Question

We have packaged the four algorithms TwoSumFast and TwoSum, in a jar file that you can download from (https: //github.com/idl020/lab2-runningtimes/blob/master/runningtimes.jar? raw=true). Also, a simple program has been added to measure the execution |time of each of the algorithms for some given input. For example, if you want to measure the time taken by TwoSum for a file of 1000 numbers, you should run > java -jar runningtimes.jar 2sum 1000 1000 0.006 The program prints back the input size which is 1000 and the time taken which is 0.006 seconds. Estimate the amount of time it would take to run TwoSumFast and TwoSum, on your computer to solve the problems for a file of 1048576 numbers. Notice that measuring the execution time is not feasible for all points, so you have to think about predicting time for those point you can't measure. Answer with at least 50 words to explain which of the alternatives are correct: a) miliseconds or seconds b) minutes or hours c) hours or days d) days or months e) years

Answer 1

Two sum The 2sum algorithm was checked with running a sum of variable number of elements and 5 observations were recorded. 1st Run on total 1,000 elements -- time taken to complete the process - 0.013 seconds 2nd Run on total 5,000 elements -- time taken to complete the process - 0.025 seconds 3rd Run on total 10,000 elements -- time taken to complete the process - 0.126 seconds 4th Run on total 15,000 elements -- time taken to complete the process - 0.236 seconds 5th Run on total 20,000 elements -- time taken to complete the process - 0.453 seconds Now, studying the pattern it was found 0.025 = 1.92 x 0.013 0.126 = 9.69 x 0.013 0.236 = 18.15 x 0.013 0.453 = 34.84 x 0.013 Hence studying the above pattern the time can be calculated as approximately => 2n+1 0.013 -----------------------------where n = total elements / 5000 Hence calculating for 1,048,576 elements n = 1048576 / 5000 = 209.71 = 210 approx Putting the value of n in in the formula we get, ( 2( 210 + 1 ) ) . ( 0.013 ) ( 2211 ) . ( 0.013 ) 4.2783 x 10^61 seconds Changing into hours 1.1884 x 10^58 hours Now changing hours to days we get 4.9517 x 10^56 days Now changing days to years 1.3566 x 10^54 years to complete. Hence it would take years to complete the summation using the algorithm 2sum. C:AWINDoWS system32\cmd.exe UsersUser Desktop>java -jar runningtimes-jar 2sum 1000 Users User Desktop java -jar Users User Desktop java -jar runningtines.jar 2sum 10000 000 0.013 runningtines.jar 2sun 5 000 000 0.025 0000 0.126 C:\Users\User\Desktop>java -jar runningtines..iar 2sun 15000 5000 0.236 NUsers User Desktop>java-jarr 00000.453 runningtines.jar 2sun 2 0000 Users User Desktop>

2sumfast This algorithm's time is not increasing exponentially, rather it's increasing by a fraction of 10. On running this algorithm for few observations it was found it took less than a second to sum the 10,000,000 elements. Look at the findings below.

C:\Users\User\Desktop>java -jar runningtimes.jar 2sumfast 1000 1000 0.007 C:\Users\User\Desktop>java -jar runningtimes.jar 2sumfast 5000 5000 0.013 C:\Users\User\Desktop>java -jar runningtimes.jar 2sumfast 10000 10000 0.022 C:\Users\User\Desktop>java -jar runningtimes.jar 2sumfast 15000 15000 0.03 C:\Users\User\Desktop>java -jar runningtimes.jar 2sumfast 20000 20000 0.034 C:\Users\User\Desktop>java -jar runningtimes.jar 2sumfast 100000 100000 0.089 C:\Users\User\Desktop>java -jar runningtimes.jar 2sumfast 1000000 1000000 0.353 C:\Users\User\Desktop>java -jar runningtimes.jar 2sumfast 1048576 1048576 0.395 C:\Users\User\Desktop>