Hello guys and welcome to Python programming tutorials by Amuls Academy.
In the previous two tutorials we discussed about how we can sort the numbers using Quicksort
algorithm, today in this tutorial we are discussing about the Quicksort algorithm as well as we
will write the program.
So first algorithm and to understand this tutorial you need to watch the previous two
tutorials OK so the first step is, select the pivot element so it can be first element
or last element or you can choose randomly but select the pivot element.
Second step is, find out the correct position of the pivot element in the list by rearranging
it, so we will compare other values with the pivot element and we will find out its original
place right this is about the that step.
Next step is divide the list based on the pivot element, once we found out the original
place of the pivot element then we will divide the list right?, left sublist and right sublist
ok, so we need to divide the list.
And next step is, sort the sub list recursively, we will use the same step to sort the sub
list that is, in that we will take the pivot element and we will find out its correct position
OK we will do it recursively ok.
So these are the steps .
so next we will write the program Ok actually we will use three functions ok in this program,
see the first function and second function these are the user defined function next we
will use the main function ok to take the input as well as to print the input output
ok. so here in the first function, this function
is to find out the correct position of the pivot element ok so in this function we will
find out the pivot element correct position and in the second function we will divide
the list based on the this pivot element ok and we will sort the sub list recursively
ok here we can see the recursive call in this second function ok, so we need to define two
functions in this program.
so first we will define the first function that is the function to get the correct position
of the pivot element ok so we need to define a function, so for that i will use "def"
keyword next followed by the function name so here you can give any function name but
using the proper function name will help to understand the program ok if any other user
will refer your function then he will get to know what that function actually will do.
ok so here this function is to find out the original position of the pivot element ok,
so i'll take "pivot_ place" as the function name, you can take any name ok if
you want here i'll include the comment also like, ok so this function is to get the correct
position of the pivot element see the original place of the pivot element ok.
so next here inside this function i need 3 parameters here ok so first one is the list
the entire list, whatever the input because to get the pivot element first i need list
right?.
next i need two more parameters that is first and last, i'll take name as "first" and
"last" these are the index ok so from where to where.
So this first and last parameter will tell the length of the list, whether we are applying
this function on the full list ok or on the sublist that will be get to know from these
two parameters it will tell the length of list OK.
so the "first" will be the starting index and "last" will be the last index of the
list ok. next so what is the first step.
we need to take the pivot element right?, select the pivot element.
so first in this program i'll take the first element as the pivot element ok.
so what i will do is, i will take a variable called pivot and here i'll take "list1"
that is the list name and here i'll take first, "list1 of first".
Why because it is the index of the first value ok, and here list name is "list1" so i
took "list1 of first", that means the first element is pivot now alright.
So next i need to take left and right value, two more index to compare the values right?,
here in the example here we can see i took the first element as pivot.
Now i want left and right, here in this example "0 is first" and "five is last" value
ok. so i took, this list name is "list1" so
"list1 of first" means we will get 56 ok.
so now i want left Value, left value i want one, right value 5 ok so what i'll do is,
i will take left as "first plus one" ok and here i'll take right at last correct right.
Here we can see this is last and this is "first plus one" ok zero is first here, so we want
left as one that is nothing but "first plus one".
so next i have left now, right now, and pivot, so now what i need to do?, i need to check
this condition right?, i need to check each and every value with the pivot value, i need
to compare that ok. so first condition is this right?, "left
should be less than or equal to right" if it is true then i will go for the next condition
that is, "a of left" is less than or equal to pivot, here list name is list1, so "list1
of left is less than or equal to pivot". so here first i will check "26 is less than
or equal to 56", if it is true then i need to move to the next value.
I need to check next value is less than or equal to pivot ok so here we are checking
the same condition for different value, so we will check whatever the value present in
the left index is less than or equal to pivot again and again until the condition become
false right?, so for that in the program we will use loops, we want to use the same condition
again and again for different values ok so here i have condition, these are the conditions
so I'll take while loop ok here.
so I'll take while first one is "left should be always less than or equal to right",
ok i need to check this condition every time, next condition is, "and" and means logical
and ok so i will check "list 1 of left" ok should be less than or equal to pivot value
ok so this is the condition right?, first condition ok so i need both of this condition
need to be true ok that's why i took "and" here.
if anyone of this condition is true then i don't want to execute it's body.
so if it is true then i need to increment left by 1 .
So here we can see first i will check 26<=56 right?,so before checking this condition i
will check whether left <= right ok, it is true, 1 <= 5, so that is true, that's why
i will check this condition whether 26<=56, if it is true then i need to move to the next
value right?, so left will point here, so i need to increment left . so here i did that
ok.
If this condition becomes true then i will increment the left by 1 ok.
if any one of this condition become false, i need to come out of this loop ok.
So when this condition become false i will go to the right side, and i will check the
values right?.
Here so first i will check, 26 <= 56 it is true, so i will check 93 <= 56 no it is not
right?, if it is becomes false i will stop here, and i will go to the right side and
i will check the value, now 44 >= 56 this condition, so i need to take the while loop
for that now.
So while here also "left should be less than or equal to right", ok first i will
check this condition, and if it is true then "list1 of right" the whatever the value
present in the right index should be greater than or equal to pivot, so we are writing
the program for ascending order ok so for this this condition.
Now i will do is right is equal to right minus 1.
Here this condition become true ok when, if the value present in the right side is greater
than pivot then i will move to the next value ok so that means i will move this way right?,
that's why I took right = right - 1.
Here 1 index become less that's why.
So if this condition become false then i will stop there only ok.
So next here this while loop become False in two condition OK when this condition become
false here in this loop, in this loop this condition ok.
at that time this loop can be become false or when this become false ok in any cases
this two loop can become false and control come out of this loop right?.
so now i need to write the condition for that, so i will take if condition and check when
"right value become less than left" what will happen.
so i told you in every condition here, "left should be less than or equal to right" here
also left should be less than or equal to right.
what if right become smaller than left, left become greater than right, what will happen
ok so if you remember in the previous tutorial i told you, if this happen then we need to
stop everything and now we got the correct position of the pivot element.
we need to swap now so what we need to do, we need to swap pivot and the value present
in the right index, why right index because if we take the pivot as the first element
then we need to swap right index value, if you take last element as the pivot then we
need to swap left index value i explained you about this in the previous tutorial right?.
so now we need to do this, so we need to swap pivot and the value present in the right index
ok so to swap we can use many methods ok so here I'll write in a single line.
So here i will write "list1 of first", "list1 of right" is equal to "list1
of right", list1[first].
So here list1[first] is nothing but pivot, here we can see right?,
and "list1 of right" is the value present in the right index, so now if you ask why
I am writing "list1 of first", instead of writing pivot, here we want to swap the
numbers in the list ok if i write pivot here it won't do the changes, i want to change
the value present in this first index and right index ok, i want to change the values
in the list itself that's why here i am writing "list1 of first".
if you write pivot here instead of "list1 of first" you won't get the proper output
ok. so for now, so if i took if then i will take
else also, so here ok first i'll check this condition, "left is less than or equal to
right", and "list1 of left " is less than or equal to pivot, if both this condition
is true, i need to increment left and i need to check the next value with the pivot and
if this condition become false if any one of this condition become false i will go here
and i will check this condition ok if both this condition become false, if the control
come out of this while loop, then we will execute this if condition.
So i will check, so why control came out of this while loop, whether because of this condition
fails, or this condition fails ok so here i check that.
Ok then what happens if this condition become false in this and this condition become false
in this while loop that is, this case ok . so this is the left first initially ok i'll
check "26 is less than or equal to 56" yes it is true.
So now i will point towords this value, so I'll check whether "93 is less than or equal
to 56", no right?, so i'll stop here.
I will go to the right side and I'll check whether the value present in the right index
is greater than or equal to 56, no it is not, so I'll stop here ok.
so in this condition we stop the both the while loop, ok in the program the first while
loop stops because here and next while loop fails because here this condition become false
.
In the program this condition became false first and here this condition become false
ok so i'll come out of this 2 while loop and i will check this condition whether "right
is less than left", so here check "right value is 5" and "left value is 2", No
this condition is also false right here right is 5, it is greater than left ok so this condition
satisfies.
so control won't go here, it will go to the else part,then what we need to do?, we
want to swap the value present in the left index and right index right?, so here i need
to do that, ok here in the else part i need to swap the value present in the left index
and right index, if you are not comfortable with this way you can go for that three variable
method you can take a temp variable and you can swap OK.
Here ok, we swap this 93 and 44 ok in the program, so now what i need to do, again i
need to start from the beginning right?, i need to check the value present in the left
index, i need to do this same thing again ok again i will do ok so i want to execute
this part of code again and again so i need to place this in a loop ok.
so that is because here we can see once, if i, so here 44 will come here right?, so 93
will go here ok now what i will do again i check the value right?, so i will check first
this condition whether the "left is less than or equal to right" next I'll check
value present in the left is less than or equal to right, again i will do the same thing
ok so if i want to do that again and again until this condition become false right?,
so i need to do this again and again, so what I'll do is, i will place this piece of code
in a while loop ok so first i will do is, i will cut this and here I'll take a while
loop. so I'll take while True this as the condition, so place that in the,
indent it correctly ok, ok so now i took a while loop and i place this code in the while
loop ok.
now i need a condition within this while loop body to come out of this loop right?, so now
it is infinite loop it will continuously execute because while True means it is always true.
So now i need some condition to come out of this loop ok so i want to make it finite so
what i will do is, here if this condition become true when "right becomes smaller
than left", then i need to stop everything right?, so here i need to check this condition
again and again till this condition become false so what i will do is, if this condition
become true i will cut this and here i'll write break, so that means come out of the
loop ok next here outside the loop i will execute that code.
so what i did now, so if this condition become true then i will come out of this loop and
I'll swap the value present in the first index and right, that is nothing but pivot and the
value present in the right index.
So In this example, so so i will check whether "44 is less than or equal to 56" true,
so I'll go to this 17, so "17 is less than or equal to 56", true so i will again go
to 31, " 31 is less than or equal 56" true again i'll go to 93, i will check whether
"93 is less than or equal to 56" no right?, so this condition becomes false so i will
stop here only.
So i will goto the right side now so right is here, so it will check whether "93 is
greater than 56" true, so it will go to the next value, left is greater than right,
right is "right value is 4", "left value is 5" so this condition become false, ok
if this condition is become false, so i need to stop everything now i need to swap the
value present in the first index or pivot value and the value whatever the present in
the right index right?, so that's what we did here ok .
so when this condition become true I'll stop everything that's why here i wrote break it
will come out of the loop and here i will swap the value present in the first index
that is pivot and the value present in the right index ok.
And next i want to return some value from this function ok we came to the end of this
function so here I'll return right index, the index where pivot element is present now,
ok here i need to swap 56 and 31, so this is the right index right?, after swapping
56 will come here, 56 will present in the right index so we got the correct index of
the pivot element, so we get to know where actually pivot element should be present ok
so that's why i return right here ok so done with this one function.
so now i need to write the 2nd function, so next function is to divide the list and for
the recursive call.
Here I'll take define here I'll take the function name as quicksort itself ok if you want you
can change, here also i want first last ok parameters are same here.
first thing what i will do is, I'll call this pivot_palce function, this function, so to
divide the list i want the index of the pivot element ok, it will return that, that's why
I'll call that function now here.
so I'll take one variable called "p" it will hold the return result and here I'll
call pivot list1 first last ok, this is the function call to this function, so this will
return the index ok where the pivot element is present that will be stored in this variable.
Next what i will do is, i'll divide the list ok, how?, i'll call , i will recursively solve
that list so here I'll take list1, here you can take the index as zero or you can go for
first and here i will take p -1 ok next, p plus one to last.
Ok if you ask how i divided this like this, so I'll explain you so here i need to swap
31 and 56 right?, so 31 will come here, 56 here.
this is the right that's why i return the index of 56 now what i need to do is, so now
i got the actual index of the pivot element, ok that is this 4 .
4th index pivot element is present and it is the correct position of this pivot element
now i need to divide this right?, so how i will divide it,
So 31 26 44 and 17 and here the 2nd sublist is, only 1 element 93 .
Ok so here 0 1 2 3 56 and here from 5 , ok so here this is the
one sublist, here we can see the starting index that is zero and the ending index that
is 3, that is nothing but 4-1, what is 4?, 4 is the index of pivot element that is called
"p" in our program . So here i took p-1, 0 to p-1, or first to
p-1.
Here what is 5, 5 is p+1 so p+1.
That's why in this program first i took list1 first and p-1 this is one sublist that
is left sublist.
next here list1 p+1 last, the next sublist, right sublist ok.
So it will do the work recursively and next here this function is the recursive function
right?, here we can see the function call inside this function body also, so whenever
we write the recursive function we will write two case right?, that is base case and recursive
case, base case will be the stopping condition and recursive case contains the recursive
call, so here we can see the recursive case that is we can see the recursive call.
but where is the base case?, here what is the stopping condition for this Quicksort,
when we get a list with single element right?,in the previous example also i explained about
this, when we will get the single element in a list we will stop that, so here that
is the condition, that is the base case, here we can take like this OK so the condition
is when "first index is equal to last index" that is if it contains single element then
the first is also this, last is also this right?, first index is the starting index
and last index is the last index of the list, so if both are same then we need to stop ok.
no need to do anything we need to stop, if first is smaller than last, then we need to
do this recursive case ok, here because in the base case we don't need to do anything,
that is when "first is equal to last" here we don't want to do anything, that's
why here i take the condition like this, here i will take if condition and here i will check,
ok if "first is less than last", then only execute this code , that is partition
the list and and solve that sub list recursively OK when a list contains single element then
no need to execute anything stop everything ok so here base case is when "first is equal
to equal to last" or when "first becomes equal to last" ok that time no need to do
anything that's why i didn't write the condition here.
ok so this is the recursive case and also this function is not returning any value to
the main function where we will call this function because in this program we are not
getting any new list ok we are sorting the original list itself ok that's why we are
not returning any list or value to the main function.
Next i need to take main, here you need to take the input, you can take the user input
or you can directly take the input like this ok so i will enter few elements.
Next what I'll do is, I'll call the quick sort function ok so this function and here
i will pass the list1 and i need to mention the first and last index ok.
so first index will be zero always and the last index will be length of list1 - 1.
Here in this case, here we can see 0 1 2 3 4 5 ok i want to write 5 here, so what is
5?, it is length of list1 - 1 right?, So if i take length of list1 i will get 6, because
the index will start from zero so here i want 5, so i will write n-1 ok so next print list1.
so here this function is not returning anything because here so we are modifying the original
list itself.
So now if i save this and run this, 17 26 31 44 56 93 these are all numbers are in the
ascending order So if you want descending order then just
change the symbol here, ok here go for greater than or equal to, here less than or equal
to.
93 56 44 31 26 17 all the numbers are in descending order now.
And remaining everything i will explain in the next tutorial, so that's it for now
guys thank you for watching don't forget to subscribe to my channel i will meet you
in next class till then take care.
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