Welcome to the Login form tutorial. This tutorial will help you create your own HTML form, login form, or signup form so that you can use it in your own websites, mobile apps, and other software. Login form design – SignUp form design free
If you have a website for your shop or want to learn login form development on html and css. The login form is a great way of getting more visitors and giving them the option to not just browse your website but also make a purchase. One of the main tasks in making a login form is to make it eye-catching. This tutorial will show you how to create a login form from start to finish.
Login form design – SignUp form design free Tutorials HTML – CSS -JavaScript
For Fibonacci we already know the result of f(0),f(1). We can save these two values in a table and build up the results in the order f(2),f(3)….f(n).
When solving dynamic programming, you first need to work out the recursive equation in your mind or notebook. Then you can write the code recursively or iteratively if you want. Writing code recursively is very easy, just writing the equation as code will bring out the solution like magic.
To write iteratively, you have to think about the ordering of subproblems, which becomes a bit more difficult if the subproblem has multiple parameters. But we also need to know the iterative method because iterative method can often optimize the space. As in the above code, except for the first two values of our array, the rest are useless, so n
There is no need for size arrays.
There are some rules for attacking dynamic programming problems, if we learn to think according to those rules, we will understand which problem can be solved with dynamic programming and how to find the solution. Fibonacci is a very simple example but not a very good one because nothing is optimized here. In the next section we will look at an optimization problem that will further clarify our concept of DP.
Probabilistic Data Structures: Count-Mean Sketch
A few days ago I wrote an article about the Bloom filter. A count-mean sketch is a similar probabilistic data structure. They also work in much the same way, although the working patterns and usage are completely different. The count-mean sketch is an excellent example of how to handle large amounts of data with minimal resource consumption if the algorithm is known. Even if you don’t know how the Bloom filter works, you will understand this article.
Suppose you are given an array of strings. You need to tell how many times a string is in the array, i.e. find out the frequency of the strings.
An example is shown in the image above. There are 8 strings in the input array, the number of times which string is there is shown in the table.
This is a very simple problem, you can easily find the frequency using a simple hashmap. The space complexity of HashMap is O(n) and the average complexity of adding new values to HashMap or finding values is O(1).
The solution is pretty good, we don’t need extra space, we can get the frequency out very quickly, right? Now imagine you have a search engine like Google. You want to find out how often a word is searched for there. Whenever a user searches for a term, you can increase the frequency of that term in the hashmap as before. You can imagine your incoming data as a stream of data, one word stream at a time, that you process and store in a hashmap.
The problem is that about 1GB of data comes through your stream per day, about 30GB of data per month. If only 50% or 15 GB of data are unique among them, you will need a hashmap of 15 GB per month to calculate the frequency.
Handling such huge data is not very easy. You can’t put this data in a common database, you have to use some kind of distributed system. If you use cloud services then the bill will also come huge.
The linear space complex doesn’t look very good anymore. While scaling the system we often have to make some trade-offs. Maybe sometimes space can be saved in exchange for time, sometimes time can be saved in exchange for reliability. It is possible to solve this problem in sub-linear space using count-mean sketches if we are willing to sacrifice some accuracy.
In this case, the space will be very less but sometimes we will over-count the frequency. That is, maybe a word is searched 122312 times, but we might get 122318 times. In this type of scenario, sometimes the accuracy is a little more or less, but actually there is no such problem, it is not a critical system that requires exact numbers.
Count-Mean Sketch
A sketch is a type of data structure that stores a summary of the original data. Sometimes there is some inaccuracy in that summary but it is at a tolerable level. You can compare it with the picture sketch. Many times the artist makes a pencil sketch before the main picture size. There may not be many details but there is a lot of necessary information.
Login form design – SignUp form design free Tutorials HTML – CSS -JavaScript
Our sketch for this problem is a simple 2-D matrix of fixed size. It looks like this:
To solve this problem we need n hash functions, the number of rows in the sketch matrix will indicate the number of hash functions. In this case we have assumed n=3 as an example. Each hash function returns a number of fixed size, each between 0 and m-1. In our example m=6. So the size of our matrix is 3∗6
. We will now see how to calculate the frequency using this matrix.
Now when a word comes from the stream, we will hash that word 3 times using 3 functions. Consider the names of the 3 hash functions H1, H2 and H3.
Since we’re not writing actual hash functions right now, let’s make a chart of what we’d get if we hashed a word with an imaginary function:
This is an imaginary hash-chart. For example, hashing “Freddy” with H1 will return 3, hashing “Brian” with H2 will return 1. Since the size of the table is very small, the probability of collision is quite good. For example, if we hash “Brian” and “Alice” with H1, we get the same number 2
getting As we will see later this will cause some over-counts.
The first word in our stream is “Alice”. Hashing “Alice” gives H1(Alice)=2,H2(Alice)=1,H3(Alice)=4
. Then we add 1 to the cells (H1, 2), (H2, 1), (H3, 4) in the frequency table.
(Note, I’m updating the table here using the convenience hash-chart, in practice it’s not possible to save such a chart, so the hash has to be recalculated each time.)
The next word is “Dion”. Now update (H1, 5), (H2, 4), (H3, 0).
Updates for “Brian” will be (H1, 2), (H2, 1), (H3, 5). “Brian” occurs twice in a row, adding 2 at once:
Hope you understand how the table is updated. Every time we get a word we are hashing it 3 times and updating the frequency in the table accordingly. All that remains is “Freddy”, “Brian”, “Freddy”, “Dion”, updating these words in the same way will end up looking like this:
Now using this table we can find the frequency of any word. For example say “Dion”, we need to hash again 3 times and as before we get 3 cells (H1, 5), (H2, 4), (H3, 0).
For “Dion” we have incremented these 3 houses. As such, the frequency of “Dion” should be there for these 3 hours. But since hash collisions are possible, the same cell can be incremented by multiple words. So we will choose the minimum from these 3 cells, in this case the minimum is 2. That means the frequency of “Dion” is 2
Which is true indeed.
The problem will be when the collisions become too large. If a new word Mary arrives and the word updates cells (H1, 5), (H2, 3), (H3, 1), the table will look like this:
I intentionally left the “Dion” cells still highlighted. But now we get the frequency of “Dion” 3
which is wrong
As mentioned earlier the min-count sketch will over-count in the middle for hash collisions. It will perform very well in scenarios where few errors can be tolerated. No matter how large your dataset is, the time and space complexity remains constant. Accuracy in this case depends on how many hash functions you use (n) and the bucket number (m) of each hash function.
The bigger they are, the less collisions will occur. But remember, string hashing is a very expensive operation, so it is better not to increase the hash function too much and use a hash function that works very fast. In that case cryptographic hash functions such as SHA-256 will not work very well, an analysis on the speed of hash functions can be found here.
One thing to note, the count-mean sketch can only over-count, not under-count. So it is a kind of Bias that there is some technique to remove which is called Count-mean-min-sketch. In this case, after hashing, the middle number (mean) is taken out and subtracted from all cells.
You can see how we easily prepared a system for large amount of data with knowledge of data structure! Happy Coding!
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