## Python: Random Pixel Color – P2

**Learning : Python, Math**

** Subject: Random Coloring Pixels**

[

NOTE:To keep the code as simple as we can,We WILL NOT ADDany user input Varevecations. Assuming that our user will Enter the right inputs.]

Our last post about Random Pixel Color, we generate a Numpy Array of Row, Coloum and color then we Plot it on the screen [Read the Post Here], now in this post we will use some Math consepts to try if we can get some patterns out of ramdom Function.

Our Tools: In this post we will use the following:

1. Jupyter-NoteBook.

2. numpy.

3. random.

4. matplotlib.

5. PIL or Pillow.

In this version we will use **“Fibonacci Sequence”** Fibonacci Sequence is the sum of the two preceding ones, starting from 0 and 1 such as [1, 1, 2, 3, 5, 8, 13 … n], in our code we will have three variables:

cw: canvas width,

ch: canvas hight,

offset: the offset will be the value that will reset the Fibonacci Sequence to 1.

So, if we run the application, we will generate three numbers that will present the colors R,G,B (Will be Generated __ONE__ time) then for each pixcel in (cw*ch) we will calculate a v as Fibonacci Sequence from fs1 =1, fs2 = 1 here is the code:

v = fs1 + fs2

fs1,fs2 = fs2, v

this value v will be added to the colors r,g,b (on each pixcel) untill the v is grater the the offset numbre that we pass to the Function. If v > offset then we will re-set the fs1 = 1, fs2 = 1,.. Here is the Code ..

Run No.1 | Run No.2 |

Run No.3 |
Run No.4 |

The above is just 25×25 and i change the offset, feel free to download the code and change the numbers .. see what you will get …

..:: Have Fun with Coding ::.. 🙂

To Download my Python code (.py) files

Click-Here

By: Ali Radwani

## Python Sorting Algorithm – Heap Sorting -P1

**Learning : Python, Math, Algorithm **

** Subject: Sorting Algorithm, Heap Sort**

[

NOTE:To keep the code as simple as we can,We WILL NOT ADDany user input Varevecations. Assuming that our user will Enter the right inputs.]

Once I start preparing and writing the code for Heap Sorting I fond that I can’t jump to the Heap Sorting without some introductions, So in this post we will cover the Array, Binary Tree, Binary Array, Max-Heap, how to know if a given Array is in Max-Heap or not, Add node to a Max-Heap and Delete a node from a Max-heap. For all this, we will have two or three posts to cover what i think we must know.

So First:

**Binary Tree:** A Binary Tree is a set of Nodes and each Node may have a Maximum of TWO Childs, called Left-Child and Right-Child. Going down to the next level, each of the Child’s (the left one and the right one) again may have TWO Child’s (Left and Right) .. and so on. The last level were there is no more child’s that level is the Leaves. Here are some sample of Binary Tree’s..

All the above are Binary Tree’s, But we will talk about Three Definitions for a Binary Trees:

Full Binary Tree, Complete Binary Tree, Perfect Binary Tree

**Full Binary Tree:**

A Tree is a __Full Binary Tree__ in which Every/All Nodes Except Leaf Nodes(last level) have __ Zero or Two__ Children.

**Complete Binary Tree:**

A Binary Tree called a {__complete binary tree__} in which All/Each levels are completely filled __except__ possibly the last level has all keys as left as possible

__Practical example of Complete Binary Tree is Binary Heap.__

**Perfect Binary Tree:**

A Binary Tree is {__a Perfect Binary Tree__} IF all the internal nodes have Two children **and** all leaf nodes are at the same level.

NOTE: Every Full Binary Tree is A Complete.

FULL BINARY TREE | FULL BINARY TRTEE |

COMPLETE BINARY TREE | COMPLETE BINARY TREE |

PERFECT BINARY TREE | PERFECT BINARY TREE Figure 1 |

**Binary Tree And Array:** To convert a binary tree into array or to present a Binary Tree as an Array we need to consider the following :

1. To Taking all the elements in the Binary Tree.

2. To Keeping the relations between the nodes, who is the parent and what are the childerns for each parents [Left child and Right child].

**1. Taking all the elements in the Binary Tree:**

So for a given tree as __Figure 1:[in above example] __, we can see that (A) is the First Element [Root] (First Parent) and has 2 childs (B) (Left Child) & (C) (Right Child), –> Then Element (B) as parent has Two childs (D) (Left Child) & (E) (Right Child), –> Then Element (C) as parent has Two Childs (F) (Left Child) & (G) (Right Child) .. this is the end of the tree, leaves level.

Now, IF we want to present this Tree as an Array we will start with (A) in index 0, then will write all the elements level by level, from Left to Right. So we will have the array **a1** as follow:

** a1 = [A,B,C,D,E,F,G]**

**2. Keeping the relations between the Nodes:** Using the Method of filling the Array as in point One (above) we Save the relations between the Parents and Childs. For a given Array **a1 = [A,B,C,D,E,F,G]** we can user three formulas to know the Parent and the Childs of any given Node as following:

Assuming we are at index (x) then:

1. Left Child Index of Node (x) : 2 * x + 1

2. Right Child Index of Node (x) : 2 * x + 2

3. Parent Index of Node (x) : x//2 (absolute value of the division)

So, if we refer to a1 Array and (Figure-1), and say we want to know the childrens of node (A), Node (A) is in index [0] so:

The Left child index of Node (A) is : 2 * 0 + 1 = 0 + 1 = 1, the Element in index 1 in the Array a1[1] = B.

The Right child index of Node (A) is : 2 * 0 + 2 = 0 + 2 = 2, the Element in index 2 in the Array a1[2] = C.

The Left child index of Node (C) is : 2 * 2 + 1 = 4 + 1 = 5, the Element in index 5 in the Array a1[5] = F.

The Right child index of Node (C) is : 2 * 2 + 2 = 4 + 2 = 6, the Element in index 6 in the Array a1[6] = (G).

The Parent of Node (E) will be: 4//2 = 2, so the parent of the Element (E) is a1[2] = (B)

**Heap Tree:** Is a Binary Essentially an almost Complete Tree. So a **Heap Tree is**: Tree with All/Each levels are completely Filled except possibly the last level has all keys as left as possible. In Heap The Nodes represents as Integer Numbers.

**Max-Heap:** In Max-Heap Tree the Child Node is Smaller than his Parent.

**Mini-Heap:** In Mini-Heap Tree the Child Node is Larger than his Parent.

We will stop here in this part and will start doing some coding in Python Sorting Algorithm – Heap Sorting – P2.

..:: Have Fun with Coding ::.. 🙂

To Download my Python code (.py) files

Click-Here

By: Ali Radwani

## Python: Sorting Algorithm. 7- Radix Sorting

**Learning : Python Coding, Math, Algorithm **

** Subject: Python Code to Applying Radix Sorting Algorithm **

[

NOTE:To keep the code as simple as we can,We WILL NOT ADDany user input Varevecations. Assuming that our user will Enter the right inputs.]

**Sorting Algorithm** is a way to sort a given list/Array of numbers, there are several sorting Algorithm as follow:

**Type of Sorting Algorithm**

1. Quick Sort. [**Click to Read the Post.**]

2. Bubble Sort. [**Click to Read the Post.**]

3. Merge Sort. [**Click to Read the Post.**]

4. Insertion Sort. [Click to Read the Post.]

5. Selection Sort. [Click to Read the Post.]

6. Heap Sort. [Click to Read the Post.]

7. Radix Sort. [Click to Read the Post.]

8. Bucket Sort. [Click to Read the Post.]

Here in this post we will write a function to take a given list/Array and sort it then pass it back. We assume the user will enter a serial of numbers, that he want to sort, our function will sort it using Radix Sorting Algorithm and print out the original Array and the sorted one.

**Radix Sort Algorithm**: In Radix Sort, we will apply coming Steps:

1. Get the Maximum Number of Digits in the Array. [length of Maximum Number]

2. Add Zeros [0] to the Left of Each Number so All Numbers in the Array will be Same Lenght.

3. Sort the Array Based on The Most Right Digit [digit index] =[-i]. This was Iteration 1.

4. Repeat Step 3, and for each Iteration We Sort based on [digit index] = [-iteration].

5. If [digit index] = 0, Thats mean we did sort until Most left Digit in the Numbers. Then we Stop the Loop.

6. Return the Array.

Coding: In our Radix Sorting Application we will have several Functions to help us completing our task. First let’s see the functions:

Main-menu: To Show the Main Menu of the Application.

header: Just a Decoration Function to Print the Header of the Application.

digits_equalizer: To Add Zeros to the Left of Each Number in the Array.

create_list: Let the User to Enter the Array.

radix_sort: Applying Radix Sorting Algorithm in a Fast-Run

radix_sort_details: Applying Radix Sorting Algorithm Step-by-Step.

Just to be a short artical, i will not go thought Functions like the def main_menu() , def create_list() and def header().

So, let’s start with digits_equalizer() Function, in Radix Sorting we start comparing all numbers based on it’s digites and sorting cording that, but if a number has three digits and another one has two, then we may face an error [index out of range], so first we will convert the array to a string and will add zero.. Here is the code..

This Function will return two arguments, the Array after adding zeros and the maximum digits.

Now, we will write the function of Radix Sorting (Fast-Run) the details function will be a copy with some print-statement.

So here is the code..

# Radix Sort Fast-Run Function def radix_sort() : arr = create_list() temp_arr = [] # Convert to srting and Add Zeros to left side of each number in the array. arr,max_d = digits_equalizer(arr) # Loop for all digits of numbers. for d in range (1,max_d+1): # Loop for sort numbers 0 to 9. for sn in range (0,10): # Check each right digits of each number. for each in arr: if each[-d] == str(sn): temp_arr.append(each) arr = temp_arr temp_arr = [] return(arr)

End of this Post..

All Code as .py file format is available in Download Page.

..:: Have Fun with Coding ::.. 🙂

To Download my Python code (.py) files

Click-Here

By: Ali Radwani

## Python: Kadane’s Algorithm

**Learning : Python, Algorithm, Math **

** Subject: Implement the Kadane’s Algorithm**

**Definition:** Kadane’s Algorithm is to search in a one Dimensional Array [integer positive and negative numbers] for a we will largest Sum of contiguous subarray.

NOTE:To keep the code as simple as we can,We WILL NOT ADDany user input Varevecations. Assuming that our user will Enter the right inputs.]

**Algorithm** To find the largest subset sum, we apply coming step:

We will use two variables:

current_max: to hold the max sum of thesub-set

start_again: will be as a flag to re-set the current_max

__ Algorithm: __

1. Start from Element in the array index = 1, save it as start_again. Set Current_max to Array Element in index = 0.

2. Do sumation of start_again with the next element index + 1.

3. If current_max < start_again then re-set current_manx = start_again

4. If start_again < 0 then re-set start_again = 0

5. Repeat from 2 to 4 until the end of the array.

6. If we reach end of the Array, then return the current_max

More from Kadane’s Algorithm:

The aim of Kadane’s Algorithm is to return the Maximum sum of sub-set. But in our code here we will return the following:

1. Maximum sum of largest subset

2. The start Index and the End Index of the subset.

3. printing out the subset.

We will have three options in our application, as following:

1. Kadane’s Algorithm – Fast Run.

2. Kadane’s Algorithm – Step By Step.

9. Exit.

As we are doing in our Algorithms coding, we will use a Main-Menu, and a Function to help the user to enter the Array.

**Coding**

We will start with def create_array(): and will return the Array that the user will enter. here is the code..

Now, here is the code for the Main-Menu and the Main application body. In Main application body code, we will use the while True : loop and calling the main_menu() function then with if statement we will check on the user_selection

The Main-Menu |

Here is the Main Application body code.. |

Last, we will write the Function to get the Kadane’s Sum in a Fast-Run, the details one will be a copy with mode print-out statement to show the steps .. __[All code is in Download Page.]__

As we mentioned, Our Kadane’s function will return three things, the Grates Sum of a sub-set, and to position of that sub-set as start index and end index. Here is the code ..

Here is a Run-Time screen .. |

We done with another Algorithm, looking forwards to solve new one in coming days.

..:: Have Fun with Coding ::.. 🙂

To Download my Python code (.py) files

Click-Here

By: Ali Radwani

## Python: Sorting Algorithm (3. Merge Sort)

**Learning : Python coding, Math, Algorithm, **

** Subject: Writing Merge Sorting Algorithm in Python**

NOTE:To keep the code as simple as we can,We WILL NOT ADDany user input Varevecations. Assuming that our user will Enter the right inputs.]

**Sorting Algorithm** is a way to sort a given list/Array of numbers, there are several sorting Algorithm as follow:

**Type of Sorting Algorithm**

1. Quick Sort. [**Click Here**]

2. Bubble Sort. [Click Here]

3. Merge Sort. [Click Here]

4. Insertion Sort. [Click Here]

5. Selection Sort. [Click Here]

6. Heap Sort. [Click Here]

7. Radix Sort. [Click Here]

8. Bucket Sort. [Click Here]

Here in this post we will write a function to take a given list and sort it then pass it back. We assume the user will enter a serial of numbers, that he want to sort, our function will sort it and print out the original numbers and the sorted one.

**Merge Sort:** Steps of Merge Sorting Algorithm are:

1. If the Array has 1 Element then return it.

2. If the givin Array has more than 1 Element then we Divide it into 2 Parts.

Left = from Element 0 T0 Element len(arr)//2

and Right = from Element len(arr)//2 To Element len(arr). And we keep repeating step 2 for each part.

3. Once we have All parts divided we tart merge them in a sorted order.

**Coding:** In this Post we will write the Function for Main-Mnu, another one to collect the Array [Not Sorted] Elements from the user, then we will write the Main Function, here we will have One to Divide the Array into parts and One to Merge the Element together again. And as we done with Quick & Bubble Sort projects we will have one Fast-Run Function and another one with Details Step-By-Step run to show the Algorithm.

__ NOTE: __ All the Code will be Available in the Download Page.

Let’s start with the Main-menu to list down three option were the user will select one among them, the menu options are: 1. Merge Sort Algorithm – Fast Run. & 2. Merge Sort Algorithm – Step By Step and the last one is 3. Exit.

Here is the code.

I will Not post the code for collecting the Array Element from the user [Find it in the .py file for this project]. Here is the code for merge_sort_divider Function, it takes two arguments the Array and the user_selection, so if the user selection is 2 (2. Merge Sort Algorithm – Step By Step) We will print-out the Dividing Steps and some other Text. [We are using If Statement to print-out Text lines]. Here is the Code ..

Now for **merging function**, for merging function we will have two copies, one as Fast-Run and another for Details to print-out the running Steps, this will make the Fast-Run Function short and easy to follow-up. So, here is the Fast-Run Function code for merge the two part of array returned from the merge_sort_divider. Here is the Code ..

Run time screen .. |

End of Merge Sorting Algorithm.

To Download my Python code (.py) files

Click-Here

By: Ali Radwani

## Python Project: Disarium Number

**Learning : Python to solve Mathematics Problems **** Subject: Disarium Number **

In Mathematics there are some formulas or let say rules that generate a sequence of given a certen result, and accordingly we gave that number or that sequence a name, such as even numbers, odd numbers, prime numbers and so on.

Here in this post we will talk about the **Disarium Number** and will write a code to check if a given number Disarium or Not.**Defenition: **A Number is a Disarium if the Sum of its digits powered with their respective position is equal to the original number. Example: If we have 25 as a Number we will say: if (2^1 + 5^2) = 25 then 25 is Disarium.

So: 2^1 = 2, 5^2 = 25, 2+25 = 27; 25 NOT Equal to 27 then 25 is NOT Disarium.

Let’s take n = 175:

1^1 = 1

7^2 = 49

5^3 = 125

(1 + 49 + 125) = 175 thats EQUAL to n so 175 is a Disarium Number.

In the bellow code, we will write a function to take a number from the user the check if it is a Disarium Number or not. In this function we will print out the calculation on the screen. Let’s start by writing the function

# is_disarium function.

def is_disarium(num) :

"""

Project Name: Disarium Number

By: Ali Radwani

Date: 2.4.2021

"""

the_sum = []

l = len(num)

for x in range (0,l):

print(num[x] , '^',x+1,'=', (int(num[x])**(x+1)))

the_sum.append((int(num[x])**(x+1)))

if int(num) == sum(the_sum) :

print ("\n The sum is {}, and the original Number is {} So {} is a Disarium Number.".format(sum(the_sum),num,num))

else:

print ('\n The sum is {}, and the original Number is {} So it is NOT Disarium.'.format(sum(the_sum),num))

num = input('\n Enter a Number to check if it is Disarium. > ')

# Call the function and pass the num.

is_disarium(num)

To Download my Python code (.py) files

Click-Here

By: Ali Radwani