### Archive

Archive for June, 2021

## Python Sorting Algorithm – Heap Sorting -P2

Learning : Python, Math, Algorithm
Subject: Sorting Algorithm, Heap Sort P2

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

In this post we will start writing some codes for the Heap Sorting application, we will start with the following Functions:

• Entering/Creating the Array.
• Print-Out or to Display the Array.

So First: We will start with the Main_menu Function and will return user_choice also the main application body.. Here is the code ..

``` # Main Menu function and the main application body..

os.system('clear')
print(' '*5,' 1. Enter the Binary Tree as an Array.')
print(' '*5,' 2. Print out the Binary Tree. {Text Mode}')
print(' '*5,' 3. Check if it is a Max Heap.')
print(' '*5,' 4. Convert an Array (Binary Tree) to a Max-Heap.')
print(' '*5,' 5. Add New Node to the Binary Tree.')
print(' '*5,' 6. Delete a Node From the Binary Tree.')
print(' '*5,' 9. Exit.')

user_choice = input("\n Select from the Menu: > ")

return user_choice

# This is the Main application body.
while True :

if user_select == '1' :
print(' Enter the Binary Tree as a Array.')
arr = create_array_node_b_node()

if user_select == '2' :
try:
print_bt_text (arr)
except :
input('\n   You Must First Enter/Create the Array... Press any key then Select Option 1. > ')

if user_select == '3' :
print(' Check if the Array is a Max Heap.')

if user_select == '4' :
print(' Convert an Array (Binary Tree) to a Max-Heap.')

if user_select == '5' :
print(' Add New Node to the Binary Tree.')

if user_select == '6' :
print(' Delete a Node from the Binary Tree.')
#delete_node(arr)

if user_select == '9' :
print('\n\n   Thank you for using this Appliation. ')
input('\n         Press any key .. ')
break

```

Next we will write the function def create_array_node_b_node() in this function the user will start to enter the nodes in the Heap Tree starting from the Root and level-by-level. With every/each Node if the user just press Enter the Node will be as None,then will ask the user if there is any more nodes in the level and if the user answer with [N] then we will complete the level with None. Also in starting of each level we will ask the user if there is any more Nodes remain in the level.
Here is the code ..

In the last Function in this part, we will print-out the Heap-Array as text of Parents and Childs. Here is the code ..

``` # Function to print-out the Heap-Array Tree

def print_bt_text (arr):
"""
Function will Write/Print-out the Tree as Text Showing the Parents and the Childs.

Arguments: The Array as arr

return None
"""
os.system('clear')
print("\n\n==========[ Print out the Binary Tree. {Text Mode} ]==========\n\n")

print('   The array we Have is: ',arr)

for x in range (0,len(arr)):
print(' ')
if arr[x] != None :

try:  # For left childs
l_child = 2 * x + 1

if arr[l_child] != None :
print(f'   Parent Node ({arr[x]}) has a Left Child ({arr[l_child]})',end="")

elif arr[l_child] == None:
print(f'   Parent Node ({arr[x]}) has NO Left Child',end="")
except:
pass

try:   # For right Childs
r_child = 2 * x + 2

if (arr[l_child] == None) and (arr[r_child] != None) :
print(f' But it Has a Right Child ({arr[r_child]}).')

elif (arr[l_child] != None) and (arr[r_child] != None) :

print(f' and a Right Child ({arr[r_child]})')

elif (arr[r_child] == None):
print(f' and Has NO Rigth Child.')
except:
pass

input('   DONE ... Here is a Print out of the Heap Tree Array in {Text Mode}')
```

We will stop here in this part and will do more Functions in Part 3

..:: Have Fun with Coding ::.. 🙂 Follow me on Twitter..

## Sketch: The Shark

The Shark To keep improve my drawing skills i keep my self busy with sketching every day .. OK .. trying to stick to this challenge #asketchaday, also i keep searching the web and learning from other people. Days ago i fond an instagram account for an amazing artist with reall talent and has a beautiful style in coloring, i go though here paints and the Shark just catch my eye’s, I send her a message asking if she allow me to just try to re-drawing her work.. and she say ” YES .. “ so here she is on the Net

and this is her website: https://sophielongart.co.uk/

Back to the Shark I start with pencil, adding some marks and points, then with a 005 very fine black pen draw or say sketched the Shark .. I try to do some coloring .. so here is my draw .. and again Thanks to Sophielongart for her kind.

Here is my sketch.. [ Click to Enlarg] ## 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 ADD any 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.

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

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

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

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

The Parent of Node (E) will be: 4//2 = 2, so the parent of the Element (E) is a1 = (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 ::.. 🙂 Follow me on Twitter..

## Another sketch challenge: A Fish

This week sketch challenge @1hour1sketch on Twitter is to Draw a A Fish so here is my sketch using pencil then black Pen and some watercolor, it takes around 30min [off and on]. More Sketches on my Sketch page ..

Here is my sketch.. ## 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 ADD any 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.]
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.

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

2. Add Zeros  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:
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.

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

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..

..:: Have Fun with Coding ::.. 🙂 Follow me on Twitter..

Learning : Python, Algorithm, Math

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 ADD any 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

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

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 ..

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

..:: Have Fun with Coding ::.. 🙂 Follow me on Twitter..

## Another sketch challenge: Black Cheetah

This week sketch challenge @1hour1sketch on Twitter is to Draw a Black Cheetah so here is my sketch using pencil then black Pen, it takes around 50min [off and on]. More Sketches on my Sketch page ..

Here is my sketch.. ## Python: Sorting Algorithm.- 4-Selection

Learning : Python coding, Math, Algorithm,
Subject: Writing Selection Sorting Algorithm in Python

[NOTE: To keep the code as simple as we can, We WILL NOT ADD any 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.]
8. Bucket Sort. [Click to Read the Post.]

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 using Selection Sorting Algorithm and print out the original numbers and the sorted one.

Selection Sort Algorithm: In Selection Sort, we will apply coming Steps:
1. Select the Element (e) in Index i = 0.
2. Find the Smallest Element in the Array from Index i Until index = length of Array.
3. SWAP the Smallest number in the Array with the Element (e) in index i=0.
4. Select the Element (e) in index i = i+1.
5. Repeat the Algorithm from step 2, until i+1 > length of the Array.

In our Application we will have three Functions, one to collect the Array numbers from the user. [This is the main function in all our sort applications] here is the code

We are calling this Function within the Main Selection Sort Function.
Now we will write the Selection Sort Function .

``` # Selection Sorting Function

def selection_sort(arr):

for i in range (0,len(arr)):
e = arr[i]
s_ind = i
for j in range (i,len(arr)):
if arr[j] < e :
e = arr[j]
s_ind = j

arr[i], arr[s_ind] = arr[s_ind], arr[i]

return arr
```

We will have a copy of same Function with some print-statement to show the iterations and elements in each steps. Here is the code .. Here is screen shot of only three iteration of the Algorithm run-time.. We Done !! .. Another coding for Sorting Algorithms, New one will be published in coming days..

… Have fun with Coding … 🙂 Follow me on Twitter..

## Python: Sort Algorithm – 3 – Insertion 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 ADD any 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

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.

Insertion Sort: Steps of Insertion Sorting Algorithm are:

1. Start with index (x = 1), Compare the Element (k) in index [x] with the Element in index [x-1].
1.1 If Element in [x-1] SMALLER than Element in [x] we swap the two elements.
1.2 Once we Swap we will have new index for k , and again we will compare the (k) in (new index) with element before it (new index -1), and keep moving it to left until we stop at index  or we face an Element GRATER than k.

2. If the Element k GRATER than the element before it, we left k and take the Next Element (to be k) and start comparing K [in x index] with Element in [x-1] index.

3. We do this until k will be in index (length on the list)

Now starting with the codes, as our standard we follow in Sorting Algorithm Applications we will have a Main-Menu and three Items the user will chose among them, and Function to let the user to enter the Numbers [The List or the Array] to be sorted. The Options in the Main-Menu are :
1. Insertion Sort Algorithm – Fast Run.
2. Insertion Sort Algorithm – Step By Step.
9. Exit.

The Fasr-Run we call the create_list(): Function first so the user will Enter the Numbers in the Array, then the Fast-Run will show the sorted Array on the screen.
In the Step-By-Step (Option 2 in the Menu) again calling create_list(): Function first, after the user Enters the Array, we will print-out on the screen each steps of selecting the index, and index-1, the k values and when/if we will SWAP or not.
The last option in the Menu is to Exit the Application (option 9).

Now we start coding.. Here is the Main-Menu.

``` # Main-Menu

os.system('clear')
print('\n\n',' '*5,'******************************')
print(' '*5,' ***','  Sorting Algorithm ',' '*1,'***')
print(' '*5,' ***','     Insertion Sort     ',' '*1,'***')
print(' '*5,' ***',' '*22,'***')
print(' '*5,' ******************************\n\n')
print(' '*7,'1. Insertion Sort Algorithm - Fast Run.')
print(' '*7,'2. Insertion Sort Algorithm - Step By Step.')
print(' '*7,'9. Exit.')

user_choice = input('\n   Select your choice.  > ')
return user_choice ```

Here is the codes for create_list(): to collect the Array from the user..

Finaly, here is the code for the Step-by-Step running for the Insetion Sort Algorithm. It is the same copy of the Fast-Run but with some print statements to show what is happening.

We Done another coding for Sorting Algorithms, another one will be published in coming days..

… Have fun with Coding … 🙂 Follow me on Twitter..

Categories: Learning, Lesson

## Project: Knapsack Problem

Learning : Python, Math, Algorithm
Subject: Solving Knapsack Problem using Python

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

Definition: The knapsack problem is a Problem in Combinatorial Optimization: Given a set of Items, Each with a Weight and a Value or Profit, We need to Determine the Number of Each Item to Include in a Collection so that the Total Weight is Less than or Equal to a Given Limit and the Total Value is as Large as Possible.
Source: Wikipedia

In this post we will write three Functions, The Main Menu, one to Collect the data and another to solve the problem. So first, let’s see the Main-Menu ..

```# Main Menu of the Project
os.system('clear')
print('\n',' '*5,'******************************')
print(' '*5,' ***','   Knapsack Problem','   '*1,'***')
print(' '*5,' ***',' '*22,'***')
print(' '*5,' ******************************')
print(' '*5,' 1. About Knapsack Problem.')
print(' '*5,' 2. Collect the Items.')
print(' '*5,' 3. Solve the Problem.')
print(' '*5,' 9. Exit.')

user_choice = input("\n   Select from the Menu: > ")

return user_choice
```

Above Menu will display three option that the user can select from:
1. About Knapsack Problem. [To give simple information about what is Knapsack Problem]
2. Collect the Items. [Will ask the user to Enter the Items and their coresponding Weights and Profits.]
3. Solve the Problem. [The user will Enter the Weight limit we have then we will Solve the problem]

Now we will write the Function to collect the Data from the user we will call it def collect_items(): the user will Enter the Item Name, the Weight and the Value or Profit and will save it in a list, then will return it as item_list. Here is the code and run-time screen.

After Collecting the Items, the user can select Number (3) from the Menu to Solve the Knapsack Problem. First we will ask user to Enter the Weights Limit we have, then calculating the Profit over Weight for each Items. In Knapsack we select the Items based on the Max w/p for each and store the indexs in a list, and with each selection we must not exceed the weight limits. Here is the code.. ..

So from the above example, we can achieve the Maximum Profit with weight limits to 50Kg if we take Full Amount of Item a, and Full Amount of Item b and 0.666666666 (0.67) amount of Item c.

1 * 60 = 60
1 * 100 = 100
0.67 * 120 = 80

60 + 100 + 80 = 240

NOTE: The Weight in Knapsack Problem can be weight in kg, or Number/Amount of the item (60 bags, 100 bags ..) or any Unit.

Have fun and do some coding .. 🙂 Follow me on Twitter..