Best Case, Worst Case and Average Case Analysis of an Algorithm (With
Notes)
CodeWithHarry
To define an algorithm, To define the events in the life of an algorithm
, We have , Best Case Worst Case and Expected Case. And along with that,
I 've packed one more thing into this video : The definition of Log. If
you watch this video till the end , Then you will find out what this 'Log
' really is. 1. . . 5. . . 7. . . 9 and 24 are the numbers in it; They
're in ascending order , You can see for yourself. If you know even a bit
of maths, You 'll know that it is in an ascending order. Now what I say
is that I 'll give a number : 'A' And I 'd like you to tell me If this
number exists within the array , or not. Suppose the value of A is 8. So
what will be your answer ? Yes. Meaning 1. If A is. . . Sorry, your
answer will be no , because it is n't there. If the value is 9, What will
the answer be ? Your answer will Algo 1 is a simple person. It does n't
have much of a brain. It is comparing it with all the numbers. Is this
the best way to do this work ? Obviously not. Because Algo. 1 is lucky ,
He will get A=1. It will tell us in the first comparison itself. In one
comparison only.
If Algo 1 is in luck, The time needed is ' k ' - T=k. This means that it
does n't depend on 'n '. Take a 10-element array, take a single element
array or take a 10,000 element array. It only has to make one comparison
because it is only searching for the first element in the array. Now,
AlGo 1 's luck is bad. Till now, he was fortunate ; But now he 's not so
lucky anymore. Average Case complexity is equal to. . . the sum of the
run time for the total number of possibilities. The O ( Sum of all
possible run times divided by the number of possibility ) is O ( n ) The
average case complexity is the sum. Average Case is equal. to. . . The
sum of all. possible run. times divided. by the total. number of possible
run time. So for an array size of 5, We saw six cases. 't ' ; I 'll
calculate ' O ' later. n+1 If 'n ' is the size of the array , Then there
is 'n+1 '' number of possibilities. 'n' possibilities is when there is
1st element, 2nd element, 3rd element, 4th element, 5th element and 6th
element. If the element is here, How many comparisons will it have to
make ? It will have to do. . . 1. . . 2. . . 3 comparisons. I 've taken '
k ' as common out of everything. I removed this because this is
different. And this I have added separately.
K is an integer ) SO now I 'll write it like this K n ( K is an integer )
So now I 'll write it Like this K n ( K is an integer ) So now I 'll
write it like this. K n ( K is an integer ) And now what will happen? The
value of 'k ' will become very large And so 2n will be going down. The
graph of ( n^2+n ) ; graph of n ; graph of ( N^2+n ) will go below 2n.
THe Average Case Complexity for a given algorithm is the time it takes to
run through all possible cases, divided by the total number of
possibilities..?" This passage discusses Algo 2, which is a cunning
person who is smart. Birbal. Algo 2 says that he will not make useless
comparisons, and provides an example. An example of how he does this..
Algo 2 first takes the first and last element of an array, and then
compares them. IF. They match, Algo 2 is good; if they don't match., Algo
2 will find the mid--point of the array and be okay..
AP is Arithmetic Progression and GP is a geometric progression. AP is
used in 'O ' a lot. APs are made as well as GPs sometimes. When there are
questions on 'O' APs and GPs are used in the answers to questions on O.
The formula of Average Case Complexity is All possible run times divided
Notes)
CodeWithHarry
To define an algorithm, To define the events in the life of an algorithm
, We have , Best Case Worst Case and Expected Case. And along with that,
I 've packed one more thing into this video : The definition of Log. If
you watch this video till the end , Then you will find out what this 'Log
' really is. 1. . . 5. . . 7. . . 9 and 24 are the numbers in it; They
're in ascending order , You can see for yourself. If you know even a bit
of maths, You 'll know that it is in an ascending order. Now what I say
is that I 'll give a number : 'A' And I 'd like you to tell me If this
number exists within the array , or not. Suppose the value of A is 8. So
what will be your answer ? Yes. Meaning 1. If A is. . . Sorry, your
answer will be no , because it is n't there. If the value is 9, What will
the answer be ? Your answer will Algo 1 is a simple person. It does n't
have much of a brain. It is comparing it with all the numbers. Is this
the best way to do this work ? Obviously not. Because Algo. 1 is lucky ,
He will get A=1. It will tell us in the first comparison itself. In one
comparison only.
If Algo 1 is in luck, The time needed is ' k ' - T=k. This means that it
does n't depend on 'n '. Take a 10-element array, take a single element
array or take a 10,000 element array. It only has to make one comparison
because it is only searching for the first element in the array. Now,
AlGo 1 's luck is bad. Till now, he was fortunate ; But now he 's not so
lucky anymore. Average Case complexity is equal to. . . the sum of the
run time for the total number of possibilities. The O ( Sum of all
possible run times divided by the number of possibility ) is O ( n ) The
average case complexity is the sum. Average Case is equal. to. . . The
sum of all. possible run. times divided. by the total. number of possible
run time. So for an array size of 5, We saw six cases. 't ' ; I 'll
calculate ' O ' later. n+1 If 'n ' is the size of the array , Then there
is 'n+1 '' number of possibilities. 'n' possibilities is when there is
1st element, 2nd element, 3rd element, 4th element, 5th element and 6th
element. If the element is here, How many comparisons will it have to
make ? It will have to do. . . 1. . . 2. . . 3 comparisons. I 've taken '
k ' as common out of everything. I removed this because this is
different. And this I have added separately.
K is an integer ) SO now I 'll write it like this K n ( K is an integer )
So now I 'll write it Like this K n ( K is an integer ) So now I 'll
write it like this. K n ( K is an integer ) And now what will happen? The
value of 'k ' will become very large And so 2n will be going down. The
graph of ( n^2+n ) ; graph of n ; graph of ( N^2+n ) will go below 2n.
THe Average Case Complexity for a given algorithm is the time it takes to
run through all possible cases, divided by the total number of
possibilities..?" This passage discusses Algo 2, which is a cunning
person who is smart. Birbal. Algo 2 says that he will not make useless
comparisons, and provides an example. An example of how he does this..
Algo 2 first takes the first and last element of an array, and then
compares them. IF. They match, Algo 2 is good; if they don't match., Algo
2 will find the mid--point of the array and be okay..
AP is Arithmetic Progression and GP is a geometric progression. AP is
used in 'O ' a lot. APs are made as well as GPs sometimes. When there are
questions on 'O' APs and GPs are used in the answers to questions on O.
The formula of Average Case Complexity is All possible run times divided
