This document analyzes the running time of an algorithm using pseudo code. It breaks down the algorithm into three nested loops: an inner while loop, a middle for loop, and an outer for loop. It calculates the running time of each loop level and derives that the overall running time of the algorithm is O(n^3).

1. Calculating
Running Time Of
Algorithm

2. BY: Adeel Rasheed
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 https://www.slideshare.net/adeel02

3. Pseudo Code
 For i  1 to n
 Do for j  1 to 2i
 Do k = j
 While(k ≥ 0)
 Do k = k – 1

4. While Loop
 Let I() Time Spend in while loop
 While(k ≥ 0)
 Do k = k – 1
I(j) = 𝑘=0
𝑗
1 = 𝑗 + 1

5. Middle For Loop
 Let M() be the time spend for for loop
 Its running time determined by I
 Do for j  1 to 2i
M(i) = 𝑗=1
2𝑖
𝐼(𝑗)

6. 2
1
2
1
2 2
1 1
2
M(i) = ( )
M(i) = ( 1)
M(i) = 1
2 (2 1)
2
2
2 3
i
j
i
j
i i
j j
I j
j
j
i i
i
i i


 



 
 


 

7. Outer For Loop
 T(n) be the running time of entire algorithm.
 For i  1 to n
T(n) = 𝑖=1
𝑛
𝑀(𝑖)

8. 2
1 1
2
1 1
3 2
3 2
3
T(n) = ( ) (2 3 )
2 3
2 3 ( 1)
2 3
6 2
4 15 11
6
( )
n n
i i
n n
i i
M i i i
i i
n n n n n
n n n
n
 
 
 
 
  
 
 

 
 
 