Connor Mills

Connor Mills

1573010602

The 3 Algorithms Concepts Data Scientists Need to Know

Algorithms are an integral part of data science. While most of us data scientists don’t take a proper algorithms course while studying, they are important all the same.

Many companies ask data structures and algorithms as part of their interview process for hiring data scientists.

Now the question that many people ask here is what is the use of asking a data scientist such questions. The way I like to describe it is that a data structure question may be thought of as a coding aptitude test.

We all have given aptitude tests at various stages of our life, and while they are not a perfect proxy to judge someone, almost nothing ever really is. So, why not a standard algorithm test to judge people’s coding ability.

But let’s not kid ourselves, they will require the same zeal to crack as your Data Science interviews, and thus, you might want to give some time for the study of algorithms.

This post is about fast-tracking that study and panning some essential algorithms concepts for the data scientists in an easy to understand way.

1. Recursion/Memoization

Recursion is where a function being defined is applied within its own definition. Put simply; recursion is when a function calls itself. Google does something pretty interesting when you search for recursion there.
3 Programming Concepts for Data Scientists

Hope you get the joke. While recursion may seem a little bit daunting to someone just starting, it is pretty simple to understand. And it is a beautiful concept once you know it.

The best example I find for explaining recursion is to calculate the factorial of a number.

def factorial(n):
    if n==0:
        return 1
    return n*factorial(n-1)

We can see how factorial is a recursive function quite easily.

Factorial(n) = n*Factorial(n-1)

So how does it translates to programming?

A function for a recursive call generally consists of two things:

  • A base case — The case where the recursion ends.
  • A recursive formulation- a formulaic way to move towards the base case.

A lot of problems you end up solving are recursive. It applies to data science, as well.

For example, A decision tree is just a binary tree, and tree algorithms are generally recursive. Or, we do use sort in a lot of times. The algorithm responsible for that is called mergesort, which in itself is a recursive algorithm. Another one is binary search, which includes finding an element in an array.

Now we have got a basic hang of recursion, let us try to find the nth Fibonacci Number. Fibonacci series is a series of numbers in which each number ( Fibonacci number ) is the sum of the two preceding numbers. The simplest is the series 1, 1, 2, 3, 5, 8, etc. The answer is:

def fib(n):
    if n<=1:
        return 1
    return fib(n-1) + fib(n-2)

But do you spot the problem here?

If you try to calculate fib(n=7) it runs fib(5) twice, fib(4) thrice, fib(3) five times. As n becomes larger, a lot of calls are made for the same number, and our recursive function calculates it again and again.
3 Programming Concepts for Data Scientists

Can we do better? Yes, we can. We can change our implementation a little bit an add a dictionary to add some storage to our method. Now, this memo dictionary gets updated any time a number has been calculated. If that number appears again, we don’t calculate it again but give results from the memo dictionary. This addition of storage is called Memoization.

memo = {}
def fib_memo(n):
    if n in memo:
        return memo[n]
    if n<=1:
        memo[n]=1
        return 1
    memo[n] = fib_memo(n-1) + fib_memo(n-2)
    return memo[n]

Usually, I like to write the recursive function first, and if it is making a lot of calls to the same parameters again and again, I add a dictionary to memorize solutions.

How much does it help?
3 Programming Concepts for Data Scientists

This is the run time comparison for different values of n. We can see the runtime for Fibonacci without Memoization increases exponentially, while for the memoized function, the time is linear.

2. Dynamic programming

Recursion is essentially a top-down approach. As in when calculating Fibonacci number n we start from n and then do recursive calls for n-2 and n-1 and so on.

In Dynamic programming, we take a bottom-up approach. It is essentially a way to write recursion iteratively. We start by calculating fib(0) and fib(1) and then use previous results to generate new results.

def fib_dp(n):
    dp_sols = {0:1,1:1}
    for i in range(2,n+1):
        dp_sols[i] = dp_sols[i-1] + dp_sols[i-2] 
    return dp_sols[n]

3 Programming Concepts for Data Scientists

Above is the comparison of runtimes for DP vs. Memoization. We can see that they are both linear, but DP still is a little bit faster.

Why? Because Dynamic Programming made only one call exactly to each subproblem in this case.

There is an excellent story on how Bellman who developed Dynamic Programming framed the term_:_

Where did the name, dynamic programming, come from? The 1950s were not good years for mathematical research. We had a very interesting gentleman in Washington named Wilson. He was Secretary of Defense, and he actually had a pathological fear and hatred of the word research. What title, what name, could I choose? In the first place, I was interested in planning, in decision making, in thinking. But planning, is not a good word for various reasons. I decided therefore to use the word “programming”. I wanted to get across the idea that this was dynamic, this was multistage, this was time-varying. I thought, let’s kill two birds with one stone. Thus, I thought dynamic programming was a good name. It was something not even a Congressman could object to. So I used it as an umbrella for my activities.

3. Binary Search

Let us say we have a sorted array of numbers, and we want to find out a number from this array. We can go the linear route that checks every number one by one and stops if it finds the number. The problem is that it takes too long if the array contains millions of elements. Here we can use a Binary search.
3 Programming Concepts for Data Scientists

# Returns index of target in nums array if present, else -1 
def binary_search(nums, left, right, target):   
    # Base case 
    if right >= left: 
        mid = int((left + right)/2)
        # If target is present at the mid, return
        if nums[mid] == target: 
            return mid 
        # Target is smaller than mid search the elements in left
        elif nums[mid] > target: 
            return binary_search(nums, left, mid-1, target) 
        # Target is larger than mid, search the elements in right
        else: 
            return binary_search(nums, mid+1, right, target) 
    else: 
        # Target is not in nums 
        return -1nums = [1,2,3,4,5,6,7,8,9]
print(binary_search(nums, 0, len(nums)-1,7))

This is an advanced case of a recursion based algorithm where we make use of the fact that the array is sorted. Here we recursively look at the middle element and see if we want to search in the left or right of the middle element. This makes our searching space go down by a factor of 2 every step.

And thus the run time of this algorithm is O(logn) as opposed to O(n) for linear search.

How much does that matter? Below is a comparison in run times. We can see that the Binary search is pretty fast compared to Linear search.
3 Programming Concepts for Data Scientists

Conclusion

In this post, I talked about some of the most exciting algorithms that form the basis for programming.

These algorithms are behind some of the most asked questions in Data Science interviews, and a good understanding of these might help you land your dream job.

And while you can go a fair bit in data science without learning them, you can learn them just for a little bit of fun and maybe to improve your programming skills.

#data-science #machine-learning #deep-learning

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The 3 Algorithms Concepts Data Scientists Need to Know
Veronica  Roob

Veronica Roob

1653475560

A Pure PHP Implementation Of The MessagePack Serialization Format

msgpack.php

A pure PHP implementation of the MessagePack serialization format.

Features

Installation

The recommended way to install the library is through Composer:

composer require rybakit/msgpack

Usage

Packing

To pack values you can either use an instance of a Packer:

$packer = new Packer();
$packed = $packer->pack($value);

or call a static method on the MessagePack class:

$packed = MessagePack::pack($value);

In the examples above, the method pack automatically packs a value depending on its type. However, not all PHP types can be uniquely translated to MessagePack types. For example, the MessagePack format defines map and array types, which are represented by a single array type in PHP. By default, the packer will pack a PHP array as a MessagePack array if it has sequential numeric keys, starting from 0 and as a MessagePack map otherwise:

$mpArr1 = $packer->pack([1, 2]);               // MP array [1, 2]
$mpArr2 = $packer->pack([0 => 1, 1 => 2]);     // MP array [1, 2]
$mpMap1 = $packer->pack([0 => 1, 2 => 3]);     // MP map {0: 1, 2: 3}
$mpMap2 = $packer->pack([1 => 2, 2 => 3]);     // MP map {1: 2, 2: 3}
$mpMap3 = $packer->pack(['a' => 1, 'b' => 2]); // MP map {a: 1, b: 2}

However, sometimes you need to pack a sequential array as a MessagePack map. To do this, use the packMap method:

$mpMap = $packer->packMap([1, 2]); // {0: 1, 1: 2}

Here is a list of type-specific packing methods:

$packer->packNil();           // MP nil
$packer->packBool(true);      // MP bool
$packer->packInt(42);         // MP int
$packer->packFloat(M_PI);     // MP float (32 or 64)
$packer->packFloat32(M_PI);   // MP float 32
$packer->packFloat64(M_PI);   // MP float 64
$packer->packStr('foo');      // MP str
$packer->packBin("\x80");     // MP bin
$packer->packArray([1, 2]);   // MP array
$packer->packMap(['a' => 1]); // MP map
$packer->packExt(1, "\xaa");  // MP ext

Check the "Custom types" section below on how to pack custom types.

Packing options

The Packer object supports a number of bitmask-based options for fine-tuning the packing process (defaults are in bold):

NameDescription
FORCE_STRForces PHP strings to be packed as MessagePack UTF-8 strings
FORCE_BINForces PHP strings to be packed as MessagePack binary data
DETECT_STR_BINDetects MessagePack str/bin type automatically
  
FORCE_ARRForces PHP arrays to be packed as MessagePack arrays
FORCE_MAPForces PHP arrays to be packed as MessagePack maps
DETECT_ARR_MAPDetects MessagePack array/map type automatically
  
FORCE_FLOAT32Forces PHP floats to be packed as 32-bits MessagePack floats
FORCE_FLOAT64Forces PHP floats to be packed as 64-bits MessagePack floats

The type detection mode (DETECT_STR_BIN/DETECT_ARR_MAP) adds some overhead which can be noticed when you pack large (16- and 32-bit) arrays or strings. However, if you know the value type in advance (for example, you only work with UTF-8 strings or/and associative arrays), you can eliminate this overhead by forcing the packer to use the appropriate type, which will save it from running the auto-detection routine. Another option is to explicitly specify the value type. The library provides 2 auxiliary classes for this, Map and Bin. Check the "Custom types" section below for details.

Examples:

// detect str/bin type and pack PHP 64-bit floats (doubles) to MP 32-bit floats
$packer = new Packer(PackOptions::DETECT_STR_BIN | PackOptions::FORCE_FLOAT32);

// these will throw MessagePack\Exception\InvalidOptionException
$packer = new Packer(PackOptions::FORCE_STR | PackOptions::FORCE_BIN);
$packer = new Packer(PackOptions::FORCE_FLOAT32 | PackOptions::FORCE_FLOAT64);

Unpacking

To unpack data you can either use an instance of a BufferUnpacker:

$unpacker = new BufferUnpacker();

$unpacker->reset($packed);
$value = $unpacker->unpack();

or call a static method on the MessagePack class:

$value = MessagePack::unpack($packed);

If the packed data is received in chunks (e.g. when reading from a stream), use the tryUnpack method, which attempts to unpack data and returns an array of unpacked messages (if any) instead of throwing an InsufficientDataException:

while ($chunk = ...) {
    $unpacker->append($chunk);
    if ($messages = $unpacker->tryUnpack()) {
        return $messages;
    }
}

If you want to unpack from a specific position in a buffer, use seek:

$unpacker->seek(42); // set position equal to 42 bytes
$unpacker->seek(-8); // set position to 8 bytes before the end of the buffer

To skip bytes from the current position, use skip:

$unpacker->skip(10); // set position to 10 bytes ahead of the current position

To get the number of remaining (unread) bytes in the buffer:

$unreadBytesCount = $unpacker->getRemainingCount();

To check whether the buffer has unread data:

$hasUnreadBytes = $unpacker->hasRemaining();

If needed, you can remove already read data from the buffer by calling:

$releasedBytesCount = $unpacker->release();

With the read method you can read raw (packed) data:

$packedData = $unpacker->read(2); // read 2 bytes

Besides the above methods BufferUnpacker provides type-specific unpacking methods, namely:

$unpacker->unpackNil();   // PHP null
$unpacker->unpackBool();  // PHP bool
$unpacker->unpackInt();   // PHP int
$unpacker->unpackFloat(); // PHP float
$unpacker->unpackStr();   // PHP UTF-8 string
$unpacker->unpackBin();   // PHP binary string
$unpacker->unpackArray(); // PHP sequential array
$unpacker->unpackMap();   // PHP associative array
$unpacker->unpackExt();   // PHP MessagePack\Type\Ext object

Unpacking options

The BufferUnpacker object supports a number of bitmask-based options for fine-tuning the unpacking process (defaults are in bold):

NameDescription
BIGINT_AS_STRConverts overflowed integers to strings [1]
BIGINT_AS_GMPConverts overflowed integers to GMP objects [2]
BIGINT_AS_DECConverts overflowed integers to Decimal\Decimal objects [3]

1. The binary MessagePack format has unsigned 64-bit as its largest integer data type, but PHP does not support such integers, which means that an overflow can occur during unpacking.

2. Make sure the GMP extension is enabled.

3. Make sure the Decimal extension is enabled.

Examples:

$packedUint64 = "\xcf"."\xff\xff\xff\xff"."\xff\xff\xff\xff";

$unpacker = new BufferUnpacker($packedUint64);
var_dump($unpacker->unpack()); // string(20) "18446744073709551615"

$unpacker = new BufferUnpacker($packedUint64, UnpackOptions::BIGINT_AS_GMP);
var_dump($unpacker->unpack()); // object(GMP) {...}

$unpacker = new BufferUnpacker($packedUint64, UnpackOptions::BIGINT_AS_DEC);
var_dump($unpacker->unpack()); // object(Decimal\Decimal) {...}

Custom types

In addition to the basic types, the library provides functionality to serialize and deserialize arbitrary types. This can be done in several ways, depending on your use case. Let's take a look at them.

Type objects

If you need to serialize an instance of one of your classes into one of the basic MessagePack types, the best way to do this is to implement the CanBePacked interface in the class. A good example of such a class is the Map type class that comes with the library. This type is useful when you want to explicitly specify that a given PHP array should be packed as a MessagePack map without triggering an automatic type detection routine:

$packer = new Packer();

$packedMap = $packer->pack(new Map([1, 2, 3]));
$packedArray = $packer->pack([1, 2, 3]);

More type examples can be found in the src/Type directory.

Type transformers

As with type objects, type transformers are only responsible for serializing values. They should be used when you need to serialize a value that does not implement the CanBePacked interface. Examples of such values could be instances of built-in or third-party classes that you don't own, or non-objects such as resources.

A transformer class must implement the CanPack interface. To use a transformer, it must first be registered in the packer. Here is an example of how to serialize PHP streams into the MessagePack bin format type using one of the supplied transformers, StreamTransformer:

$packer = new Packer(null, [new StreamTransformer()]);

$packedBin = $packer->pack(fopen('/path/to/file', 'r+'));

More type transformer examples can be found in the src/TypeTransformer directory.

Extensions

In contrast to the cases described above, extensions are intended to handle extension types and are responsible for both serialization and deserialization of values (types).

An extension class must implement the Extension interface. To use an extension, it must first be registered in the packer and the unpacker.

The MessagePack specification divides extension types into two groups: predefined and application-specific. Currently, there is only one predefined type in the specification, Timestamp.

Timestamp

The Timestamp extension type is a predefined type. Support for this type in the library is done through the TimestampExtension class. This class is responsible for handling Timestamp objects, which represent the number of seconds and optional adjustment in nanoseconds:

$timestampExtension = new TimestampExtension();

$packer = new Packer();
$packer = $packer->extendWith($timestampExtension);

$unpacker = new BufferUnpacker();
$unpacker = $unpacker->extendWith($timestampExtension);

$packedTimestamp = $packer->pack(Timestamp::now());
$timestamp = $unpacker->reset($packedTimestamp)->unpack();

$seconds = $timestamp->getSeconds();
$nanoseconds = $timestamp->getNanoseconds();

When using the MessagePack class, the Timestamp extension is already registered:

$packedTimestamp = MessagePack::pack(Timestamp::now());
$timestamp = MessagePack::unpack($packedTimestamp);

Application-specific extensions

In addition, the format can be extended with your own types. For example, to make the built-in PHP DateTime objects first-class citizens in your code, you can create a corresponding extension, as shown in the example. Please note, that custom extensions have to be registered with a unique extension ID (an integer from 0 to 127).

More extension examples can be found in the examples/MessagePack directory.

To learn more about how extension types can be useful, check out this article.

Exceptions

If an error occurs during packing/unpacking, a PackingFailedException or an UnpackingFailedException will be thrown, respectively. In addition, an InsufficientDataException can be thrown during unpacking.

An InvalidOptionException will be thrown in case an invalid option (or a combination of mutually exclusive options) is used.

Tests

Run tests as follows:

vendor/bin/phpunit

Also, if you already have Docker installed, you can run the tests in a docker container. First, create a container:

./dockerfile.sh | docker build -t msgpack -

The command above will create a container named msgpack with PHP 8.1 runtime. You may change the default runtime by defining the PHP_IMAGE environment variable:

PHP_IMAGE='php:8.0-cli' ./dockerfile.sh | docker build -t msgpack -

See a list of various images here.

Then run the unit tests:

docker run --rm -v $PWD:/msgpack -w /msgpack msgpack

Fuzzing

To ensure that the unpacking works correctly with malformed/semi-malformed data, you can use a testing technique called Fuzzing. The library ships with a help file (target) for PHP-Fuzzer and can be used as follows:

php-fuzzer fuzz tests/fuzz_buffer_unpacker.php

Performance

To check performance, run:

php -n -dzend_extension=opcache.so \
-dpcre.jit=1 -dopcache.enable=1 -dopcache.enable_cli=1 \
tests/bench.php

Example output

Filter: MessagePack\Tests\Perf\Filter\ListFilter
Rounds: 3
Iterations: 100000

=============================================
Test/Target            Packer  BufferUnpacker
---------------------------------------------
nil .................. 0.0030 ........ 0.0139
false ................ 0.0037 ........ 0.0144
true ................. 0.0040 ........ 0.0137
7-bit uint #1 ........ 0.0052 ........ 0.0120
7-bit uint #2 ........ 0.0059 ........ 0.0114
7-bit uint #3 ........ 0.0061 ........ 0.0119
5-bit sint #1 ........ 0.0067 ........ 0.0126
5-bit sint #2 ........ 0.0064 ........ 0.0132
5-bit sint #3 ........ 0.0066 ........ 0.0135
8-bit uint #1 ........ 0.0078 ........ 0.0200
8-bit uint #2 ........ 0.0077 ........ 0.0212
8-bit uint #3 ........ 0.0086 ........ 0.0203
16-bit uint #1 ....... 0.0111 ........ 0.0271
16-bit uint #2 ....... 0.0115 ........ 0.0260
16-bit uint #3 ....... 0.0103 ........ 0.0273
32-bit uint #1 ....... 0.0116 ........ 0.0326
32-bit uint #2 ....... 0.0118 ........ 0.0332
32-bit uint #3 ....... 0.0127 ........ 0.0325
64-bit uint #1 ....... 0.0140 ........ 0.0277
64-bit uint #2 ....... 0.0134 ........ 0.0294
64-bit uint #3 ....... 0.0134 ........ 0.0281
8-bit int #1 ......... 0.0086 ........ 0.0241
8-bit int #2 ......... 0.0089 ........ 0.0225
8-bit int #3 ......... 0.0085 ........ 0.0229
16-bit int #1 ........ 0.0118 ........ 0.0280
16-bit int #2 ........ 0.0121 ........ 0.0270
16-bit int #3 ........ 0.0109 ........ 0.0274
32-bit int #1 ........ 0.0128 ........ 0.0346
32-bit int #2 ........ 0.0118 ........ 0.0339
32-bit int #3 ........ 0.0135 ........ 0.0368
64-bit int #1 ........ 0.0138 ........ 0.0276
64-bit int #2 ........ 0.0132 ........ 0.0286
64-bit int #3 ........ 0.0137 ........ 0.0274
64-bit int #4 ........ 0.0180 ........ 0.0285
64-bit float #1 ...... 0.0134 ........ 0.0284
64-bit float #2 ...... 0.0125 ........ 0.0275
64-bit float #3 ...... 0.0126 ........ 0.0283
fix string #1 ........ 0.0035 ........ 0.0133
fix string #2 ........ 0.0094 ........ 0.0216
fix string #3 ........ 0.0094 ........ 0.0222
fix string #4 ........ 0.0091 ........ 0.0241
8-bit string #1 ...... 0.0122 ........ 0.0301
8-bit string #2 ...... 0.0118 ........ 0.0304
8-bit string #3 ...... 0.0119 ........ 0.0315
16-bit string #1 ..... 0.0150 ........ 0.0388
16-bit string #2 ..... 0.1545 ........ 0.1665
32-bit string ........ 0.1570 ........ 0.1756
wide char string #1 .. 0.0091 ........ 0.0236
wide char string #2 .. 0.0122 ........ 0.0313
8-bit binary #1 ...... 0.0100 ........ 0.0302
8-bit binary #2 ...... 0.0123 ........ 0.0324
8-bit binary #3 ...... 0.0126 ........ 0.0327
16-bit binary ........ 0.0168 ........ 0.0372
32-bit binary ........ 0.1588 ........ 0.1754
fix array #1 ......... 0.0042 ........ 0.0131
fix array #2 ......... 0.0294 ........ 0.0367
fix array #3 ......... 0.0412 ........ 0.0472
16-bit array #1 ...... 0.1378 ........ 0.1596
16-bit array #2 ........... S ............. S
32-bit array .............. S ............. S
complex array ........ 0.1865 ........ 0.2283
fix map #1 ........... 0.0725 ........ 0.1048
fix map #2 ........... 0.0319 ........ 0.0405
fix map #3 ........... 0.0356 ........ 0.0665
fix map #4 ........... 0.0465 ........ 0.0497
16-bit map #1 ........ 0.2540 ........ 0.3028
16-bit map #2 ............. S ............. S
32-bit map ................ S ............. S
complex map .......... 0.2372 ........ 0.2710
fixext 1 ............. 0.0283 ........ 0.0358
fixext 2 ............. 0.0291 ........ 0.0371
fixext 4 ............. 0.0302 ........ 0.0355
fixext 8 ............. 0.0288 ........ 0.0384
fixext 16 ............ 0.0293 ........ 0.0359
8-bit ext ............ 0.0302 ........ 0.0439
16-bit ext ........... 0.0334 ........ 0.0499
32-bit ext ........... 0.1845 ........ 0.1888
32-bit timestamp #1 .. 0.0337 ........ 0.0547
32-bit timestamp #2 .. 0.0335 ........ 0.0560
64-bit timestamp #1 .. 0.0371 ........ 0.0575
64-bit timestamp #2 .. 0.0374 ........ 0.0542
64-bit timestamp #3 .. 0.0356 ........ 0.0533
96-bit timestamp #1 .. 0.0362 ........ 0.0699
96-bit timestamp #2 .. 0.0381 ........ 0.0701
96-bit timestamp #3 .. 0.0367 ........ 0.0687
=============================================
Total                  2.7618          4.0820
Skipped                     4               4
Failed                      0               0
Ignored                     0               0

With JIT:

php -n -dzend_extension=opcache.so \
-dpcre.jit=1 -dopcache.jit_buffer_size=64M -dopcache.jit=tracing -dopcache.enable=1 -dopcache.enable_cli=1 \
tests/bench.php

Example output

Filter: MessagePack\Tests\Perf\Filter\ListFilter
Rounds: 3
Iterations: 100000

=============================================
Test/Target            Packer  BufferUnpacker
---------------------------------------------
nil .................. 0.0005 ........ 0.0054
false ................ 0.0004 ........ 0.0059
true ................. 0.0004 ........ 0.0059
7-bit uint #1 ........ 0.0010 ........ 0.0047
7-bit uint #2 ........ 0.0010 ........ 0.0046
7-bit uint #3 ........ 0.0010 ........ 0.0046
5-bit sint #1 ........ 0.0025 ........ 0.0046
5-bit sint #2 ........ 0.0023 ........ 0.0046
5-bit sint #3 ........ 0.0024 ........ 0.0045
8-bit uint #1 ........ 0.0043 ........ 0.0081
8-bit uint #2 ........ 0.0043 ........ 0.0079
8-bit uint #3 ........ 0.0041 ........ 0.0080
16-bit uint #1 ....... 0.0064 ........ 0.0095
16-bit uint #2 ....... 0.0064 ........ 0.0091
16-bit uint #3 ....... 0.0064 ........ 0.0094
32-bit uint #1 ....... 0.0085 ........ 0.0114
32-bit uint #2 ....... 0.0077 ........ 0.0122
32-bit uint #3 ....... 0.0077 ........ 0.0120
64-bit uint #1 ....... 0.0085 ........ 0.0159
64-bit uint #2 ....... 0.0086 ........ 0.0157
64-bit uint #3 ....... 0.0086 ........ 0.0158
8-bit int #1 ......... 0.0042 ........ 0.0080
8-bit int #2 ......... 0.0042 ........ 0.0080
8-bit int #3 ......... 0.0042 ........ 0.0081
16-bit int #1 ........ 0.0065 ........ 0.0095
16-bit int #2 ........ 0.0065 ........ 0.0090
16-bit int #3 ........ 0.0056 ........ 0.0085
32-bit int #1 ........ 0.0067 ........ 0.0107
32-bit int #2 ........ 0.0066 ........ 0.0106
32-bit int #3 ........ 0.0063 ........ 0.0104
64-bit int #1 ........ 0.0072 ........ 0.0162
64-bit int #2 ........ 0.0073 ........ 0.0174
64-bit int #3 ........ 0.0072 ........ 0.0164
64-bit int #4 ........ 0.0077 ........ 0.0161
64-bit float #1 ...... 0.0053 ........ 0.0135
64-bit float #2 ...... 0.0053 ........ 0.0135
64-bit float #3 ...... 0.0052 ........ 0.0135
fix string #1 ....... -0.0002 ........ 0.0044
fix string #2 ........ 0.0035 ........ 0.0067
fix string #3 ........ 0.0035 ........ 0.0077
fix string #4 ........ 0.0033 ........ 0.0078
8-bit string #1 ...... 0.0059 ........ 0.0110
8-bit string #2 ...... 0.0063 ........ 0.0121
8-bit string #3 ...... 0.0064 ........ 0.0124
16-bit string #1 ..... 0.0099 ........ 0.0146
16-bit string #2 ..... 0.1522 ........ 0.1474
32-bit string ........ 0.1511 ........ 0.1483
wide char string #1 .. 0.0039 ........ 0.0084
wide char string #2 .. 0.0073 ........ 0.0123
8-bit binary #1 ...... 0.0040 ........ 0.0112
8-bit binary #2 ...... 0.0075 ........ 0.0123
8-bit binary #3 ...... 0.0077 ........ 0.0129
16-bit binary ........ 0.0096 ........ 0.0145
32-bit binary ........ 0.1535 ........ 0.1479
fix array #1 ......... 0.0008 ........ 0.0061
fix array #2 ......... 0.0121 ........ 0.0165
fix array #3 ......... 0.0193 ........ 0.0222
16-bit array #1 ...... 0.0607 ........ 0.0479
16-bit array #2 ........... S ............. S
32-bit array .............. S ............. S
complex array ........ 0.0749 ........ 0.0824
fix map #1 ........... 0.0329 ........ 0.0431
fix map #2 ........... 0.0161 ........ 0.0189
fix map #3 ........... 0.0205 ........ 0.0262
fix map #4 ........... 0.0252 ........ 0.0205
16-bit map #1 ........ 0.1016 ........ 0.0927
16-bit map #2 ............. S ............. S
32-bit map ................ S ............. S
complex map .......... 0.1096 ........ 0.1030
fixext 1 ............. 0.0157 ........ 0.0161
fixext 2 ............. 0.0175 ........ 0.0183
fixext 4 ............. 0.0156 ........ 0.0185
fixext 8 ............. 0.0163 ........ 0.0184
fixext 16 ............ 0.0164 ........ 0.0182
8-bit ext ............ 0.0158 ........ 0.0207
16-bit ext ........... 0.0203 ........ 0.0219
32-bit ext ........... 0.1614 ........ 0.1539
32-bit timestamp #1 .. 0.0195 ........ 0.0249
32-bit timestamp #2 .. 0.0188 ........ 0.0260
64-bit timestamp #1 .. 0.0207 ........ 0.0281
64-bit timestamp #2 .. 0.0212 ........ 0.0291
64-bit timestamp #3 .. 0.0207 ........ 0.0295
96-bit timestamp #1 .. 0.0222 ........ 0.0358
96-bit timestamp #2 .. 0.0228 ........ 0.0353
96-bit timestamp #3 .. 0.0210 ........ 0.0319
=============================================
Total                  1.6432          1.9674
Skipped                     4               4
Failed                      0               0
Ignored                     0               0

You may change default benchmark settings by defining the following environment variables:

NameDefault
MP_BENCH_TARGETSpure_p,pure_u, see a list of available targets
MP_BENCH_ITERATIONS100_000
MP_BENCH_DURATIONnot set
MP_BENCH_ROUNDS3
MP_BENCH_TESTS-@slow, see a list of available tests

For example:

export MP_BENCH_TARGETS=pure_p
export MP_BENCH_ITERATIONS=1000000
export MP_BENCH_ROUNDS=5
# a comma separated list of test names
export MP_BENCH_TESTS='complex array, complex map'
# or a group name
# export MP_BENCH_TESTS='-@slow' // @pecl_comp
# or a regexp
# export MP_BENCH_TESTS='/complex (array|map)/'

Another example, benchmarking both the library and the PECL extension:

MP_BENCH_TARGETS=pure_p,pure_u,pecl_p,pecl_u \
php -n -dextension=msgpack.so -dzend_extension=opcache.so \
-dpcre.jit=1 -dopcache.enable=1 -dopcache.enable_cli=1 \
tests/bench.php

Example output

Filter: MessagePack\Tests\Perf\Filter\ListFilter
Rounds: 3
Iterations: 100000

===========================================================================
Test/Target            Packer  BufferUnpacker  msgpack_pack  msgpack_unpack
---------------------------------------------------------------------------
nil .................. 0.0031 ........ 0.0141 ...... 0.0055 ........ 0.0064
false ................ 0.0039 ........ 0.0154 ...... 0.0056 ........ 0.0053
true ................. 0.0038 ........ 0.0139 ...... 0.0056 ........ 0.0044
7-bit uint #1 ........ 0.0061 ........ 0.0110 ...... 0.0059 ........ 0.0046
7-bit uint #2 ........ 0.0065 ........ 0.0119 ...... 0.0042 ........ 0.0029
7-bit uint #3 ........ 0.0054 ........ 0.0117 ...... 0.0045 ........ 0.0025
5-bit sint #1 ........ 0.0047 ........ 0.0103 ...... 0.0038 ........ 0.0022
5-bit sint #2 ........ 0.0048 ........ 0.0117 ...... 0.0038 ........ 0.0022
5-bit sint #3 ........ 0.0046 ........ 0.0102 ...... 0.0038 ........ 0.0023
8-bit uint #1 ........ 0.0063 ........ 0.0174 ...... 0.0039 ........ 0.0031
8-bit uint #2 ........ 0.0063 ........ 0.0167 ...... 0.0040 ........ 0.0029
8-bit uint #3 ........ 0.0063 ........ 0.0168 ...... 0.0039 ........ 0.0030
16-bit uint #1 ....... 0.0092 ........ 0.0222 ...... 0.0049 ........ 0.0030
16-bit uint #2 ....... 0.0096 ........ 0.0227 ...... 0.0042 ........ 0.0046
16-bit uint #3 ....... 0.0123 ........ 0.0274 ...... 0.0059 ........ 0.0051
32-bit uint #1 ....... 0.0136 ........ 0.0331 ...... 0.0060 ........ 0.0048
32-bit uint #2 ....... 0.0130 ........ 0.0336 ...... 0.0070 ........ 0.0048
32-bit uint #3 ....... 0.0127 ........ 0.0329 ...... 0.0051 ........ 0.0048
64-bit uint #1 ....... 0.0126 ........ 0.0268 ...... 0.0055 ........ 0.0049
64-bit uint #2 ....... 0.0135 ........ 0.0281 ...... 0.0052 ........ 0.0046
64-bit uint #3 ....... 0.0131 ........ 0.0274 ...... 0.0069 ........ 0.0044
8-bit int #1 ......... 0.0077 ........ 0.0236 ...... 0.0058 ........ 0.0044
8-bit int #2 ......... 0.0087 ........ 0.0244 ...... 0.0058 ........ 0.0048
8-bit int #3 ......... 0.0084 ........ 0.0241 ...... 0.0055 ........ 0.0049
16-bit int #1 ........ 0.0112 ........ 0.0271 ...... 0.0048 ........ 0.0045
16-bit int #2 ........ 0.0124 ........ 0.0292 ...... 0.0057 ........ 0.0049
16-bit int #3 ........ 0.0118 ........ 0.0270 ...... 0.0058 ........ 0.0050
32-bit int #1 ........ 0.0137 ........ 0.0366 ...... 0.0058 ........ 0.0051
32-bit int #2 ........ 0.0133 ........ 0.0366 ...... 0.0056 ........ 0.0049
32-bit int #3 ........ 0.0129 ........ 0.0350 ...... 0.0052 ........ 0.0048
64-bit int #1 ........ 0.0145 ........ 0.0254 ...... 0.0034 ........ 0.0025
64-bit int #2 ........ 0.0097 ........ 0.0214 ...... 0.0034 ........ 0.0025
64-bit int #3 ........ 0.0096 ........ 0.0287 ...... 0.0059 ........ 0.0050
64-bit int #4 ........ 0.0143 ........ 0.0277 ...... 0.0059 ........ 0.0046
64-bit float #1 ...... 0.0134 ........ 0.0281 ...... 0.0057 ........ 0.0052
64-bit float #2 ...... 0.0141 ........ 0.0281 ...... 0.0057 ........ 0.0050
64-bit float #3 ...... 0.0144 ........ 0.0282 ...... 0.0057 ........ 0.0050
fix string #1 ........ 0.0036 ........ 0.0143 ...... 0.0066 ........ 0.0053
fix string #2 ........ 0.0107 ........ 0.0222 ...... 0.0065 ........ 0.0068
fix string #3 ........ 0.0116 ........ 0.0245 ...... 0.0063 ........ 0.0069
fix string #4 ........ 0.0105 ........ 0.0253 ...... 0.0083 ........ 0.0077
8-bit string #1 ...... 0.0126 ........ 0.0318 ...... 0.0075 ........ 0.0088
8-bit string #2 ...... 0.0121 ........ 0.0295 ...... 0.0076 ........ 0.0086
8-bit string #3 ...... 0.0125 ........ 0.0293 ...... 0.0130 ........ 0.0093
16-bit string #1 ..... 0.0159 ........ 0.0368 ...... 0.0117 ........ 0.0086
16-bit string #2 ..... 0.1547 ........ 0.1686 ...... 0.1516 ........ 0.1373
32-bit string ........ 0.1558 ........ 0.1729 ...... 0.1511 ........ 0.1396
wide char string #1 .. 0.0098 ........ 0.0237 ...... 0.0066 ........ 0.0065
wide char string #2 .. 0.0128 ........ 0.0291 ...... 0.0061 ........ 0.0082
8-bit binary #1 ........... I ............. I ........... F ............. I
8-bit binary #2 ........... I ............. I ........... F ............. I
8-bit binary #3 ........... I ............. I ........... F ............. I
16-bit binary ............. I ............. I ........... F ............. I
32-bit binary ............. I ............. I ........... F ............. I
fix array #1 ......... 0.0040 ........ 0.0129 ...... 0.0120 ........ 0.0058
fix array #2 ......... 0.0279 ........ 0.0390 ...... 0.0143 ........ 0.0165
fix array #3 ......... 0.0415 ........ 0.0463 ...... 0.0162 ........ 0.0187
16-bit array #1 ...... 0.1349 ........ 0.1628 ...... 0.0334 ........ 0.0341
16-bit array #2 ........... S ............. S ........... S ............. S
32-bit array .............. S ............. S ........... S ............. S
complex array ............. I ............. I ........... F ............. F
fix map #1 ................ I ............. I ........... F ............. I
fix map #2 ........... 0.0345 ........ 0.0391 ...... 0.0143 ........ 0.0168
fix map #3 ................ I ............. I ........... F ............. I
fix map #4 ........... 0.0459 ........ 0.0473 ...... 0.0151 ........ 0.0163
16-bit map #1 ........ 0.2518 ........ 0.2962 ...... 0.0400 ........ 0.0490
16-bit map #2 ............. S ............. S ........... S ............. S
32-bit map ................ S ............. S ........... S ............. S
complex map .......... 0.2380 ........ 0.2682 ...... 0.0545 ........ 0.0579
fixext 1 .................. I ............. I ........... F ............. F
fixext 2 .................. I ............. I ........... F ............. F
fixext 4 .................. I ............. I ........... F ............. F
fixext 8 .................. I ............. I ........... F ............. F
fixext 16 ................. I ............. I ........... F ............. F
8-bit ext ................. I ............. I ........... F ............. F
16-bit ext ................ I ............. I ........... F ............. F
32-bit ext ................ I ............. I ........... F ............. F
32-bit timestamp #1 ....... I ............. I ........... F ............. F
32-bit timestamp #2 ....... I ............. I ........... F ............. F
64-bit timestamp #1 ....... I ............. I ........... F ............. F
64-bit timestamp #2 ....... I ............. I ........... F ............. F
64-bit timestamp #3 ....... I ............. I ........... F ............. F
96-bit timestamp #1 ....... I ............. I ........... F ............. F
96-bit timestamp #2 ....... I ............. I ........... F ............. F
96-bit timestamp #3 ....... I ............. I ........... F ............. F
===========================================================================
Total                  1.5625          2.3866        0.7735          0.7243
Skipped                     4               4             4               4
Failed                      0               0            24              17
Ignored                    24              24             0               7

With JIT:

MP_BENCH_TARGETS=pure_p,pure_u,pecl_p,pecl_u \
php -n -dextension=msgpack.so -dzend_extension=opcache.so \
-dpcre.jit=1 -dopcache.jit_buffer_size=64M -dopcache.jit=tracing -dopcache.enable=1 -dopcache.enable_cli=1 \
tests/bench.php

Example output

Filter: MessagePack\Tests\Perf\Filter\ListFilter
Rounds: 3
Iterations: 100000

===========================================================================
Test/Target            Packer  BufferUnpacker  msgpack_pack  msgpack_unpack
---------------------------------------------------------------------------
nil .................. 0.0001 ........ 0.0052 ...... 0.0053 ........ 0.0042
false ................ 0.0007 ........ 0.0060 ...... 0.0057 ........ 0.0043
true ................. 0.0008 ........ 0.0060 ...... 0.0056 ........ 0.0041
7-bit uint #1 ........ 0.0031 ........ 0.0046 ...... 0.0062 ........ 0.0041
7-bit uint #2 ........ 0.0021 ........ 0.0043 ...... 0.0062 ........ 0.0041
7-bit uint #3 ........ 0.0022 ........ 0.0044 ...... 0.0061 ........ 0.0040
5-bit sint #1 ........ 0.0030 ........ 0.0048 ...... 0.0062 ........ 0.0040
5-bit sint #2 ........ 0.0032 ........ 0.0046 ...... 0.0062 ........ 0.0040
5-bit sint #3 ........ 0.0031 ........ 0.0046 ...... 0.0062 ........ 0.0040
8-bit uint #1 ........ 0.0054 ........ 0.0079 ...... 0.0062 ........ 0.0050
8-bit uint #2 ........ 0.0051 ........ 0.0079 ...... 0.0064 ........ 0.0044
8-bit uint #3 ........ 0.0051 ........ 0.0082 ...... 0.0062 ........ 0.0044
16-bit uint #1 ....... 0.0077 ........ 0.0094 ...... 0.0065 ........ 0.0045
16-bit uint #2 ....... 0.0077 ........ 0.0094 ...... 0.0063 ........ 0.0045
16-bit uint #3 ....... 0.0077 ........ 0.0095 ...... 0.0064 ........ 0.0047
32-bit uint #1 ....... 0.0088 ........ 0.0119 ...... 0.0063 ........ 0.0043
32-bit uint #2 ....... 0.0089 ........ 0.0117 ...... 0.0062 ........ 0.0039
32-bit uint #3 ....... 0.0089 ........ 0.0118 ...... 0.0063 ........ 0.0044
64-bit uint #1 ....... 0.0097 ........ 0.0155 ...... 0.0063 ........ 0.0045
64-bit uint #2 ....... 0.0095 ........ 0.0153 ...... 0.0061 ........ 0.0045
64-bit uint #3 ....... 0.0096 ........ 0.0156 ...... 0.0063 ........ 0.0047
8-bit int #1 ......... 0.0053 ........ 0.0083 ...... 0.0062 ........ 0.0044
8-bit int #2 ......... 0.0052 ........ 0.0080 ...... 0.0062 ........ 0.0044
8-bit int #3 ......... 0.0052 ........ 0.0080 ...... 0.0062 ........ 0.0043
16-bit int #1 ........ 0.0089 ........ 0.0097 ...... 0.0069 ........ 0.0046
16-bit int #2 ........ 0.0075 ........ 0.0093 ...... 0.0063 ........ 0.0043
16-bit int #3 ........ 0.0075 ........ 0.0094 ...... 0.0062 ........ 0.0046
32-bit int #1 ........ 0.0086 ........ 0.0122 ...... 0.0063 ........ 0.0044
32-bit int #2 ........ 0.0087 ........ 0.0120 ...... 0.0066 ........ 0.0046
32-bit int #3 ........ 0.0086 ........ 0.0121 ...... 0.0060 ........ 0.0044
64-bit int #1 ........ 0.0096 ........ 0.0149 ...... 0.0060 ........ 0.0045
64-bit int #2 ........ 0.0096 ........ 0.0157 ...... 0.0062 ........ 0.0044
64-bit int #3 ........ 0.0096 ........ 0.0160 ...... 0.0063 ........ 0.0046
64-bit int #4 ........ 0.0097 ........ 0.0157 ...... 0.0061 ........ 0.0044
64-bit float #1 ...... 0.0079 ........ 0.0153 ...... 0.0056 ........ 0.0044
64-bit float #2 ...... 0.0079 ........ 0.0152 ...... 0.0057 ........ 0.0045
64-bit float #3 ...... 0.0079 ........ 0.0155 ...... 0.0057 ........ 0.0044
fix string #1 ........ 0.0010 ........ 0.0045 ...... 0.0071 ........ 0.0044
fix string #2 ........ 0.0048 ........ 0.0075 ...... 0.0070 ........ 0.0060
fix string #3 ........ 0.0048 ........ 0.0086 ...... 0.0068 ........ 0.0060
fix string #4 ........ 0.0050 ........ 0.0088 ...... 0.0070 ........ 0.0059
8-bit string #1 ...... 0.0081 ........ 0.0129 ...... 0.0069 ........ 0.0062
8-bit string #2 ...... 0.0086 ........ 0.0128 ...... 0.0069 ........ 0.0065
8-bit string #3 ...... 0.0086 ........ 0.0126 ...... 0.0115 ........ 0.0065
16-bit string #1 ..... 0.0105 ........ 0.0137 ...... 0.0128 ........ 0.0068
16-bit string #2 ..... 0.1510 ........ 0.1486 ...... 0.1526 ........ 0.1391
32-bit string ........ 0.1517 ........ 0.1475 ...... 0.1504 ........ 0.1370
wide char string #1 .. 0.0044 ........ 0.0085 ...... 0.0067 ........ 0.0057
wide char string #2 .. 0.0081 ........ 0.0125 ...... 0.0069 ........ 0.0063
8-bit binary #1 ........... I ............. I ........... F ............. I
8-bit binary #2 ........... I ............. I ........... F ............. I
8-bit binary #3 ........... I ............. I ........... F ............. I
16-bit binary ............. I ............. I ........... F ............. I
32-bit binary ............. I ............. I ........... F ............. I
fix array #1 ......... 0.0014 ........ 0.0059 ...... 0.0132 ........ 0.0055
fix array #2 ......... 0.0146 ........ 0.0156 ...... 0.0155 ........ 0.0148
fix array #3 ......... 0.0211 ........ 0.0229 ...... 0.0179 ........ 0.0180
16-bit array #1 ...... 0.0673 ........ 0.0498 ...... 0.0343 ........ 0.0388
16-bit array #2 ........... S ............. S ........... S ............. S
32-bit array .............. S ............. S ........... S ............. S
complex array ............. I ............. I ........... F ............. F
fix map #1 ................ I ............. I ........... F ............. I
fix map #2 ........... 0.0148 ........ 0.0180 ...... 0.0156 ........ 0.0179
fix map #3 ................ I ............. I ........... F ............. I
fix map #4 ........... 0.0252 ........ 0.0201 ...... 0.0214 ........ 0.0167
16-bit map #1 ........ 0.1027 ........ 0.0836 ...... 0.0388 ........ 0.0510
16-bit map #2 ............. S ............. S ........... S ............. S
32-bit map ................ S ............. S ........... S ............. S
complex map .......... 0.1104 ........ 0.1010 ...... 0.0556 ........ 0.0602
fixext 1 .................. I ............. I ........... F ............. F
fixext 2 .................. I ............. I ........... F ............. F
fixext 4 .................. I ............. I ........... F ............. F
fixext 8 .................. I ............. I ........... F ............. F
fixext 16 ................. I ............. I ........... F ............. F
8-bit ext ................. I ............. I ........... F ............. F
16-bit ext ................ I ............. I ........... F ............. F
32-bit ext ................ I ............. I ........... F ............. F
32-bit timestamp #1 ....... I ............. I ........... F ............. F
32-bit timestamp #2 ....... I ............. I ........... F ............. F
64-bit timestamp #1 ....... I ............. I ........... F ............. F
64-bit timestamp #2 ....... I ............. I ........... F ............. F
64-bit timestamp #3 ....... I ............. I ........... F ............. F
96-bit timestamp #1 ....... I ............. I ........... F ............. F
96-bit timestamp #2 ....... I ............. I ........... F ............. F
96-bit timestamp #3 ....... I ............. I ........... F ............. F
===========================================================================
Total                  0.9642          1.0909        0.8224          0.7213
Skipped                     4               4             4               4
Failed                      0               0            24              17
Ignored                    24              24             0               7

Note that the msgpack extension (v2.1.2) doesn't support ext, bin and UTF-8 str types.

License

The library is released under the MIT License. See the bundled LICENSE file for details.

Author: rybakit
Source Code: https://github.com/rybakit/msgpack.php
License: MIT License

#php 

Garry Taylor

Garry Taylor

1669952228

Dijkstra's Algorithm Explained with Examples

In this tutorial, you'll learn: What is Dijkstra's Algorithm and how Dijkstra's algorithm works with the help of visual guides.

You can use algorithms in programming to solve specific problems through a set of precise instructions or procedures.

Dijkstra's algorithm is one of many graph algorithms you'll come across. It is used to find the shortest path from a fixed node to all other nodes in a graph.

There are different representations of Dijkstra's algorithm. You can either find the shortest path between two nodes, or the shortest path from a fixed node to the rest of the nodes in a graph.

In this article, you'll learn how Dijkstra's algorithm works with the help of visual guides.

How Does Dijkstra’s Algorithm Work?

Before we dive into more detailed visual examples, you need to understand how Dijkstra's algorithm works.

Although the theoretical explanation may seem a bit abstract, it'll help you understand the practical aspect better.

In a given graph containing different nodes, we are required to get the shortest path from a given node to the rest of the nodes.

These nodes can represent any object like the names of cities, letters, and so on.

Between each node is a number denoting the distance between two nodes, as you can see in the image below:

nodes-1

We usually work with two arrays – one for visited nodes, and another for unvisited nodes. You'll learn more about the arrays in the next section.

When a node is visited, the algorithm calculates how long it took to get to the node and stores the distance. If a shorter path to a node is found, the initial value assigned for the distance is updated.

Note that a node cannot be visited twice.

The algorithm runs recursively until all the nodes have been visited.

Dijkstra's Algorithm Example

In this section, we'll take a look at a practical example that shows how Dijkstra's algorithm works.

Here's the graph we'll be working with:

nodes

We'll use the table below to put down the visited nodes and their distance from the fixed node:

NODESHORTEST DISTANCE FROM FIXED NODE
A
B
C
D
E

Visited nodes = []
Unvisited nodes = [A,B,C,D,E]

Above, we have a table showing each node and the shortest distance from the that node to the fixed node. We are yet to choose the fixed node.

Note that the distance for each node in the table is currently denoted as infinity (∞). This is because we don't know the shortest distance yet.

We also have two arrays – visited and unvisited. Whenever a node is visited, it is added to the visited nodes array.

Let's get started!

To simplify things, I'll break the process down into iterations. You'll see what happens in each step with the aid of diagrams.

Iteration #1

The first iteration might seem confusing, but that's totally fine. Once we start repeating the process in each iteration, you'll have a clearer picture of how the algorithm works.

Step #1 - Pick an unvisited node

We'll choose A as the fixed node. So we'll find the shortest distance from A to every other node in the graph.

node1-1

We're going to give A a distance of 0 because it is the initial node. So the table would look like this:

NODESHORTEST DISTANCE FROM FIXED NODE
A0
B
C
D
E

Step #2 - Find the distance from current nodenode1a-3

The next thing to do after choosing a node is to find the distance from it to the unvisited nodes around it.

The two unvisited nodes directly linked to A are B and C.

To get the distance from A to B:

0 + 4 = 4

0 being the value of the current node (A), and 4 being the distance between A and B in the graph.

To get the distance from A to C:

0 + 2 = 2

Step #3 - Update table with known distances

In the last step, we got 4 and 2 as the values of B and C respectively. So we'll update the table with those values:

NODESHORTEST DISTANCE FROM FIXED NODE
A0
B4
C2
D
E

Step #4 - Update arrays

At this point, the first iteration is complete. We'll move node A to the visited nodes array:

Visited nodes = [A]
Unvisited nodes = [B,C,D,E]

Before we proceed to the next iteration, you should know the following:

  • Once a node has been visited, it cannot be linked to the current node. Refer to step #2 in the iteration above and step #2 in the next iteration.
  • A node cannot be visited twice.
  • You can only update the shortest known distance if you get a value smaller than the recorded distance.

Iteration #2

Step #1 - Pick an unvisited node

We have four unvisited nodes — [B,C,D,E]. So how do you know which node to pick for the next iteration?

Well, we pick the node with the smallest known distance recorded in the table. Here's the table:

NODESHORTEST DISTANCE FROM FIXED NODE
A0
B4
C2
D
E

So we're going with node C.

node2-2

Step #2 - Find the distance from current node

To find the distance from the current node to the fixed node, we have to consider the nodes linked to the current node.

The nodes linked to the current node are A and B.

But A has been visited in the previous iteration so it will not be linked to the current node. That is:

node2a-1

From the diagram above,

  • The green color denotes the current node.
  • The blue color denotes the visited nodes. We cannot link to them or visit them again.
  • The red color shows the link from the unvisited nodes to the current node.

To find the distance from C to B:

2 + 1 = 3

2 above is recorded distance for node C while 1 is the distance between C and B in the graph.

Step #3 - Update table with known distances

In the last step, we got the value of B to be 3. In the first iteration, it was 4.

We're going to update the distance in the table to 3.

NODESHORTEST DISTANCE FROM FIXED NODE
A0
B3
C2
D
E

So, A --> B = 4 (First iteration).

A --> C --> B = 3 (Second iteration).

The algorithm has helped us find the shortest path to B from A.

Step #4 - Update arrays

We're done with the last visited node. Let's add it to the visited nodes array:

Visited nodes = [A,C]
Unvisited nodes = [B,D,E]

Iteration #3

Step #1 - Pick an unvisited node

We're down to three unvisited nodes — [B,D,E]. From the array, B has the shortest known distance.

node3-2

To restate what is going on in the diagram above:

  • The green color denotes the current node.
  • The blue color denotes the visited nodes. We cannot link to them or visit them again.
  • The red color shows the link from the unvisited nodes to the current node.

Step #2 - Find the distance from current node

The nodes linked to the current node are D and E.

B (the current node) has a value of 3. Therefore,

For node D, 3 + 3 = 6.

For node E, 3 + 2 = 5.

Step #3 - Update table with known distances

NODESHORTEST DISTANCE FROM FIXED NODE
A0
B3
C2
D6
E5

Step #4 - Update arrays

Visited nodes = [A,C,B]
Unvisited nodes = [D,E]

Iteration #4

Step #1 - Pick an unvisited node

Like other iterations, we'll go with the unvisited node with the shortest known distance. That is E.

node4-1

Step #2 - Find the distance from current node

According to our table, E has a value of 5.

For D in the current iteration,

5 + 5 = 10.

The value gotten for D here is 10, which is greater than the recorded value of 6 in the previous iteration. For this reason, we'll not update the table.

Step #3 - Update table with known distances

Our table remains the same:

NODESHORTEST DISTANCE FROM FIXED NODE
A0
B3
C2
D6
E5

Step #4 - Update arrays

Visited nodes = [A,C,B,E]
Unvisited nodes = [D]

Iteration #5

Step #1 - Pick an unvisited node

We're currently left with one node in the unvisited array — D.

node5-1

Step #2 - Find the distance from current node

The algorithm has gotten to the last iteration. This is because all nodes linked to the current node have been visited already so we can't link to them.

Step #3 - Update table with known distances

Our table remains the same:

NODESHORTEST DISTANCE FROM FIXED NODE
A0
B3
C2
D6
E5

At this point, we have updated the table with the shortest distance from the fixed node to every other node in the graph.

Step #4 - Update arrays

Visited nodes = [A,C,B,E,D]
Unvisited nodes = []

As can be seen above, we have no nodes left to visit. Using Dijkstra's algorithm, we've found the shortest distance from the fixed node to others nodes in the graph.

Dijkstra's Algorithm Pseudocode Example

The pseudocode example in this section was gotten from Wikipedia. Here it is:

 1  function Dijkstra(Graph, source):
 2      
 3      for each vertex v in Graph.Vertices:
 4          dist[v] ← INFINITY
 5          prev[v] ← UNDEFINED
 6          add v to Q
 7      dist[source] ← 0
 8      
 9      while Q is not empty:
10          u ← vertex in Q with min dist[u]
11          remove u from Q
12          
13          for each neighbor v of u still in Q:
14              alt ← dist[u] + Graph.Edges(u, v)
15              if alt < dist[v]:
16                  dist[v] ← alt
17                  prev[v] ← u
18
19      return dist[], prev[]

Applications of Dijkstra's Algorithm

Here are some of the common applications of Dijkstra's algorithm:

  • In maps to get the shortest distance between locations. An example is Google Maps.
  • In telecommunications to determine transmission rate.
  • In robotic design to determine shortest path for automated robots.

Summary

In this article, we talked about Dijkstra's algorithm. It is used to find the shortest distance from a fixed node to all other nodes in a graph.

We started by giving a brief summary of how the algorithm works.

We then had a look at an example that further explained Dijkstra's algorithm in steps using visual guides.

We concluded with a pseudocode example and some of the applications of Dijkstra's algorithm.

Happy coding!

Original article source at https://www.freecodecamp.org

#algorithm #datastructures

 iOS App Dev

iOS App Dev

1620466520

Your Data Architecture: Simple Best Practices for Your Data Strategy

If you accumulate data on which you base your decision-making as an organization, you should probably think about your data architecture and possible best practices.

If you accumulate data on which you base your decision-making as an organization, you most probably need to think about your data architecture and consider possible best practices. Gaining a competitive edge, remaining customer-centric to the greatest extent possible, and streamlining processes to get on-the-button outcomes can all be traced back to an organization’s capacity to build a future-ready data architecture.

In what follows, we offer a short overview of the overarching capabilities of data architecture. These include user-centricity, elasticity, robustness, and the capacity to ensure the seamless flow of data at all times. Added to these are automation enablement, plus security and data governance considerations. These points from our checklist for what we perceive to be an anticipatory analytics ecosystem.

#big data #data science #big data analytics #data analysis #data architecture #data transformation #data platform #data strategy #cloud data platform #data acquisition

Java Questions

Java Questions

1599137520

50 Data Science Jobs That Opened Just Last Week

Our latest survey report suggests that as the overall Data Science and Analytics market evolves to adapt to the constantly changing economic and business environments, data scientists and AI practitioners should be aware of the skills and tools that the broader community is working on. A good grip in these skills will further help data science enthusiasts to get the best jobs that various industries in their data science functions are offering.

In this article, we list down 50 latest job openings in data science that opened just last week.

(The jobs are sorted according to the years of experience r

1| Data Scientist at IBM

**Location: **Bangalore

Skills Required: Real-time anomaly detection solutions, NLP, text analytics, log analysis, cloud migration, AI planning, etc.

Apply here.

2| Associate Data Scientist at PayPal

**Location: **Chennai

Skills Required: Data mining experience in Python, R, H2O and/or SAS, cross-functional, highly complex data science projects, SQL or SQL-like tools, among others.

Apply here.

3| Data Scientist at Citrix

Location: Bangalore

Skills Required: Data modelling, database architecture, database design, database programming such as SQL, Python, etc., forecasting algorithms, cloud platforms, designing and developing ETL and ELT processes, etc.

Apply here.

4| Data Scientist at PayPal

**Location: **Bangalore

Skills Required: SQL and querying relational databases, statistical programming language (SAS, R, Python), data visualisation tool (Tableau, Qlikview), project management, etc.

Apply here.

5| Data Science at Accenture

**Location: **Bibinagar, Telangana

Skills Required: Data science frameworks Jupyter notebook, AWS Sagemaker, querying databases and using statistical computer languages: R, Python, SLQ, statistical and data mining techniques, distributed data/computing tools such as Map/Reduce, Flume, Drill, Hadoop, Hive, Spark, Gurobi, MySQL, among others.


#careers #data science #data science career #data science jobs #data science news #data scientist #data scientists #data scientists india

Gerhard  Brink

Gerhard Brink

1620629020

Getting Started With Data Lakes

Frameworks for Efficient Enterprise Analytics

The opportunities big data offers also come with very real challenges that many organizations are facing today. Often, it’s finding the most cost-effective, scalable way to store and process boundless volumes of data in multiple formats that come from a growing number of sources. Then organizations need the analytical capabilities and flexibility to turn this data into insights that can meet their specific business objectives.

This Refcard dives into how a data lake helps tackle these challenges at both ends — from its enhanced architecture that’s designed for efficient data ingestion, storage, and management to its advanced analytics functionality and performance flexibility. You’ll also explore key benefits and common use cases.

Introduction

As technology continues to evolve with new data sources, such as IoT sensors and social media churning out large volumes of data, there has never been a better time to discuss the possibilities and challenges of managing such data for varying analytical insights. In this Refcard, we dig deep into how data lakes solve the problem of storing and processing enormous amounts of data. While doing so, we also explore the benefits of data lakes, their use cases, and how they differ from data warehouses (DWHs).


This is a preview of the Getting Started With Data Lakes Refcard. To read the entire Refcard, please download the PDF from the link above.

#big data #data analytics #data analysis #business analytics #data warehouse #data storage #data lake #data lake architecture #data lake governance #data lake management