## Python: Random Pixel Color

**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.]

Last week I start reading and studying about “Image Processing”, in some point I was reading about converting an image to Array of numbers, and re-converting that Array back to an Image, at that moment popped into my mind what if we just generate an Array with random numbers and then show it as an Image.

In this article we will write a first simple Function to generate a random numbers presenting the three main color Red, Blue and Green; then storing the numbers in an Array then using matplotlib library to display the Image.

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

1. Jupyter-NoteBook.

2. numpy.

3. random.

4. matplotlib.

5. PIL or Pillow.

**Coding** I am user Jupyter NoteBook on samsung Tab S4. First we will do all imports we need as:

from PIL import Image

import numpy as np, matplotlib.pyplot as plt

import random

%matplotlib inline

Now, we will write a Function called rand_color, we will run a nested for loop to generate the Row and Column (width and height) and in/for each row we will generate thee numbers of colors range(0,255) as one pixel and storing them in an array, then we display the Array using:

Image.fromarray and plt.imshow(). Here is the Code ..

Run No.1 |
Run No.2 |

Run No.3 |
Run No.4 |

The above is just 25×25 image with random color pixels, this is the first function using default random, in coming posts we will use some Math variables [such: log,sin], constants [such: pi, golden ratio] to see if we can get a pattern from random.

..:: Have Fun with Coding ::.. 🙂

To Download my Python code (.py) files

Click-Here

By: Ali Radwani

## Python Sorting Algorithm – Heap Sorting -P5

**Learning : Python, Math, Algorithm **

** Subject: Sorting Algorithm, Heap Sort P5**

[

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.]

In Last Parts (2, 3 and 4) we wort the Following Functions:

- Sections Header.
- Main Menu Function.
- Entering/Creating the Array.
- Print-Out or to Display the Array.
- Check If Array in Max-Heap.
- Convert Array to Max-Heap.
- Add Node to Max-Heap.
- Delete a Node from a Max-Heap.

**I****n** this last part-5 we will write the last main Function to aplay the **Heap Sorting Algorithm.**

**Scope of Work:** Deleting a Node from a Max-Heap Array is the main function in sorting an Array using Max-Heap Algorithm, the Deleting is always from the Root Node, So if we delete the most top Node [Root] (and store it in index[0] in a temp_array) then we move the Last Node to it’s position and by doing that we miss the Max-Heap state of the Array, so we convert the array to a Max-heap, then we Delete the Root again until we delete all the elements in the Array.. Here the Algorithm:

Assuming we have a Max-Heap Array:

1. Delete the Root Element, and Store it in index[0] in Temp_array.

2. Move the Last Element in the Array to index[0].

3. If the Array not in Max-Heap then Convert it to a Max-Heap.

4. Repeat Steps 1 to 3 Until length of Array is 0.

In our list of Functions up, we have the three Functions we Need to complete/apply a Max-Heap Sorting:

We Delete a Node using def delete_node(arr,inside):

then in a while loop we call both

def check_if_max_heap (arr,inside): and

def convert_to_max_heap (arr,inside): so let’s see the code..

We finish Max-Heap Sorting Algorithm, ..

..:: Have Fun with Coding ::.. 🙂

To Download my Python code (.py) files

Click-Here

By: Ali Radwani

## Python Sorting Algorithm – Heap Sorting -P4

**Learning : Python, Math, Algorithm **

** Subject: Sorting Algorithm, Heap Sort P2**

[

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.]

In Last Parts (2 & 3) we wort the Following Functions:

- Sections Header.
- Main Menu Function.
- Entering/Creating the Array.
- Print-Out or to Display the Array.
- Check If Array in Max-Heap.
- Convert Array to Max-Heap.

**I****n** this Part-4 we will cover another Two important Functions that we need to talk about in our mission to understand the **Heap Sorting Algorithm.** In a Max-Heap Array we may need to Add new Node to the Array and we may need to Delete a Node. Also I just add Item No.7 style=”color:#2662ee;”>print(‘ ‘*5,’ 7. Start Heap Sorting.’) to the main-menu so we can do Heap Sorting to a given Array.

Starting with Add New Node, Simply we Add the Node to the end of the Array using arrat.append(new_node) then we need to Check If still the Array in Max-Heap If NOT, We MUST Convert it to a Max-Heap.

**Scope of Work** Ask the user to Enter the New Node Value, Add The Node to the End of the Array, in While Loop Call convert_to_max_heap (arr,True), check_if_max_heap (arr,True) as following:

while not is_max:

arr = convert_to_max_heap (arr,True)

is_max = check_if_max_heap (arr,True)

this will keep check and convert the Array to Max-Heap. Here is the Full code and run screen ..

Now we will write a Function to Delete a Node from the Max-Heap Array. Deleting a Node is just by removing the first node in the Array (Array[0]), then moving the last element in the Array to it’s position, by doing this we may not having a Max-Heap Array any-more, so we need to convert the array to a Max-Heap. In our application here, we will have a while loop and calling the functions (check_if_max_heap and convert_to_max_heap) until we have the Array in a Max-Heap. Here is the code ..

We will stop here in this part. In Part-5 we will Sort any Array using the Max-Heap Sort Algorithm.

..:: Have Fun with Coding ::.. 🙂

To Download my Python code (.py) files

Click-Here

By: Ali Radwani

## Python Sorting Algorithm – Heap Sorting -P3

**Learning : Python, Math, Algorithm **

** Subject: Sorting Algorithm, Heap Sort P2**

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.]

First let’s just remember that in Part-1 we wort the Following Functions:

- Main Menu Function.
- Entering/Creating the Array.
- Print-Out or to Display the Array.
- Sections Header.

**I****n** this Part-3 we will cover another Two important Functions that we need to talk about in our mission to understand the **Heap Sorting Algorithm.**

__First Function__

**Check If The Array is in Max Heap:** After the user Giveing/Entering the Array [Selecting Option 1 in the Menu] we need to Examen/Check if it is in a Max-Heap, to do so we will call the Function def check_if_max_heap(arr, inside): the Function will take Two arguments:

arr : The Array.

inside: Boolean Flag showing are we calling the Function from within another Function or Not.

**Scope of Work:** We will check and compare each Node [__starting from last node in the leaves__] with it’s Parent using this formula parent_index = ((child_index-1)//2) to get the parent index, then comparing the Values of the Child and Parent, If the Child is __GRATER Than__ his Parent we SWAP them. Then going to the Next Child and so-on until the Root-Node. .. Here is the Code ..

for each print statement I am using this code __if not inside :__ then print ..

**Example:** if not inside : print(‘\n The Array is a Max-Heap Array.’)

So if the **inside = True ** then the print code will not work, that’s mean we are calling the Function from inside another function and we just want the return value, the return here will be a boolean True/False as is_max [if the array is in Max-Heap].

__Second Function__

**Convert to Max-Heap:** In this Function we will convert a given Array to a Max-Heap Array. The way this Function is working is by checking/Examining all the Childs starting from the Leaves, and if any Child is Grater than his Parent we do a SWAP. After we Finish, we will call the Function def check_if_max_heap(arr, inside): to check if the Array is in Max-Heap, If NOT we will call the convert Function and so-on until we get the is_max = True from the def check_if_max_heap(arr, inside):. Both Functions def check_if_max_heap(arr, inside): and def convert_to_max_heap (arr,inside): will be run in a while loop until def check_if_max_heap(arr, inside): will return **True.** .. Here is the code for **def convert_to_max_heap (arr,inside):**

And here is the while loop to keep Examining the Array until fully converted to a Max-Heap Array.

# While loop in Option 3 from the Main-Menu, In the main body code.. while not is_max: arr = convert_to_max_heap (arr,True) is_max = check_if_max_heap (arr,True)

We will stop here in this part. In Part-4 we will Add new Node to the Array, and Delete a Node from the Array.

..:: Have Fun with Coding ::.. 🙂

To Download my Python code (.py) files

Click-Here

By: Ali Radwani

## 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 ADDany 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:

- Main Menu Function.
- Entering/Creating the Array.
- Print-Out or to Display the Array.
- Sections Header.

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.. def main_menu(): os.system('clear') header() print("\n\n"," "*4,"==============[ Main Menu ]==============\n") 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 : user_select = main_menu() 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.') #add_node(arr) 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 ..

**I****n** 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') header() 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 ::.. 🙂

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.- 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 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 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 … 🙂

To Download my Python code (.py) files

Click-Here

By: Ali Radwani

## 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 ADDany 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 def main_menu (): os.system('clear') print('\n',' '*5,'******************************') print(' '*5,' ***',' Knapsack Problem',' '*1,'***') print(' '*5,' ***',' '*22,'***') print(' '*5,' ******************************') print('\n',' '*5,"==========[ Main Menu ]==========") 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.

**A**fter 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 .. 🙂

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By: Ali Radwani