.
I found this channel just a few weeks ago, glad they updated
Ooo, new sorting videos! I love these!
I had no idea you were still making videos and I am so glad you are. Keep up the good work! I love these vids
I know nothing about computing, but I do like those hardworking bots moving the balls.
I would absolutely watch a 1 hour video of this style animation with the robots sorting a 100-element list or whatever the max you could do in an hour or so. Maybe get more algorithms going at once even.
I would like to see gnome sort next, you explain sorting algorithms really well and i cant understand the difference between gnome sort and insertion sort so making a video about it would help me a lot, thanks.
Edit: i finally understood it, but a video about it would be cool!
i would want to see it just for the sake of seeing a robot in a funny little gnome hat and beard
@@claw25533 Actually me too, but as of now, I STILL DON´T KNOW THE DIFFERENCE OF GNOME SORT AND INSERTION SOTR, PLEASE EXPLAIN!
Thank you Uriprod, your videos are so helpful and intuitive!!
Thanks! I didn't know how shell sort worked until I saw this video!
Thank you for continuing this series!
While using "the jet engines" do not forget it doesn't always work like this in the real life where we have caches and bus widths. Chances are the comparisons (let's assume we just sort some 8-bit values) will take the addresses far enough to make the memory controller trigger a full-width read for every byte it needs, see ya performance :)
Thanks once again for these extremely informative videos!
I really enjoyed this demonstration of shell and insertion sorting. Thank you so much for making these videos :)
what a beauty this channel is!
its always a great surprise when you upload !
Hey this is actually really easy to understand
Yay! Another sorting video! We sub for these and we will always come back no matter how long!
"This is a sorting algorithm, it loses. So lets give it alot of extra advantages and see it win"
I never thought I'd understand Shell sort. Thank you
Thanks. I now know shell sort. I was confused what shell sort does. This video helped me.
Amazing! Very well explained
The Ciura gaps are said to be the most optimal for shell sort of no specific input length, and shell sort is preferred over quicksort in tight applications because of its small code size, but it's cache unfriendly because of why the robot lags behind in comparisons per second. One reason why the optimal gaps barely beat insertion is because its best case is O(n log n) instead of O(n)
yoooo new sorting method video just dropped
These videos r kinda helpful to learn sorts
babe wake up new udiprod sorting algorithm video
I love these robot dudes so much. 24 ball race when
Babe wake up new udiprod sorting video
Love the animation. Keep up the good work.
Hello! What is the best way to contact you, because I have a question about your work in general. I have tried email in the past and failed.
I replied you email just now, I think. Sorry I must have missed it.
@@udiprod Thank you, I have replied to your reply.
i have wanted more of these so bad
Babe wake up, there's a new sorting robot video
Let's goo, another sorting video
New sorting algorithm dropped. All my friendsove sorting algorithms.
I Appreciate this video
this is the best channel
wake up babe. new uniprod video just dropped.
Finally, a new algorithm! Could you please do a video on Cocktail Shaker Sort, or maybe Gravity Sort?
Could we get some comparisons on MUCH larger sets? I feel like some only truly shine when the amount of data grows.
Like Bogo sort
Or std::sort
@@typhoonzebra there's a Bogosort video
it's hilarious
it's 40 minutes long, and 35 of it is literally waiting for Bogosort to actually finish randomizing
@@musicexams5258 Just came back from that. Glad to see they have recognised the ultimate sorting method.
HUGE UPSET!! LETS GO INSERTION SORT
Shell sort training arc went crazy though
Great video!
Other people: Watching Netflix Stranger Things 4
Me: Watching two robots sorting color balls
This is a blessing
Nobody:
Nosoul:
These videos lore if robots weren't shortsighted:
He is back
Honestly this editing was better imo
In the last shell sort step, is each ball guaranteed to be either in its correct position or next to it? Or can it be further away?
Not in the gap sequences used in the video, but for some gap sequences it's true. For example a gap sequence of 3-2-1 guarantees it. Other gap sequence guarantee larger bounds. I'll soon post more details on that.
If the second to last gap size is n (assuming the last gap size is 1) then I'm pretty sure each element is guaranteed to be n-1 positions away from it's final position at most. Assuming my math is good, I feel like you could improve the worst case speed of the algorithm pretty significantly by having it move on to the next element after n-1 comparisons since the nth comparison would be guaranteed to show the two elements don't need to swap. You might even be able to use a similar rule for every sub-sort after the first.
Yes a new video!
Never had I felt this tense between two robots in a sorting competition. Shell sort should work better in theory due to moving elements closer and closer, but the time it took moving and the lack of optimization made me nervous in this match.
The advantage of shell sort over insertion sort grows substantially as the size of the set rises.
Great sorting explanation as always! If you guys take requests, can you show the way a Circle Sort acts? Or a Comb Sort? Either one would be really fun to see.
I eventually want to see a large competition of all sorts. Not only to see all the different screens of each sort all together, but a "look how far we've come" from slower but vaguely effective sorts to...shell and beyond.
i love the classic solution of "lets add jet boosters!" when something isnt fast enough
I remember watching these in high school! I don’t know if you thought about visualizing quantum algorithms, and most quantum sorts don’t outperform classical sorts, but if you could figure out how to visualize Grover’s algorithm or Shor’s that’d be so cool!
Oh this is amaaaaziingg!
Finally another one
Now I want to see shell vs merge sort
I think the lag in comparisons per second has to do with the fact that insertion sort does most of its comparisons with one ball at a time, and so it only has to pick up and put down one ball at a time. Shell sort has more putting down and picking up of two
Id love to see how you tackle Sleep sort 😅
So good animation 👌 😍
I wish you would sometimes do a race with 100 items instead of just 10, to show the disparity in speed more obviously.
You should do a comparison on bigger lists. With 100+ elements shell sort will be significantly faster than simple insertion. Actually the biggest reason why Quick, Merge or Shell Sort are much faster is because they can easily switch elements that are far from each other. Comb sort was developed with this idea in mind. Comb sort is a simple bubble, that uses sublists with wide gaps.
However Insertion Sort works really well on small or almost sorted lists, where each element has to move just a few spaces. This is why hybrid sorts often use Insertion sort as a last step on almost sorted list, because it's the fastest way.
ua-cam.com/video/8MsTNqK3o_w/v-deo.html
i like the robots! they're so cute
Would be interesting to see binary insertion sort. Of course, the improvement would be very minor on such a small set, but it would still be interesting.