#Group members:
| Name |
|---|
| Shaunak Sompura |
| Bharat Shankar |
Problem definition: Given N and k, find all k consecutive numbers starting at 1 and upto N such that the sum of squares is itself a perfect square.
Approach: The solution to this problem is achieved using the actor facility in F# and Akka.NET. Multiple child actors are spawned and assigned computational tasks using a single parent actor. This actor model decreases time taken to compute solution by carrying out tasks in parallel.
#Steps to run
-
Unzip the file and navigate inside the folder
-
Open Terminal
-
Run the following command: dotnet fsi --langversion:preview proj1.fsx 1000000 24
Output: [Prints first number of the sequence that forms a perfect square]
Real time: <real time> in ms CPU time: <cpu time> in ms Cores Used : <cores used in computation> (ratio of CPU time to Real Time)
#Size of work unit for each worker actor
• The work unit considered was k where a sequence of numbers of size k was given to each actor.
• The actor then squares each of those values of size k and adds it up.
• Another approach was to simultaneously square all the values from 1 to N by assigning it to actors and then sum up each sequence of size k parallelly.
• But this would take more time and space, since the boss would need to wait till all the squares are computed by workers and also needs space to store it.
• For an input of 1000000 it was found that dividing the work to 1000 actors where each actor received 1000 work units, used the most cores delivering the best performance.
• But when the input N<1000 we create only N actors and assigned 1 work unit for each actor.
• When 10,000 actors were spawned it was found to be more cumbersome to maintain this number of actors than perform the squaring.
For an input N=1000000 and k=24
| No. of Actors | Work Unit Received by each actor | Cores used |
|---|---|---|
| 1000 | 1000 | 4.84 |
| 10000 | 100 | 4.59 |
| 100000 | 10 | 4.08 |
#Result of running dotnet fsi proj1.fsx 1000000 4
There are no sequences of length k = 4 for n = 1000000
#Running time for n = 1000000 and k = 4
Real Time: 3800 ms
CPU Time: 18310 ms
Num of Cores: 8 Cores Used: 4.818421
#Largest Problem solved
N = 10^8 and k = 24
9
25
197
304
353
540
856
76
121
1301
2053
3112
3597
5448
8576
12981
20425
30908
35709
54032
84996
128601
202289
306060
353585
534964
841476
1273121
2002557
3029784
3500233
5295700
8329856
12602701
19823373
29991872
34648837
45863965
52422128
82457176
Real Time: 538246 ms
CPU Time: 2844720 ms
Num of Cores: 8 Cores Used: 5.285167
Note: Please refer Readme.pdf for screenshots