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Commit ef80bb1d authored by hdd29's avatar hdd29
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Q1:
in the table, wherever stated f(n) = xxxx, it means the data in that line is T(n) /f(n)
T(n): seems to be increasing til infinity --> bound below loosely by a constant
f(n) = n: T(n)/n seems to be increasing to infinity --> it is bound below loosely by a line
f(n) = n^2: it is moving towards 0, although it did slows down but the trend is unlikely to reach a constant --> can say that it is bound above lightly by n2 although tighter than n^3
f(n) = n^3: seems to be decreasing too --> bound loosely above by a n^3 function
f(n) = nlog(n) seems to be the one with trend approaching a constant fastest ==> can say that T(n) grows similarly to a nlog(n) function
n T(n) f(n)=n*10^5 f(n)=nlog(n) f(n)=n^2*10^9 f(n)=log(n)*10^5 f(n)=n^3*10^6
1000 0.1900 19.0000 27.5053 190.0000 2750.5317 19.0000
10000 2.2400 22.4000 24.3205 22.4000 24320.4910 0.2240
20000 4.1100 20.5500 20.7503 10.2750 41500.5318 0.0514
30000 5.8000 19.3333 18.7539 6.4444 56261.7774 0.0215
40000 7.9000 19.7500 18.6380 4.9375 74551.9705 0.0123
50000 11.2200 22.4400 20.7398 4.4880 103698.9826 0.0090
60000 14.2600 23.7667 21.6019 3.9611 129611.6215 0.0066
70000 15.0400 21.4857 19.2589 3.0694 134812.3186 0.0044
80000 20.8100 26.0125 23.0407 3.2516 184325.9698 0.0041
Q2:
f(n) = n gives the numbers of swaps goes to nfinity as n goes to infinity ---> it is a lower bound
f(n) = nlog(n) was pretty close to being the theta to T(n) but it still has the decrease trend --> upper bound but much tighter than n^2
f(n) = n^2 decreases fast towards 0 --> loose upper bound
f(n) = log(n) increases --> lower bound
n T(n) f(n) = n f(n) = nlog(n) f(n) = n^2 f(n) = log(n) f(n) = n^2log(n)
1000 3425457 3425.457 1141.819 3.425457 1141819 0.168930947
10000 45721062 4572.1062 1143.02655 0.45721062 11430265.5 0.114387598
20000 98107982 4905.3991 1140.517296 0.245269955 22810345.92 0.057025093
30000 153522280 5117.409333 1143.013343 0.170580311 34290400.3 0.038183995
40000 210173451 5254.336275 1141.735719 0.131358407 45669428.78 0.028994489
50000 265180908 5303.61816 1128.676743 0.106072363 56433837.15 0.022509831
60000 319847373 5330.78955 1115.65944 0.088846493 66939566.42 0.018502093
Through these 2 tables, the data still show that the quicksort program still grows most similar with theta(nlog(n)) despite the differencce in the method of comparison: time measurement and counting number of swap function calls.
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