Heap's Algorithm implementation with python

Heap's Algorithm is used to generate all the permutations of a given object. It was first proposed by B.R. Heap in the year 1963.

In this post, we will write a program using Heap's Algorithm which will generate permutations for a given object. Remember that the object should be iterable. Otherwise, you will get an error.

If you don't know what permutations is all about then you can visit some of the following websites:

Permutations - Wikipedia
Permutation - Wolfram math
Permutations and combinations - Math is fun and
Permutations Khan Academy

Here goes the program:
This function will take an iterable object as input and will generate all the permutations possible with the items in the object.
For example, if the input is:heap(["A", "B", "C"]) then the output will be a generator object. You can use a for loop to iterate over this object to see the output.
But remember that if you have any duplicates in the input(Ex: heap(["A", "B", "B"])) then you will also get duplicate permutations. (Ex output: [["A", "B", "B"], ["B", "A", "B"], ["B", "A", "B"], ["A", "B", "B"], ["B", "B", "A"], ["B", "B", "A"]])

You can eliminate duplicates by using python sets.

One of the best ways to understand this algorithm is by looking at the pseudo-code on Wikipedia Heaps Algorithm page.

We have used the nonrecursive method.

If you are not sure of what yield does, then you can have a look at this answer on Stack overflow by e-satis for the question What does the "yield" keyword do

If you use the above code and if you give a string as an input still you will get a list as output. To overcome this problem I have written a program, a slightly modified version of the above program so that we will get the output as a string.
The program is as follows:
The above program will take a string as input and will give a generator object as output, which on further iteration will give you a list of strings.

Line 14 is just swapping of the characters a[0] , a[i] in the string.

Line 16 is again swapping of the characters a[i], a[c[i]] in the string.

As we are doing string concatenation with more than two strings, the second program takes more time for execution than the first one.

If you have any doubt or didn't understand anything, then you can comment in the comment box below and I will be glad to help you.

If you have any suggestions or if you have found any typo then please comment in the comment box. I will be very happy to see your comment.

You can also contact me.

Thank you. Have a nice day. 😃

Making a quiz web app with python and flask

Edit : When you are creating a web app with h tml templates, then y ou will have to sa ve the html file in templates folder in the Current Wor ki ng Directory( CWD). If you save the file in the C W D directl y you will get a TemplateNotFound error. Thank you Udhay for pointing it out. In this post we will create a quiz website using python . I will be using the flask framework . After reading this tutorial you will learn form submission , flask templates , python code in flask templates , shuffling the questions and options with the random module and few others. Please note that this tutorial is not big as it seems to be. Some of the code has been rewritten to maintain consistency and also font size is somewhat big so that your eyes won't get stressed reading this tutorial. Also the content has not occupied the full width of the page. In this tutorial I am assuming that you are having a very basic understanding of the flask framework . Please refer the documentation

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Largest product in a grid In the 20×20 grid below, four numbers along a diagonal line have been marked in red. 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40 04 52 08 83 97 35 99 16 07

Problem 60 Project Euler Solution with python

Prime pair sets The primes 3, 7, 109, and 673, are quite remarkable. By taking any two primes and concatenating them in any order the result will always be prime. For example, taking 7 and 109, both 7109 and 1097 are prime. The sum of these four primes, 792, represents the lowest sum for a set of four primes with this property. Find the lowest sum for a set of five primes for which any two primes concatenate to produce another prime. This problem is j u st a brute force problem. If you have come here because you don't know the limit upto which you will h ave to gener ate the prime numbers t hen go ahe ad and t r y with 10,000 . When I first start ed solving the problem I chose 1 million(beca use most of the problem s on project E uler have this limit ), but it took very long for the computer to fin d the solution. After searching on the internet then I found many people choosing 10, 000 so I have changed my in put f rom 1 million to 10000 and the output was f ast. He

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