The following is the output for msa.msa_brute_force() and msa.msa_divide_and_conquer.
Based on columns 2-4 from the data below, which of these data are consistent with the asymptotical upper bound for both of the algorithm msa.msa_brute_force()? Explain.
Answer the same question for msa.msa_divide_and_conquer().
Function msa.msa brute force() - processing datasets of size 20 through 400 (1000 runs for each dataset): elapsed / (size*size) elapsed / (size*1g(size)) elapsed size 20 0.025443946000000002005681 40 0.0933760649999999942094 60 0.199213226999999992727908 80 0.344574571000000051679280 100 0.549476846000000018754861 120 0.769533824000000032938829 140 1.036276152999999755621729 160 1.333768207999999511059741 180 1.705562632000000355958491 200 2.095818303999999798747922 220 2.557570097999999347848643 240 3.016954504000000980568075 260 3.800959146000000288267984 280 4.327605926000000380327037 300 5.108909404999998571383912 320 5.680534136999998651162969 340 6.397010897000001250489731 0.000294358738061 0.000438638324941 0.000562092762048 0.000681308308613 0.000827045062844 0.000928461480300 68 0.000058360040625 0.000055337007500 0.000053839776719 0.000053439848889 0.000052871232296 0.000052100320625 0.000052640821975 0.000052395457600 0.000052842357397 0.000052377682361 0.000056227206302 0.000055199055179 0.000056765660056 0.000055473966182 0.000055337464507 0.002334401625000 0.003320220450000 0.004307182137500 0.005494768460000 0.006412781866667 0.007401972521429 0.008336051300000 0.009475347955556 0.010479091520000 0.011625318627273 0.012570643766667 0.014619073638462 0.015455735450000 0.017029698016667 0.017751669178125 0.001138504939132 0.001264753570808 0.001370916885383 0.001589834033324 0.001822289126998 0.001901242141254 0.002069519168813 0.002133119750101 0.002237348468544 64 400 8.886604014999996081769496 0.000055541275094 0.002570208197561 0.022216510037500 msa.msa divide and conquer( processing datasets of size 20 through 400 (1000 runs for each dataset elapsed / (size*size) elapsed / (size*1g(size)) elapsed size 0.000131061557500 0.000068142739375 0.000047310870556 0.000036077578125 0.000029363621000 0.000024876107569 0.002621231150000 0.002725709575000 0.002838652233334 0.002886206250000 0.002936362100000 20 0.052424623000007386508514 40 0.109028382999994732927007 60 0.170319134000010308227502 80 0.230896500000000060026650 100 0.293636210000002506603778 120 0.358215948999998090584995 5999995876845787 160 0.477085697999996227736119 180 0.543274334999992447592376 200 0.607016102000002888416930 220 0.669495424000004391018592 240 0.744658928999996305719833 0.814699024000006488677172 0.000606495779766 0.000512165802770 0.000480566245030 0.000456538923993 0.000441966535115 0.000432196350443 0.000421948667808 1487 0.003008191471429 0.003018190750000 0.000016767726389 0.000015175402550 0.000013832550083 0.000012928106406 0.000402863044856 0.000397061435308 0.000391083452021 0.000392410328685 0.003043161018182 0.003102745537500 148 300 0.941402123000003143715730 00001046002358 282 0.000379250123370 0.000388833361653 0.003189262550000 0.003301915786111 340 360 1.188689682999992669465 380 1.212384053999997490791429 400 1.270730806999992523742549 084349266999993233184796 428 0.000009380183971 000007942067544 0.000367524279413 0.003176827017500 Function msa.msa brute force() - processing datasets of size 20 through 400 (1000 runs for each dataset): elapsed / (size*size) elapsed / (size*1g(size)) elapsed size 20 0.025443946000000002005681 40 0.0933760649999999942094 60 0.199213226999999992727908 80 0.344574571000000051679280 100 0.549476846000000018754861 120 0.769533824000000032938829 140 1.036276152999999755621729 160 1.333768207999999511059741 180 1.705562632000000355958491 200 2.095818303999999798747922 220 2.557570097999999347848643 240 3.016954504000000980568075 260 3.800959146000000288267984 280 4.327605926000000380327037 300 5.108909404999998571383912 320 5.680534136999998651162969 340 6.397010897000001250489731 0.000294358738061 0.000438638324941 0.000562092762048 0.000681308308613 0.000827045062844 0.000928461480300 68 0.000058360040625 0.000055337007500 0.000053839776719 0.000053439848889 0.000052871232296 0.000052100320625 0.000052640821975 0.000052395457600 0.000052842357397 0.000052377682361 0.000056227206302 0.000055199055179 0.000056765660056 0.000055473966182 0.000055337464507 0.002334401625000 0.003320220450000 0.004307182137500 0.005494768460000 0.006412781866667 0.007401972521429 0.008336051300000 0.009475347955556 0.010479091520000 0.011625318627273 0.012570643766667 0.014619073638462 0.015455735450000 0.017029698016667 0.017751669178125 0.001138504939132 0.001264753570808 0.001370916885383 0.001589834033324 0.001822289126998 0.001901242141254 0.002069519168813 0.002133119750101 0.002237348468544 64 400 8.886604014999996081769496 0.000055541275094 0.002570208197561 0.022216510037500 msa.msa divide and conquer( processing datasets of size 20 through 400 (1000 runs for each dataset elapsed / (size*size) elapsed / (size*1g(size)) elapsed size 0.000131061557500 0.000068142739375 0.000047310870556 0.000036077578125 0.000029363621000 0.000024876107569 0.002621231150000 0.002725709575000 0.002838652233334 0.002886206250000 0.002936362100000 20 0.052424623000007386508514 40 0.109028382999994732927007 60 0.170319134000010308227502 80 0.230896500000000060026650 100 0.293636210000002506603778 120 0.358215948999998090584995 5999995876845787 160 0.477085697999996227736119 180 0.543274334999992447592376 200 0.607016102000002888416930 220 0.669495424000004391018592 240 0.744658928999996305719833 0.814699024000006488677172 0.000606495779766 0.000512165802770 0.000480566245030 0.000456538923993 0.000441966535115 0.000432196350443 0.000421948667808 1487 0.003008191471429 0.003018190750000 0.000016767726389 0.000015175402550 0.000013832550083 0.000012928106406 0.000402863044856 0.000397061435308 0.000391083452021 0.000392410328685 0.003043161018182 0.003102745537500 148 300 0.941402123000003143715730 00001046002358 282 0.000379250123370 0.000388833361653 0.003189262550000 0.003301915786111 340 360 1.188689682999992669465 380 1.212384053999997490791429 400 1.270730806999992523742549 084349266999993233184796 428 0.000009380183971 000007942067544 0.000367524279413 0.003176827017500
