//The following data can be used to draw graphs of k to t, where n=1000,10000,100000,1000000. //You can draw a graph for each n value, with randomized and determinictic in one graph to compare //the k to t trends of this two situations(For deterministic should be almost horizental, and randomized increase) ********************** Result using deterministic algorithm ********************** n k T(Sec) nlogn 1000 1 0.000000 6907.76 1000 100 0.001000 6907.76 1000 200 0.001000 6907.76 1000 300 0.001000 6907.76 1000 400 0.001000 6907.76 1000 500 0.002000 6907.76 1000 600 0.001000 6907.76 1000 700 0.001000 6907.76 1000 800 0.001000 6907.76 1000 900 0.001000 6907.76 1000 1000 0.001000 6907.76 10000 1 0.012000 92103.40 10000 100 0.010000 92103.40 10000 200 0.010000 92103.40 10000 300 0.010000 92103.40 10000 400 0.010100 92103.40 10000 500 0.011000 92103.40 10000 600 0.010000 92103.40 10000 700 0.011000 92103.40 10000 800 0.010000 92103.40 10000 900 0.010100 92103.40 10000 1000 0.010000 92103.40 10000 1100 0.011000 92103.40 10000 1200 0.010000 92103.40 10000 1300 0.011000 92103.40 10000 1400 0.012000 92103.40 10000 1500 0.010100 92103.40 10000 1600 0.010000 92103.40 10000 1700 0.010000 92103.40 10000 1800 0.009000 92103.40 10000 1900 0.010000 92103.40 10000 2000 0.011000 92103.40 10000 2100 0.010000 92103.40 10000 2200 0.010000 92103.40 10000 2300 0.010000 92103.40 10000 2400 0.010000 92103.40 10000 2500 0.010000 92103.40 10000 2600 0.011000 92103.40 10000 2700 0.010000 92103.40 10000 2800 0.010000 92103.40 10000 2900 0.011000 92103.40 10000 3000 0.010000 92103.40 10000 3100 0.010000 92103.40 10000 3200 0.023100 92103.40 10000 3300 0.010000 92103.40 10000 3400 0.010000 92103.40 10000 3500 0.011000 92103.40 10000 3600 0.010000 92103.40 10000 3700 0.010100 92103.40 10000 3800 0.011000 92103.40 10000 3900 0.010000 92103.40 10000 4000 0.010000 92103.40 10000 4100 0.010000 92103.40 10000 4200 0.010000 92103.40 10000 4300 0.010000 92103.40 10000 4400 0.010000 92103.40 10000 4500 0.010000 92103.40 10000 4600 0.010000 92103.40 10000 4700 0.010000 92103.40 10000 4800 0.010000 92103.40 10000 4900 0.010100 92103.40 10000 5000 0.010000 92103.40 10000 5100 0.009000 92103.40 10000 5200 0.010000 92103.40 10000 5300 0.010000 92103.40 10000 5400 0.010000 92103.40 10000 5500 0.010100 92103.40 10000 5600 0.010000 92103.40 10000 5700 0.010000 92103.40 10000 5800 0.010000 92103.40 10000 5900 0.010000 92103.40 10000 6000 0.010000 92103.40 10000 6100 0.010100 92103.40 10000 6200 0.010000 92103.40 10000 6300 0.010000 92103.40 10000 6400 0.010000 92103.40 10000 6500 0.010000 92103.40 10000 6600 0.010000 92103.40 10000 6700 0.010100 92103.40 10000 6800 0.010000 92103.40 10000 6900 0.010000 92103.40 10000 7000 0.010000 92103.40 10000 7100 0.010000 92103.40 10000 7200 0.010000 92103.40 10000 7300 0.010000 92103.40 10000 7400 0.010000 92103.40 10000 7500 0.010000 92103.40 10000 7600 0.011000 92103.40 10000 7700 0.009000 92103.40 10000 7800 0.011000 92103.40 10000 7900 0.010100 92103.40 10000 8000 0.010000 92103.40 10000 8100 0.010000 92103.40 10000 8200 0.011000 92103.40 10000 8300 0.011000 92103.40 10000 8400 0.010000 92103.40 10000 8500 0.010100 92103.40 10000 8600 0.010000 92103.40 10000 8700 0.010000 92103.40 10000 8800 0.009000 92103.40 10000 8900 0.010000 92103.40 10000 9000 0.009000 92103.40 10000 9100 0.010100 92103.40 10000 9200 0.010000 92103.40 10000 9300 0.010000 92103.40 10000 9400 0.011000 92103.40 10000 9500 0.010000 92103.40 10000 9600 0.010000 92103.40 10000 9700 0.010100 92103.40 10000 9800 0.010000 92103.40 10000 9900 0.010000 92103.40 10000 10000 0.009000 92103.40 100000 1 0.116200 1151292.55 100000 100 0.117200 1151292.55 100000 200 0.117200 1151292.55 100000 300 0.117200 1151292.55 100000 400 0.120100 1151292.55 100000 500 0.115200 1151292.55 100000 600 0.115200 1151292.55 100000 700 0.118100 1151292.55 100000 800 0.117200 1151292.55 100000 900 0.116200 1151292.55 100000 1000 0.116200 1151292.55 100000 1100 0.117100 1151292.55 100000 1200 0.117100 1151292.55 100000 1300 0.115200 1151292.55 100000 1400 0.116200 1151292.55 100000 1500 0.115200 1151292.55 100000 1600 0.116200 1151292.55 100000 1700 0.115200 1151292.55 100000 1800 0.118200 1151292.55 100000 1900 0.119200 1151292.55 100000 2000 0.116000 1151292.55 100000 2100 0.114100 1151292.55 100000 2200 0.118200 1151292.55 100000 2300 0.119200 1151292.55 100000 2400 0.118200 1151292.55 100000 2500 0.112200 1151292.55 100000 2600 0.116200 1151292.55 100000 2700 0.116200 1151292.55 100000 2800 0.113200 1151292.55 100000 2900 0.116200 1151292.55 100000 3000 0.115200 1151292.55 100000 3100 0.115200 1151292.55 100000 3200 0.117200 1151292.55 100000 3300 0.116200 1151292.55 100000 3400 0.121200 1151292.55 100000 3500 0.118200 1151292.55 100000 3600 0.115200 1151292.55 100000 3700 0.115200 1151292.55 100000 3800 0.117200 1151292.55 100000 3900 0.120200 1151292.55 100000 4000 0.118200 1151292.55 100000 4100 0.116200 1151292.55 100000 4200 0.114200 1151292.55 100000 4300 0.120200 1151292.55 100000 4400 0.116200 1151292.55 100000 4500 0.115200 1151292.55 100000 4600 0.118200 1151292.55 100000 4700 0.114200 1151292.55 100000 4800 0.117000 1151292.55 100000 4900 0.115100 1151292.55 100000 5000 0.115000 1151292.55 100000 5100 0.118100 1151292.55 100000 5200 0.117100 1151292.55 100000 5300 0.116200 1151292.55 100000 5400 0.117200 1151292.55 100000 5500 0.118200 1151292.55 100000 5600 0.116200 1151292.55 100000 5700 0.117200 1151292.55 100000 5800 0.117000 1151292.55 100000 5900 0.115200 1151292.55 100000 6000 0.114200 1151292.55 100000 6100 0.119200 1151292.55 100000 6200 0.115200 1151292.55 100000 6300 0.116200 1151292.55 100000 6400 0.118200 1151292.55 100000 6500 0.114200 1151292.55 100000 6600 0.118200 1151292.55 100000 6700 0.115200 1151292.55 100000 6800 0.117200 1151292.55 100000 6900 0.119200 1151292.55 100000 7000 0.116000 1151292.55 100000 7100 0.115200 1151292.55 100000 7200 0.116200 1151292.55 100000 7300 0.118200 1151292.55 100000 7400 0.117200 1151292.55 100000 7500 0.120200 1151292.55 100000 7600 0.115200 1151292.55 100000 7700 0.116200 1151292.55 100000 7800 0.114000 1151292.55 100000 7900 0.117200 1151292.55 100000 8000 0.119200 1151292.55 100000 8100 0.115200 1151292.55 100000 8200 0.116200 1151292.55 100000 8300 0.115200 1151292.55 100000 8400 0.116200 1151292.55 100000 8500 0.115200 1151292.55 100000 8600 0.116000 1151292.55 100000 8700 0.114000 1151292.55 100000 8800 0.115000 1151292.55 100000 8900 0.116200 1151292.55 100000 9000 0.118200 1151292.55 100000 9100 0.116200 1151292.55 100000 9200 0.119200 1151292.55 100000 9300 0.115200 1151292.55 100000 9400 0.116100 1151292.55 100000 9500 0.115200 1151292.55 100000 9600 0.119200 1151292.55 100000 9700 0.114200 1151292.55 100000 9800 0.116200 1151292.55 100000 9900 0.116200 1151292.55 100000 10000 0.120200 1151292.55 100000 10100 0.118100 1151292.55 100000 10200 0.130100 1151292.55 100000 10300 0.115200 1151292.55 100000 10400 0.114200 1151292.55 100000 10500 0.118200 1151292.55 100000 10600 0.118100 1151292.55 100000 10700 0.115200 1151292.55 100000 10800 0.119200 1151292.55 100000 10900 0.119200 1151292.55 100000 11000 0.120200 1151292.55 100000 11100 0.117100 1151292.55 100000 11200 0.116100 1151292.55 100000 11300 0.115200 1151292.55 100000 11400 0.114200 1151292.55 100000 11500 0.114200 1151292.55 100000 11600 0.116200 1151292.55 100000 11700 0.116200 1151292.55 100000 11800 0.117200 1151292.55 100000 11900 0.115100 1151292.55 100000 12000 0.115200 1151292.55 100000 12100 0.117200 1151292.55 100000 12200 0.116200 1151292.55 100000 12300 0.117200 1151292.55 100000 12400 0.114200 1151292.55 100000 12500 0.116200 1151292.55 100000 12600 0.112100 1151292.55 100000 12700 0.117000 1151292.55 100000 12800 0.118200 1151292.55 100000 12900 0.115200 1151292.55 100000 13000 0.119100 1151292.55 100000 13100 0.116000 1151292.55 100000 13200 0.118200 1151292.55 100000 13300 0.114200 1151292.55 100000 13400 0.113200 1151292.55 100000 13500 0.114200 1151292.55 100000 13600 0.114200 1151292.55 100000 13700 0.119200 1151292.55 100000 13800 0.117200 1151292.55 100000 13900 0.113000 1151292.55 100000 14000 0.116200 1151292.55 100000 14100 0.117200 1151292.55 100000 14200 0.115200 1151292.55 100000 14300 0.118200 1151292.55 100000 14400 0.117200 1151292.55 100000 14500 0.121200 1151292.55 100000 14600 0.118200 1151292.55 100000 14700 0.115200 1151292.55 100000 14800 0.117200 1151292.55 100000 14900 0.119200 1151292.55 100000 15000 0.123200 1151292.55 100000 15100 0.124200 1151292.55 100000 15200 0.122200 1151292.55 100000 15300 0.122200 1151292.55 100000 15400 0.121100 1151292.55 100000 15500 0.119200 1151292.55 100000 15600 0.116200 1151292.55 100000 15700 0.115100 1151292.55 100000 15800 0.115200 1151292.55 100000 15900 0.115200 1151292.55 100000 16000 0.114200 1151292.55 100000 16100 0.118200 1151292.55 100000 16200 0.114200 1151292.55 100000 16300 0.116100 1151292.55 100000 16400 0.113200 1151292.55 100000 16500 0.117100 1151292.55 100000 16600 0.115100 1151292.55 100000 16700 0.116200 1151292.55 100000 16800 0.116200 1151292.55 100000 16900 0.117200 1151292.55 100000 17000 0.115100 1151292.55 100000 17100 0.116200 1151292.55 100000 17200 0.113200 1151292.55 100000 17300 0.117200 1151292.55 100000 17400 0.119200 1151292.55 100000 17500 0.117200 1151292.55 100000 17600 0.115200 1151292.55 100000 17700 0.115100 1151292.55 100000 17800 0.114100 1151292.55 100000 17900 0.121200 1151292.55 100000 18000 0.120200 1151292.55 100000 18100 0.119200 1151292.55 100000 18200 0.117200 1151292.55 100000 18300 0.117200 1151292.55 100000 18400 0.114200 1151292.55 100000 18500 0.119100 1151292.55 100000 18600 0.117200 1151292.55 100000 18700 0.117200 1151292.55 100000 18800 0.114200 1151292.55 100000 18900 0.114200 1151292.55 100000 19000 0.114100 1151292.55 100000 19100 0.115100 1151292.55 100000 19200 0.115200 1151292.55 100000 19300 0.115200 1151292.55 100000 19400 0.113200 1151292.55 100000 19500 0.116200 1151292.55 100000 19600 0.116100 1151292.55 100000 19700 0.119200 1151292.55 100000 19800 0.120200 1151292.55 100000 19900 0.118000 1151292.55 100000 20000 0.116200 1151292.55 100000 20100 0.117200 1151292.55 100000 20200 0.116200 1151292.55 100000 20300 0.115100 1151292.55 100000 20400 0.116100 1151292.55 100000 20500 0.115200 1151292.55 100000 20600 0.114200 1151292.55 100000 20700 0.117200 1151292.55 100000 20800 0.115100 1151292.55 100000 20900 0.117100 1151292.55 100000 21000 0.115200 1151292.55 100000 21100 0.114200 1151292.55 100000 21200 0.111200 1151292.55 100000 21300 0.118200 1151292.55 100000 21400 0.117100 1151292.55 100000 21500 0.116200 1151292.55 100000 21600 0.118200 1151292.55 100000 21700 0.114200 1151292.55 100000 21800 0.119200 1151292.55 100000 21900 0.116200 1151292.55 100000 22000 0.114200 1151292.55 100000 22100 0.114000 1151292.55 100000 22200 0.115200 1151292.55 100000 22300 0.116200 1151292.55 100000 22400 0.117200 1151292.55 100000 22500 0.117100 1151292.55 100000 22600 0.117000 1151292.55 100000 22700 0.116200 1151292.55 100000 22800 0.116200 1151292.55 100000 22900 0.117200 1151292.55 100000 23000 0.114200 1151292.55 100000 23100 0.117000 1151292.55 100000 23200 0.117200 1151292.55 100000 23300 0.120200 1151292.55 100000 23400 0.119100 1151292.55 100000 23500 0.118000 1151292.55 100000 23600 0.117100 1151292.55 100000 23700 0.118200 1151292.55 100000 23800 0.115200 1151292.55 100000 23900 0.113200 1151292.55 100000 24000 0.116000 1151292.55 100000 24100 0.116200 1151292.55 100000 24200 0.118200 1151292.55 100000 24300 0.116100 1151292.55 100000 24400 0.116200 1151292.55 100000 24500 0.118200 1151292.55 100000 24600 0.114200 1151292.55 100000 24700 0.112000 1151292.55 100000 24800 0.118200 1151292.55 100000 24900 0.111200 1151292.55 100000 25000 0.114200 1151292.55 100000 25100 0.117100 1151292.55 100000 25200 0.120200 1151292.55 100000 25300 0.116200 1151292.55 100000 25400 0.118100 1151292.55 100000 25500 0.116200 1151292.55 100000 25600 0.117200 1151292.55 100000 25700 0.114200 1151292.55 100000 25800 0.116200 1151292.55 100000 25900 0.115200 1151292.55 100000 26000 0.118200 1151292.55 100000 26100 0.115000 1151292.55 100000 26200 0.116200 1151292.55 100000 26300 0.117200 1151292.55 100000 26400 0.112200 1151292.55 100000 26500 0.118100 1151292.55 100000 26600 0.114200 1151292.55 100000 26700 0.116200 1151292.55 100000 26800 0.120200 1151292.55 100000 26900 0.118200 1151292.55 100000 27000 0.114000 1151292.55 100000 27100 0.115200 1151292.55 100000 27200 0.114200 1151292.55 100000 27300 0.117200 1151292.55 100000 27400 0.115200 1151292.55 100000 27500 0.115200 1151292.55 100000 27600 0.115200 1151292.55 100000 27700 0.119100 1151292.55 100000 27800 0.115200 1151292.55 100000 27900 0.115200 1151292.55 100000 28000 0.118000 1151292.55 100000 28100 0.116200 1151292.55 100000 28200 0.117200 1151292.55 100000 28300 0.117200 1151292.55 100000 28400 0.113100 1151292.55 100000 28500 0.113200 1151292.55 100000 28600 0.120200 1151292.55 100000 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0.113100 1151292.55 100000 31800 0.113200 1151292.55 100000 31900 0.117200 1151292.55 100000 32000 0.118100 1151292.55 100000 32100 0.120200 1151292.55 100000 32200 0.116200 1151292.55 100000 32300 0.116200 1151292.55 100000 32400 0.115200 1151292.55 100000 32500 0.114100 1151292.55 100000 32600 0.117200 1151292.55 100000 32700 0.114200 1151292.55 100000 32800 0.115100 1151292.55 100000 32900 0.114200 1151292.55 100000 33000 0.115200 1151292.55 100000 33100 0.115100 1151292.55 100000 33200 0.115100 1151292.55 100000 33300 0.116200 1151292.55 100000 33400 0.117200 1151292.55 100000 33500 0.113100 1151292.55 100000 33600 0.113100 1151292.55 100000 33700 0.117200 1151292.55 100000 33800 0.120300 1151292.55 100000 33900 0.113200 1151292.55 100000 34000 0.115200 1151292.55 100000 34100 0.115200 1151292.55 100000 34200 0.118000 1151292.55 100000 34300 0.127200 1151292.55 100000 34400 0.120100 1151292.55 100000 34500 0.115100 1151292.55 100000 34600 0.117200 1151292.55 100000 34700 0.114200 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13815510.56 1000000 708000 1.323900 13815510.56 1000000 709000 1.313800 13815510.56 1000000 710000 1.326900 13815510.56 1000000 711000 1.318800 13815510.56 1000000 712000 1.309000 13815510.56 1000000 713000 1.325800 13815510.56 1000000 714000 1.324900 13815510.56 1000000 715000 1.320900 13815510.56 1000000 716000 1.327900 13815510.56 1000000 717000 1.323700 13815510.56 1000000 718000 1.311900 13815510.56 1000000 719000 1.332000 13815510.56 1000000 720000 1.304800 13815510.56 1000000 721000 1.315900 13815510.56 1000000 722000 1.314800 13815510.56 1000000 723000 1.334900 13815510.56 1000000 724000 1.315800 13815510.56 1000000 725000 1.319900 13815510.56 1000000 726000 1.328000 13815510.56 1000000 727000 1.324000 13815510.56 1000000 728000 1.325800 13815510.56 1000000 729000 1.310900 13815510.56 1000000 730000 1.327900 13815510.56 1000000 731000 1.319900 13815510.56 1000000 732000 1.332800 13815510.56 1000000 733000 1.350900 13815510.56 1000000 734000 1.327000 13815510.56 1000000 735000 1.311000 13815510.56 1000000 736000 1.318900 13815510.56 1000000 737000 1.323900 13815510.56 1000000 738000 1.311800 13815510.56 1000000 739000 1.327900 13815510.56 1000000 740000 1.320000 13815510.56 1000000 741000 1.310000 13815510.56 1000000 742000 1.325000 13815510.56 1000000 743000 1.316800 13815510.56 1000000 744000 1.324900 13815510.56 1000000 745000 1.327900 13815510.56 1000000 746000 1.317000 13815510.56 1000000 747000 1.321800 13815510.56 1000000 748000 1.316000 13815510.56 1000000 749000 1.321000 13815510.56 1000000 750000 1.324900 13815510.56 1000000 751000 1.340800 13815510.56 1000000 752000 1.318000 13815510.56 1000000 753000 1.328800 13815510.56 1000000 754000 1.326700 13815510.56 1000000 755000 1.317900 13815510.56 1000000 756000 1.320900 13815510.56 1000000 757000 1.325000 13815510.56 1000000 758000 1.318000 13815510.56 1000000 759000 1.311000 13815510.56 1000000 760000 1.316000 13815510.56 1000000 761000 1.320900 13815510.56 1000000 762000 1.324000 13815510.56 1000000 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1000000 791000 1.306000 13815510.56 1000000 792000 1.320000 13815510.56 1000000 793000 1.318800 13815510.56 1000000 794000 1.318000 13815510.56 1000000 795000 1.322800 13815510.56 1000000 796000 1.320700 13815510.56 1000000 797000 1.322900 13815510.56 1000000 798000 1.314000 13815510.56 1000000 799000 1.328000 13815510.56 1000000 800000 1.318800 13815510.56 1000000 801000 1.312800 13815510.56 1000000 802000 1.320900 13815510.56 1000000 803000 1.323900 13815510.56 1000000 804000 1.313700 13815510.56 1000000 805000 1.341000 13815510.56 1000000 806000 1.337000 13815510.56 1000000 807000 1.321800 13815510.56 1000000 808000 1.319000 13815510.56 1000000 809000 1.324000 13815510.56 1000000 810000 1.317700 13815510.56 1000000 811000 1.329000 13815510.56 1000000 812000 1.324900 13815510.56 1000000 813000 1.320900 13815510.56 1000000 814000 1.313900 13815510.56 1000000 815000 1.318000 13815510.56 1000000 816000 1.323900 13815510.56 1000000 817000 1.315000 13815510.56 1000000 818000 1.315800 13815510.56 1000000 819000 1.312900 13815510.56 1000000 820000 1.322000 13815510.56 1000000 821000 1.311900 13815510.56 1000000 822000 1.327900 13815510.56 1000000 823000 1.314800 13815510.56 1000000 824000 1.319900 13815510.56 1000000 825000 1.327000 13815510.56 1000000 826000 1.326800 13815510.56 1000000 827000 1.316000 13815510.56 1000000 828000 1.314900 13815510.56 1000000 829000 1.323700 13815510.56 1000000 830000 1.316800 13815510.56 1000000 831000 1.323000 13815510.56 1000000 832000 1.322000 13815510.56 1000000 833000 1.317000 13815510.56 1000000 834000 1.311900 13815510.56 1000000 835000 1.324000 13815510.56 1000000 836000 1.320000 13815510.56 1000000 837000 1.318000 13815510.56 1000000 838000 1.323000 13815510.56 1000000 839000 1.318900 13815510.56 1000000 840000 1.323900 13815510.56 1000000 841000 1.319800 13815510.56 1000000 842000 1.334900 13815510.56 1000000 843000 1.324800 13815510.56 1000000 844000 1.321900 13815510.56 1000000 845000 1.342900 13815510.56 1000000 846000 1.328000 13815510.56 1000000 847000 1.317900 13815510.56 1000000 848000 1.315900 13815510.56 1000000 849000 1.329900 13815510.56 1000000 850000 1.309800 13815510.56 1000000 851000 1.324000 13815510.56 1000000 852000 1.340000 13815510.56 1000000 853000 1.321900 13815510.56 1000000 854000 1.315900 13815510.56 1000000 855000 1.325700 13815510.56 1000000 856000 1.322900 13815510.56 1000000 857000 1.321800 13815510.56 1000000 858000 1.331900 13815510.56 1000000 859000 1.332800 13815510.56 1000000 860000 1.323800 13815510.56 1000000 861000 1.319900 13815510.56 1000000 862000 1.319800 13815510.56 1000000 863000 1.327900 13815510.56 1000000 864000 1.326700 13815510.56 1000000 865000 1.324700 13815510.56 1000000 866000 1.326700 13815510.56 1000000 867000 1.313700 13815510.56 1000000 868000 1.327800 13815510.56 1000000 869000 1.325000 13815510.56 1000000 870000 1.347000 13815510.56 1000000 871000 1.327000 13815510.56 1000000 872000 1.332000 13815510.56 1000000 873000 1.313900 13815510.56 1000000 874000 1.323900 13815510.56 1000000 875000 1.316900 13815510.56 1000000 876000 1.322800 13815510.56 1000000 877000 1.329900 13815510.56 1000000 878000 1.336000 13815510.56 1000000 879000 1.335100 13815510.56 1000000 880000 1.318900 13815510.56 1000000 881000 1.326900 13815510.56 1000000 882000 1.312900 13815510.56 1000000 883000 1.313900 13815510.56 1000000 884000 1.326000 13815510.56 1000000 885000 1.318900 13815510.56 1000000 886000 1.328000 13815510.56 1000000 887000 1.323000 13815510.56 1000000 888000 1.325900 13815510.56 1000000 889000 1.330900 13815510.56 1000000 890000 1.313900 13815510.56 1000000 891000 1.318000 13815510.56 1000000 892000 1.324000 13815510.56 1000000 893000 1.307900 13815510.56 1000000 894000 1.318800 13815510.56 1000000 895000 1.316800 13815510.56 1000000 896000 1.321800 13815510.56 1000000 897000 1.311800 13815510.56 1000000 898000 1.319000 13815510.56 1000000 899000 1.312800 13815510.56 1000000 900000 1.325000 13815510.56 1000000 901000 1.326000 13815510.56 1000000 902000 1.312900 13815510.56 1000000 903000 1.318900 13815510.56 1000000 904000 1.319800 13815510.56 1000000 905000 1.315900 13815510.56 1000000 906000 1.323900 13815510.56 1000000 907000 1.321000 13815510.56 1000000 908000 1.326000 13815510.56 1000000 909000 1.311800 13815510.56 1000000 910000 1.314800 13815510.56 1000000 911000 1.317900 13815510.56 1000000 912000 1.340000 13815510.56 1000000 913000 1.321900 13815510.56 1000000 914000 1.324000 13815510.56 1000000 915000 1.316800 13815510.56 1000000 916000 1.335900 13815510.56 1000000 917000 1.323000 13815510.56 1000000 918000 1.327800 13815510.56 1000000 919000 1.327900 13815510.56 1000000 920000 1.316000 13815510.56 1000000 921000 1.320000 13815510.56 1000000 922000 1.332000 13815510.56 1000000 923000 1.322900 13815510.56 1000000 924000 1.320900 13815510.56 1000000 925000 1.336000 13815510.56 1000000 926000 1.336000 13815510.56 1000000 927000 1.313800 13815510.56 1000000 928000 1.316900 13815510.56 1000000 929000 1.322800 13815510.56 1000000 930000 1.314900 13815510.56 1000000 931000 1.330900 13815510.56 1000000 932000 1.312800 13815510.56 1000000 933000 1.317900 13815510.56 1000000 934000 1.323900 13815510.56 1000000 935000 1.313900 13815510.56 1000000 936000 1.317900 13815510.56 1000000 937000 1.331000 13815510.56 1000000 938000 1.323900 13815510.56 1000000 939000 1.324000 13815510.56 1000000 940000 1.317900 13815510.56 1000000 941000 1.308800 13815510.56 1000000 942000 1.317900 13815510.56 1000000 943000 1.328800 13815510.56 1000000 944000 1.310000 13815510.56 1000000 945000 1.324800 13815510.56 1000000 946000 1.319900 13815510.56 1000000 947000 1.332000 13815510.56 1000000 948000 1.317000 13815510.56 1000000 949000 1.310900 13815510.56 1000000 950000 1.312900 13815510.56 1000000 951000 1.330900 13815510.56 1000000 952000 1.311900 13815510.56 1000000 953000 1.330700 13815510.56 1000000 954000 1.358000 13815510.56 1000000 955000 1.314900 13815510.56 1000000 956000 1.322000 13815510.56 1000000 957000 1.343000 13815510.56 1000000 958000 1.349900 13815510.56 1000000 959000 1.329000 13815510.56 1000000 960000 1.338900 13815510.56 1000000 961000 1.349000 13815510.56 1000000 962000 1.341800 13815510.56 1000000 963000 1.324000 13815510.56 1000000 964000 1.322700 13815510.56 1000000 965000 1.326000 13815510.56 1000000 966000 1.326900 13815510.56 1000000 967000 1.323700 13815510.56 1000000 968000 1.331900 13815510.56 1000000 969000 1.322800 13815510.56 1000000 970000 1.321900 13815510.56 1000000 971000 1.325900 13815510.56 1000000 972000 1.323900 13815510.56 1000000 973000 1.314900 13815510.56 1000000 974000 1.323900 13815510.56 1000000 975000 1.317900 13815510.56 1000000 976000 1.322800 13815510.56 1000000 977000 1.317800 13815510.56 1000000 978000 1.316900 13815510.56 1000000 979000 1.340800 13815510.56 1000000 980000 1.317800 13815510.56 1000000 981000 1.317900 13815510.56 1000000 982000 1.323900 13815510.56 1000000 983000 1.324900 13815510.56 1000000 984000 1.321900 13815510.56 1000000 985000 1.323000 13815510.56 1000000 986000 1.317900 13815510.56 1000000 987000 1.319900 13815510.56 1000000 988000 1.331900 13815510.56 1000000 989000 1.311800 13815510.56 1000000 990000 1.341900 13815510.56 1000000 991000 1.313900 13815510.56 1000000 992000 1.312900 13815510.56 1000000 993000 1.322900 13815510.56 1000000 994000 1.315900 13815510.56 1000000 995000 1.325000 13815510.56 1000000 996000 1.326000 13815510.56 1000000 997000 1.319800 13815510.56 1000000 998000 1.317900 13815510.56 1000000 999000 1.329900 13815510.56 1000000 1000000 1.326900 13815510.56 //The following four sections are for k=biggest, smallest, mid, 1/4, 3/4 largest. //We can draw graph of n to t with k set using these data. //In the graph t=n and t=nlogn can be included to show that the graph of deterministic is //similiar to t=n(linear), and that of randomized is similiar to t=nlogn. //Again, here we can have a graph for each k (different granuity) //If you can draw a graph with n, k, t in it that will be great. ********************** Result using deterministic algorithm ********************** n k T(Sec) nlogn 1000 1 0.001000 6907.76 5000 1 0.007000 42585.97 10000 1 0.010000 92103.40 15000 1 0.015000 144237.08 20000 1 0.021000 198069.75 25000 1 0.025100 253165.78 30000 1 0.032100 309268.58 35000 1 0.040000 366208.62 40000 1 0.045100 423865.39 45000 1 0.050100 482148.80 50000 1 0.058000 540988.91 55000 1 0.061100 600329.87 60000 1 0.068000 660125.99 65000 1 0.073000 720339.27 70000 1 0.081200 780937.54 75000 1 0.091100 841893.25 80000 1 0.095200 903182.55 85000 1 0.099200 964784.56 90000 1 0.104200 1026680.85 95000 1 0.110100 1088855.06 100000 1 0.116000 1151292.55 105000 1 0.123200 1213980.14 110000 1 0.127200 1276905.92 115000 1 0.135100 1340059.05 120000 1 0.142300 1403429.64 125000 1 0.147200 1467008.63 130000 1 0.152300 1530787.66 135000 1 0.162100 1594759.06 140000 1 0.167300 1658915.68 145000 1 0.172300 1723250.91 150000 1 0.183200 1787758.59 155000 1 0.181300 1852432.96 160000 1 0.191400 1917268.66 165000 1 0.198300 1982260.62 170000 1 0.203300 2047404.13 175000 1 0.220300 2112694.72 180000 1 0.230200 2178128.18 185000 1 0.293500 2243700.55 190000 1 0.307400 2309408.08 195000 1 0.266300 2375247.19 200000 1 0.248400 2441214.53 205000 1 0.268300 2507306.88 210000 1 0.272500 2573521.19 215000 1 0.261400 2639854.56 220000 1 0.271200 2706304.22 225000 1 0.268500 2772867.53 230000 1 0.278500 2839541.96 235000 1 0.291500 2906325.09 240000 1 0.294500 2973214.61 245000 1 0.301400 3040208.30 250000 1 0.306500 3107304.05 255000 1 0.309400 3174499.80 260000 1 0.319600 3241793.60 265000 1 0.329400 3309183.55 270000 1 0.329400 3376667.85 275000 1 0.336400 3444244.75 280000 1 0.344500 3511912.57 285000 1 0.350500 3579669.67 290000 1 0.356400 3647514.50 295000 1 0.368600 3715445.54 300000 1 0.370500 3783461.33 305000 1 0.382700 3851560.45 310000 1 0.384600 3919741.55 315000 1 0.394500 3988003.29 320000 1 0.398600 4056344.41 325000 1 0.405600 4124763.65 330000 1 0.410600 4193259.82 335000 1 0.417600 4261831.75 340000 1 0.414500 4330478.30 345000 1 0.432700 4399198.40 350000 1 0.437600 4467990.95 355000 1 0.440700 4536854.94 360000 1 0.450700 4605789.35 365000 1 0.459600 4674793.21 370000 1 0.468700 4743865.57 375000 1 0.470700 4813005.49 380000 1 0.474700 4882212.08 385000 1 0.482600 4951484.47 390000 1 0.492900 5020821.79 395000 1 0.499700 5090223.21 400000 1 0.505700 5159687.93 405000 1 0.511800 5229215.15 410000 1 0.517700 5298804.10 415000 1 0.520700 5368454.03 420000 1 0.525900 5438164.20 425000 1 0.533900 5507933.89 430000 1 0.549400 5577762.41 435000 1 0.550000 5647649.07 440000 1 0.553000 5717593.20 445000 1 0.567200 5787594.15 450000 1 0.570400 5857651.29 455000 1 0.592000 5927763.98 460000 1 0.574000 5997931.61 465000 1 0.589000 6068153.60 470000 1 0.592000 6138429.35 475000 1 0.597700 6208758.29 480000 1 0.605000 6279139.86 485000 1 0.613800 6349573.52 490000 1 0.620900 6420058.73 495000 1 0.648000 6490594.96 500000 1 0.650000 6561181.69 505000 1 0.644900 6631818.42 510000 1 0.655900 6702504.66 515000 1 0.659000 6773239.92 520000 1 0.656000 6844023.73 525000 1 0.667000 6914855.61 530000 1 0.675000 6985735.11 535000 1 0.684000 7056661.78 540000 1 0.687000 7127635.19 545000 1 0.699000 7198654.89 550000 1 0.711000 7269720.46 555000 1 0.710000 7340831.48 560000 1 0.718000 7411987.56 565000 1 0.718000 7483188.27 570000 1 0.731100 7554433.23 575000 1 0.739000 7625722.06 580000 1 0.741100 7697054.36 585000 1 0.754000 7768429.77 590000 1 0.763000 7839847.91 595000 1 0.769100 7911308.43 600000 1 0.775300 7982810.96 605000 1 0.775000 8054355.16 610000 1 0.780200 8125940.68 615000 1 0.798200 8197567.19 620000 1 0.799100 8269234.35 625000 1 0.815000 8340941.83 630000 1 0.810200 8412689.31 635000 1 0.840400 8484476.48 640000 1 0.827200 8556303.01 645000 1 0.825100 8628168.61 650000 1 0.840200 8700072.97 655000 1 0.853200 8772015.79 660000 1 0.858100 8843996.78 665000 1 0.869200 8916015.64 670000 1 0.869100 8988072.10 675000 1 0.879000 9060165.88 680000 1 0.879400 9132296.69 685000 1 0.883300 9204464.27 690000 1 0.889300 9276668.34 695000 1 0.901200 9348908.65 700000 1 0.907300 9421184.93 705000 1 0.918400 9493496.92 710000 1 0.930400 9565844.38 715000 1 0.926200 9638227.04 720000 1 0.941400 9710644.67 725000 1 0.949300 9783097.03 730000 1 0.950400 9855583.86 735000 1 0.954500 9928104.95 740000 1 0.953400 10000660.04 745000 1 0.972400 10073248.93 750000 1 0.976400 10145871.36 755000 1 0.986500 10218527.14 760000 1 0.984400 10291216.02 765000 1 1.014500 10363937.80 770000 1 1.000400 10436692.26 775000 1 1.015400 10509479.19 780000 1 1.013500 10582298.37 785000 1 1.018500 10655149.61 790000 1 1.030500 10728032.70 795000 1 1.043600 10800947.43 800000 1 1.038400 10873893.61 805000 1 1.056400 10946871.03 810000 1 1.060700 11019879.52 815000 1 1.071600 11092918.86 820000 1 1.075400 11165988.89 825000 1 1.081600 11239089.40 830000 1 1.081600 11312220.21 835000 1 1.087500 11385381.15 840000 1 1.097600 11458572.02 845000 1 1.101800 11531792.66 850000 1 1.113700 11605042.88 855000 1 1.122000 11678322.52 860000 1 1.129900 11751631.39 865000 1 1.138800 11824969.34 870000 1 1.140200 11898336.19 875000 1 1.145000 11971731.77 880000 1 1.161000 12045155.92 885000 1 1.170500 12118608.49 890000 1 1.176000 12192089.30 895000 1 1.178200 12265598.20 900000 1 1.181900 12339135.04 905000 1 1.190700 12412699.65 910000 1 1.197800 12486291.89 915000 1 1.206800 12559911.60 920000 1 1.201900 12633558.63 925000 1 1.212700 12707232.84 930000 1 1.213800 12780934.07 935000 1 1.232800 12854662.19 940000 1 1.238800 12928417.04 945000 1 1.249900 13002198.50 950000 1 1.242800 13076006.40 955000 1 1.258800 13149840.62 960000 1 1.271800 13223701.02 965000 1 1.268800 13297587.46 970000 1 1.270800 13371499.81 975000 1 1.277800 13445437.93 980000 1 1.292900 13519401.69 985000 1 1.333000 13593390.97 990000 1 1.316900 13667405.62 995000 1 1.316000 13741445.53 1000000 1 1.321900 13815510.56 ********************** Result using deterministic algorithm ********************** n k T(Sec) nlogn 1000 1000 0.001000 6907.76 5000 5000 0.005000 42585.97 10000 10000 0.011000 92103.40 15000 15000 0.018000 144237.08 20000 20000 0.022000 198069.75 25000 25000 0.027100 253165.78 30000 30000 0.033000 309268.58 35000 35000 0.038100 366208.62 40000 40000 0.042100 423865.39 45000 45000 0.050100 482148.80 50000 50000 0.055000 540988.91 55000 55000 0.060100 600329.87 60000 60000 0.069100 660125.99 65000 65000 0.073100 720339.27 70000 70000 0.079200 780937.54 75000 75000 0.086100 841893.25 80000 80000 0.090200 903182.55 85000 85000 0.097100 964784.56 90000 90000 0.104100 1026680.85 95000 95000 0.111100 1088855.06 100000 100000 0.113200 1151292.55 105000 105000 0.120100 1213980.14 110000 110000 0.129300 1276905.92 115000 115000 0.131100 1340059.05 120000 120000 0.140200 1403429.64 125000 125000 0.146300 1467008.63 130000 130000 0.152300 1530787.66 135000 135000 0.159200 1594759.06 140000 140000 0.167300 1658915.68 145000 145000 0.171200 1723250.91 150000 150000 0.177200 1787758.59 155000 155000 0.182400 1852432.96 160000 160000 0.190300 1917268.66 165000 165000 0.196300 1982260.62 170000 170000 0.203300 2047404.13 175000 175000 0.208400 2112694.72 180000 180000 0.214400 2178128.18 185000 185000 0.227200 2243700.55 190000 190000 0.227300 2309408.08 195000 195000 0.237400 2375247.19 200000 200000 0.243400 2441214.53 205000 205000 0.254300 2507306.88 210000 210000 0.253300 2573521.19 215000 215000 0.257400 2639854.56 220000 220000 0.269400 2706304.22 225000 225000 0.279200 2772867.53 230000 230000 0.282000 2839541.96 235000 235000 0.287000 2906325.09 240000 240000 0.290400 2973214.61 245000 245000 0.298500 3040208.30 250000 250000 0.306500 3107304.05 255000 255000 0.311400 3174499.80 260000 260000 0.323500 3241793.60 265000 265000 0.320500 3309183.55 270000 270000 0.329400 3376667.85 275000 275000 0.336400 3444244.75 280000 280000 0.345600 3511912.57 285000 285000 0.351600 3579669.67 290000 290000 0.362500 3647514.50 295000 295000 0.360400 3715445.54 300000 300000 0.373700 3783461.33 305000 305000 0.380600 3851560.45 310000 310000 0.382700 3919741.55 315000 315000 0.389500 3988003.29 320000 320000 0.397500 4056344.41 325000 325000 0.400600 4124763.65 330000 330000 0.409700 4193259.82 335000 335000 0.415600 4261831.75 340000 340000 0.421600 4330478.30 345000 345000 0.428400 4399198.40 350000 350000 0.433800 4467990.95 355000 355000 0.437600 4536854.94 360000 360000 0.449700 4605789.35 365000 365000 0.456600 4674793.21 370000 370000 0.462800 4743865.57 375000 375000 0.469800 4813005.49 380000 380000 0.476700 4882212.08 385000 385000 0.487700 4951484.47 390000 390000 0.492700 5020821.79 395000 395000 0.494800 5090223.21 400000 400000 0.496600 5159687.93 405000 405000 0.506600 5229215.15 410000 410000 0.525900 5298804.10 415000 415000 0.519800 5368454.03 420000 420000 0.524800 5438164.20 425000 425000 0.548400 5507933.89 430000 430000 0.544000 5577762.41 435000 435000 0.548500 5647649.07 440000 440000 0.557000 5717593.20 445000 445000 0.564000 5787594.15 450000 450000 0.562000 5857651.29 455000 455000 0.574000 5927763.98 460000 460000 0.584000 5997931.61 465000 465000 0.594700 6068153.60 470000 470000 0.595000 6138429.35 475000 475000 0.601000 6208758.29 480000 480000 0.612800 6279139.86 485000 485000 0.618800 6349573.52 490000 490000 0.629900 6420058.73 495000 495000 0.624900 6490594.96 500000 500000 0.638000 6561181.69 505000 505000 0.645000 6631818.42 510000 510000 0.646900 6702504.66 515000 515000 0.655000 6773239.92 520000 520000 0.659900 6844023.73 525000 525000 0.674000 6914855.61 530000 530000 0.684000 6985735.11 535000 535000 0.688000 7056661.78 540000 540000 0.688000 7127635.19 545000 545000 0.697000 7198654.89 550000 550000 0.706100 7269720.46 555000 555000 0.712000 7340831.48 560000 560000 0.717000 7411987.56 565000 565000 0.720100 7483188.27 570000 570000 0.724000 7554433.23 575000 575000 0.739100 7625722.06 580000 580000 0.737100 7697054.36 585000 585000 0.746000 7768429.77 590000 590000 0.757100 7839847.91 595000 595000 0.765100 7911308.43 600000 600000 0.769300 7982810.96 605000 605000 0.774300 8054355.16 610000 610000 0.788200 8125940.68 615000 615000 0.795200 8197567.19 620000 620000 0.785200 8269234.35 625000 625000 0.803100 8340941.83 630000 630000 0.813200 8412689.31 635000 635000 0.821300 8484476.48 640000 640000 0.828000 8556303.01 645000 645000 0.826100 8628168.61 650000 650000 0.839200 8700072.97 655000 655000 0.850300 8772015.79 660000 660000 0.852100 8843996.78 665000 665000 0.862500 8916015.64 670000 670000 0.862400 8988072.10 675000 675000 0.881100 9060165.88 680000 680000 0.874200 9132296.69 685000 685000 0.875300 9204464.27 690000 690000 0.891400 9276668.34 695000 695000 0.902200 9348908.65 700000 700000 0.906400 9421184.93 705000 705000 0.907400 9493496.92 710000 710000 0.922400 9565844.38 715000 715000 0.928200 9638227.04 720000 720000 0.938300 9710644.67 725000 725000 0.942400 9783097.03 730000 730000 0.937400 9855583.86 735000 735000 0.950200 9928104.95 740000 740000 0.962300 10000660.04 745000 745000 0.970400 10073248.93 750000 750000 0.966600 10145871.36 755000 755000 0.995400 10218527.14 760000 760000 0.992400 10291216.02 765000 765000 0.994600 10363937.80 770000 770000 0.997500 10436692.26 775000 775000 1.025500 10509479.19 780000 780000 1.007500 10582298.37 785000 785000 1.025500 10655149.61 790000 790000 1.031600 10728032.70 795000 795000 1.047600 10800947.43 800000 800000 1.040600 10873893.61 805000 805000 1.050300 10946871.03 810000 810000 1.059600 11019879.52 815000 815000 1.082600 11092918.86 820000 820000 1.075600 11165988.89 825000 825000 1.085600 11239089.40 830000 830000 1.088500 11312220.21 835000 835000 1.099500 11385381.15 840000 840000 1.092500 11458572.02 845000 845000 1.110600 11531792.66 850000 850000 1.127500 11605042.88 855000 855000 1.124800 11678322.52 860000 860000 1.120700 11751631.39 865000 865000 1.132000 11824969.34 870000 870000 1.150200 11898336.19 875000 875000 1.149200 11971731.77 880000 880000 1.148000 12045155.92 885000 885000 1.167800 12118608.49 890000 890000 1.177000 12192089.30 895000 895000 1.171400 12265598.20 900000 900000 1.181000 12339135.04 905000 905000 1.194300 12412699.65 910000 910000 1.195900 12486291.89 915000 915000 1.207700 12559911.60 920000 920000 1.211800 12633558.63 925000 925000 1.225900 12707232.84 930000 930000 1.219600 12780934.07 935000 935000 1.232700 12854662.19 940000 940000 1.243800 12928417.04 945000 945000 1.260900 13002198.50 950000 950000 1.252700 13076006.40 955000 955000 1.265800 13149840.62 960000 960000 1.264800 13223701.02 965000 965000 1.277900 13297587.46 970000 970000 1.270800 13371499.81 975000 975000 1.291000 13445437.93 980000 980000 1.298900 13519401.69 985000 985000 1.304000 13593390.97 990000 990000 1.316800 13667405.62 995000 995000 1.318900 13741445.53 1000000 1000000 1.343000 13815510.56 ********************** Result using deterministic algorithm ********************** n k T(Sec) nlogn 1000 500 0.001000 6907.76 5000 2500 0.006000 42585.97 10000 5000 0.011000 92103.40 15000 7500 0.013000 144237.08 20000 10000 0.021000 198069.75 25000 12500 0.025100 253165.78 30000 15000 0.037000 309268.58 35000 17500 0.039100 366208.62 40000 20000 0.044100 423865.39 45000 22500 0.049100 482148.80 50000 25000 0.055100 540988.91 55000 27500 0.060100 600329.87 60000 30000 0.069100 660125.99 65000 32500 0.071100 720339.27 70000 35000 0.079000 780937.54 75000 37500 0.088100 841893.25 80000 40000 0.094200 903182.55 85000 42500 0.098100 964784.56 90000 45000 0.105100 1026680.85 95000 47500 0.109200 1088855.06 100000 50000 0.116200 1151292.55 105000 52500 0.120200 1213980.14 110000 55000 0.125200 1276905.92 115000 57500 0.134300 1340059.05 120000 60000 0.140200 1403429.64 125000 62500 0.144300 1467008.63 130000 65000 0.152200 1530787.66 135000 67500 0.161200 1594759.06 140000 70000 0.166300 1658915.68 145000 72500 0.170300 1723250.91 150000 75000 0.177100 1787758.59 155000 77500 0.182000 1852432.96 160000 80000 0.194300 1917268.66 165000 82500 0.195300 1982260.62 170000 85000 0.203200 2047404.13 175000 87500 0.210300 2112694.72 180000 90000 0.217400 2178128.18 185000 92500 0.222400 2243700.55 190000 95000 0.228300 2309408.08 195000 97500 0.231400 2375247.19 200000 100000 0.241300 2441214.53 205000 102500 0.252400 2507306.88 210000 105000 0.258300 2573521.19 215000 107500 0.261500 2639854.56 220000 110000 0.270200 2706304.22 225000 112500 0.272300 2772867.53 230000 115000 0.277100 2839541.96 235000 117500 0.286400 2906325.09 240000 120000 0.291500 2973214.61 245000 122500 0.295500 3040208.30 250000 125000 0.308400 3107304.05 255000 127500 0.314500 3174499.80 260000 130000 0.320400 3241793.60 265000 132500 0.330400 3309183.55 270000 135000 0.328400 3376667.85 275000 137500 0.345500 3444244.75 280000 140000 0.345500 3511912.57 285000 142500 0.354600 3579669.67 290000 145000 0.357500 3647514.50 295000 147500 0.373500 3715445.54 300000 150000 0.367600 3783461.33 305000 152500 0.373600 3851560.45 310000 155000 0.391500 3919741.55 315000 157500 0.389600 3988003.29 320000 160000 0.394500 4056344.41 325000 162500 0.423700 4124763.65 330000 165000 0.418500 4193259.82 335000 167500 0.418800 4261831.75 340000 170000 0.422600 4330478.30 345000 172500 0.424600 4399198.40 350000 175000 0.435600 4467990.95 355000 177500 0.442600 4536854.94 360000 180000 0.449600 4605789.35 365000 182500 0.452700 4674793.21 370000 185000 0.461700 4743865.57 375000 187500 0.466500 4813005.49 380000 190000 0.479800 4882212.08 385000 192500 0.484600 4951484.47 390000 195000 0.491800 5020821.79 395000 197500 0.492700 5090223.21 400000 200000 0.508800 5159687.93 405000 202500 0.506700 5229215.15 410000 205000 0.518700 5298804.10 415000 207500 0.521000 5368454.03 420000 210000 0.530600 5438164.20 425000 212500 0.533700 5507933.89 430000 215000 0.543000 5577762.41 435000 217500 0.552000 5647649.07 440000 220000 0.554000 5717593.20 445000 222500 0.558000 5787594.15 450000 225000 0.565000 5857651.29 455000 227500 0.579700 5927763.98 460000 230000 0.579000 5997931.61 465000 232500 0.586600 6068153.60 470000 235000 0.594800 6138429.35 475000 237500 0.604900 6208758.29 480000 240000 0.608900 6279139.86 485000 242500 0.614800 6349573.52 490000 245000 0.624900 6420058.73 495000 247500 0.627900 6490594.96 500000 250000 0.636800 6561181.69 505000 252500 0.644000 6631818.42 510000 255000 0.647000 6702504.66 515000 257500 0.656000 6773239.92 520000 260000 0.662000 6844023.73 525000 262500 0.668000 6914855.61 530000 265000 0.672000 6985735.11 535000 267500 0.685000 7056661.78 540000 270000 0.685900 7127635.19 545000 272500 0.693000 7198654.89 550000 275000 0.726000 7269720.46 555000 277500 0.710000 7340831.48 560000 280000 0.749200 7411987.56 565000 282500 0.728000 7483188.27 570000 285000 0.727000 7554433.23 575000 287500 0.741000 7625722.06 580000 290000 0.741100 7697054.36 585000 292500 0.745100 7768429.77 590000 295000 0.763100 7839847.91 595000 297500 0.768200 7911308.43 600000 300000 0.776000 7982810.96 605000 302500 0.782200 8054355.16 610000 305000 0.798100 8125940.68 615000 307500 0.792100 8197567.19 620000 310000 0.797200 8269234.35 625000 312500 0.804100 8340941.83 630000 315000 0.812200 8412689.31 635000 317500 0.816000 8484476.48 640000 320000 0.826500 8556303.01 645000 322500 0.828500 8628168.61 650000 325000 0.846400 8700072.97 655000 327500 0.847100 8772015.79 660000 330000 0.849200 8843996.78 665000 332500 0.873300 8916015.64 670000 335000 0.907200 8988072.10 675000 337500 0.869300 9060165.88 680000 340000 0.872200 9132296.69 685000 342500 0.886300 9204464.27 690000 345000 0.884300 9276668.34 695000 347500 0.898300 9348908.65 700000 350000 0.914300 9421184.93 705000 352500 0.908300 9493496.92 710000 355000 0.922300 9565844.38 715000 357500 0.923300 9638227.04 720000 360000 0.945300 9710644.67 725000 362500 0.935300 9783097.03 730000 365000 0.946300 9855583.86 735000 367500 0.967500 9928104.95 740000 370000 0.966400 10000660.04 745000 372500 0.971400 10073248.93 750000 375000 0.979400 10145871.36 755000 377500 0.981600 10218527.14 760000 380000 0.994500 10291216.02 765000 382500 0.993200 10363937.80 770000 385000 1.002300 10436692.26 775000 387500 1.008400 10509479.19 780000 390000 1.018400 10582298.37 785000 392500 1.021600 10655149.61 790000 395000 1.038500 10728032.70 795000 397500 1.036300 10800947.43 800000 400000 1.047400 10873893.61 805000 402500 1.054600 10946871.03 810000 405000 1.058500 11019879.52 815000 407500 1.063500 11092918.86 820000 410000 1.101000 11165988.89 825000 412500 1.076200 11239089.40 830000 415000 1.085000 11312220.21 835000 417500 1.107700 11385381.15 840000 420000 1.089200 11458572.02 845000 422500 1.118000 11531792.66 850000 425000 1.120000 11605042.88 855000 427500 1.131700 11678322.52 860000 430000 1.125000 11751631.39 865000 432500 1.133000 11824969.34 870000 435000 1.138500 11898336.19 875000 437500 1.153800 11971731.77 880000 440000 1.156600 12045155.92 885000 442500 1.161600 12118608.49 890000 445000 1.164800 12192089.30 895000 447500 1.172600 12265598.20 900000 450000 1.190700 12339135.04 905000 452500 1.201800 12412699.65 910000 455000 1.199700 12486291.89 915000 457500 1.198600 12559911.60 920000 460000 1.208800 12633558.63 925000 462500 1.222700 12707232.84 930000 465000 1.223800 12780934.07 935000 467500 1.229700 12854662.19 940000 470000 1.246800 12928417.04 945000 472500 1.240800 13002198.50 950000 475000 1.258800 13076006.40 955000 477500 1.269800 13149840.62 960000 480000 1.266900 13223701.02 965000 482500 1.265800 13297587.46 970000 485000 1.276900 13371499.81 975000 487500 1.306800 13445437.93 980000 490000 1.295800 13519401.69 985000 492500 1.315800 13593390.97 990000 495000 1.305800 13667405.62 995000 497500 1.315800 13741445.53 1000000 500000 1.317800 13815510.56 ********************** Result using deterministic algorithm ********************** n k T(Sec) nlogn 1000 250 0.001000 6907.76 5000 1250 0.005000 42585.97 10000 2500 0.010000 92103.40 15000 3750 0.015000 144237.08 20000 5000 0.020100 198069.75 25000 6250 0.026000 253165.78 30000 7500 0.034100 309268.58 35000 8750 0.038000 366208.62 40000 10000 0.044000 423865.39 45000 11250 0.051000 482148.80 50000 12500 0.054100 540988.91 55000 13750 0.062000 600329.87 60000 15000 0.069100 660125.99 65000 16250 0.073200 720339.27 70000 17500 0.084100 780937.54 75000 18750 0.086200 841893.25 80000 20000 0.092100 903182.55 85000 21250 0.096200 964784.56 90000 22500 0.105200 1026680.85 95000 23750 0.108200 1088855.06 100000 25000 0.117200 1151292.55 105000 26250 0.121200 1213980.14 110000 27500 0.128200 1276905.92 115000 28750 0.134200 1340059.05 120000 30000 0.140200 1403429.64 125000 31250 0.144300 1467008.63 130000 32500 0.153300 1530787.66 135000 33750 0.156200 1594759.06 140000 35000 0.165300 1658915.68 145000 36250 0.173100 1723250.91 150000 37500 0.185100 1787758.59 155000 38750 0.183300 1852432.96 160000 40000 0.193200 1917268.66 165000 41250 0.197300 1982260.62 170000 42500 0.201400 2047404.13 175000 43750 0.209300 2112694.72 180000 45000 0.216400 2178128.18 185000 46250 0.221300 2243700.55 190000 47500 0.228200 2309408.08 195000 48750 0.240300 2375247.19 200000 50000 0.243400 2441214.53 205000 51250 0.260300 2507306.88 210000 52500 0.252500 2573521.19 215000 53750 0.259300 2639854.56 220000 55000 0.269400 2706304.22 225000 56250 0.269000 2772867.53 230000 57500 0.277000 2839541.96 235000 58750 0.291500 2906325.09 240000 60000 0.292300 2973214.61 245000 61250 0.296400 3040208.30 250000 62500 0.303500 3107304.05 255000 63750 0.314400 3174499.80 260000 65000 0.320400 3241793.60 265000 66250 0.332400 3309183.55 270000 67500 0.331400 3376667.85 275000 68750 0.343500 3444244.75 280000 70000 0.352500 3511912.57 285000 71250 0.348500 3579669.67 290000 72500 0.366700 3647514.50 295000 73750 0.367600 3715445.54 300000 75000 0.406600 3783461.33 305000 76250 0.421500 3851560.45 310000 77500 0.388500 3919741.55 315000 78750 0.397500 3988003.29 320000 80000 0.446700 4056344.41 325000 81250 0.453600 4124763.65 330000 82500 0.434700 4193259.82 335000 83750 0.444600 4261831.75 340000 85000 0.504800 4330478.30 345000 86250 0.499700 4399198.40 350000 87500 0.491800 4467990.95 355000 88750 0.493600 4536854.94 360000 90000 0.518800 4605789.35 365000 91250 0.529800 4674793.21 370000 92500 0.526600 4743865.57 375000 93750 0.550500 4813005.49 380000 95000 0.534000 4882212.08 385000 96250 0.542000 4951484.47 390000 97500 0.572000 5020821.79 395000 98750 0.509700 5090223.21 400000 100000 0.517800 5159687.93 405000 101250 0.521900 5229215.15 410000 102500 0.525500 5298804.10 415000 103750 0.542000 5368454.03 420000 105000 0.543000 5438164.20 425000 106250 0.551000 5507933.89 430000 107500 0.566000 5577762.41 435000 108750 0.575000 5647649.07 440000 110000 0.571500 5717593.20 445000 111250 0.578000 5787594.15 450000 112500 0.581000 5857651.29 455000 113750 0.606900 5927763.98 460000 115000 0.613800 5997931.61 465000 116250 0.613000 6068153.60 470000 117500 0.639800 6138429.35 475000 118750 0.598900 6208758.29 480000 120000 0.608000 6279139.86 485000 121250 0.619900 6349573.52 490000 122500 0.616800 6420058.73 495000 123750 0.657900 6490594.96 500000 125000 0.640000 6561181.69 505000 126250 0.645900 6631818.42 510000 127500 0.650000 6702504.66 515000 128750 0.695900 6773239.92 520000 130000 0.666900 6844023.73 525000 131250 0.671000 6914855.61 530000 132500 0.681900 6985735.11 535000 133750 0.678000 7056661.78 540000 135000 0.686000 7127635.19 545000 136250 0.696000 7198654.89 550000 137500 0.700000 7269720.46 555000 138750 0.706000 7340831.48 560000 140000 0.724000 7411987.56 565000 141250 0.722000 7483188.27 570000 142500 0.728000 7554433.23 575000 143750 0.745000 7625722.06 580000 145000 0.736000 7697054.36 585000 146250 0.753000 7768429.77 590000 147500 0.755100 7839847.91 595000 148750 0.760000 7911308.43 600000 150000 0.773100 7982810.96 605000 151250 0.774200 8054355.16 610000 152500 0.792000 8125940.68 615000 153750 0.793300 8197567.19 620000 155000 0.799100 8269234.35 625000 156250 0.806200 8340941.83 630000 157500 0.810200 8412689.31 635000 158750 0.827300 8484476.48 640000 160000 0.824100 8556303.01 645000 161250 0.820200 8628168.61 650000 162500 0.844300 8700072.97 655000 163750 0.845000 8772015.79 660000 165000 0.860300 8843996.78 665000 166250 0.865400 8916015.64 670000 167500 0.875300 8988072.10 675000 168750 0.879200 9060165.88 680000 170000 0.878300 9132296.69 685000 171250 0.892200 9204464.27 690000 172500 0.889200 9276668.34 695000 173750 0.897300 9348908.65 700000 175000 0.907300 9421184.93 705000 176250 0.918300 9493496.92 710000 177500 0.922300 9565844.38 715000 178750 0.923300 9638227.04 720000 180000 0.940400 9710644.67 725000 181250 0.933300 9783097.03 730000 182500 0.983500 9855583.86 735000 183750 0.962300 9928104.95 740000 185000 0.985500 10000660.04 745000 186250 0.970400 10073248.93 750000 187500 0.973300 10145871.36 755000 188750 0.977300 10218527.14 760000 190000 1.005400 10291216.02 765000 191250 0.995400 10363937.80 770000 192500 1.007400 10436692.26 775000 193750 1.016500 10509479.19 780000 195000 1.011500 10582298.37 785000 196250 1.020500 10655149.61 790000 197500 1.040500 10728032.70 795000 198750 1.033700 10800947.43 800000 200000 1.061400 10873893.61 805000 201250 1.043300 10946871.03 810000 202500 1.059600 11019879.52 815000 203750 1.058700 11092918.86 820000 205000 1.072600 11165988.89 825000 206250 1.077200 11239089.40 830000 207500 1.087500 11312220.21 835000 208750 1.095600 11385381.15 840000 210000 1.102000 11458572.02 845000 211250 1.116900 11531792.66 850000 212500 1.111700 11605042.88 855000 213750 1.127000 11678322.52 860000 215000 1.121500 11751631.39 865000 216250 1.131000 11824969.34 870000 217500 1.138800 11898336.19 875000 218750 1.152300 11971731.77 880000 220000 1.161700 12045155.92 885000 221250 1.167800 12118608.49 890000 222500 1.171500 12192089.30 895000 223750 1.174800 12265598.20 900000 225000 1.176600 12339135.04 905000 226250 1.197700 12412699.65 910000 227500 1.194700 12486291.89 915000 228750 1.203800 12559911.60 920000 230000 1.206700 12633558.63 925000 231250 1.219700 12707232.84 930000 232500 1.228900 12780934.07 935000 233750 1.228800 12854662.19 940000 235000 1.232800 12928417.04 945000 236250 1.243800 13002198.50 950000 237500 1.255800 13076006.40 955000 238750 1.268800 13149840.62 960000 240000 1.262700 13223701.02 965000 241250 1.293900 13297587.46 970000 242500 1.287800 13371499.81 975000 243750 1.274900 13445437.93 980000 245000 1.293800 13519401.69 985000 246250 1.301700 13593390.97 990000 247500 1.313800 13667405.62 995000 248750 1.313600 13741445.53 1000000 250000 1.330000 13815510.56 ********************** Result using deterministic algorithm ********************** n k T(Sec) nlogn 1000 750 0.001000 6907.76 5000 3750 0.005000 42585.97 10000 7500 0.013000 92103.40 15000 11250 0.016000 144237.08 20000 15000 0.020000 198069.75 25000 18750 0.028100 253165.78 30000 22500 0.034000 309268.58 35000 26250 0.037000 366208.62 40000 30000 0.045100 423865.39 45000 33750 0.049000 482148.80 50000 37500 0.058100 540988.91 55000 41250 0.064100 600329.87 60000 45000 0.067100 660125.99 65000 48750 0.074100 720339.27 70000 52500 0.079100 780937.54 75000 56250 0.086100 841893.25 80000 60000 0.092200 903182.55 85000 63750 0.099200 964784.56 90000 67500 0.103200 1026680.85 95000 71250 0.109200 1088855.06 100000 75000 0.118200 1151292.55 105000 78750 0.122200 1213980.14 110000 82500 0.126100 1276905.92 115000 86250 0.135200 1340059.05 120000 90000 0.140200 1403429.64 125000 93750 0.144300 1467008.63 130000 97500 0.151200 1530787.66 135000 101250 0.161300 1594759.06 140000 105000 0.165300 1658915.68 145000 108750 0.171300 1723250.91 150000 112500 0.178300 1787758.59 155000 116250 0.183300 1852432.96 160000 120000 0.191200 1917268.66 165000 123750 0.197300 1982260.62 170000 127500 0.199400 2047404.13 175000 131250 0.210300 2112694.72 180000 135000 0.213300 2178128.18 185000 138750 0.225400 2243700.55 190000 142500 0.229300 2309408.08 195000 146250 0.237300 2375247.19 200000 150000 0.245200 2441214.53 205000 153750 0.249300 2507306.88 210000 157500 0.256400 2573521.19 215000 161250 0.257300 2639854.56 220000 165000 0.267500 2706304.22 225000 168750 0.278500 2772867.53 230000 172500 0.279500 2839541.96 235000 176250 0.283400 2906325.09 240000 180000 0.296400 2973214.61 245000 183750 0.314400 3040208.30 250000 187500 0.303500 3107304.05 255000 191250 0.310400 3174499.80 260000 195000 0.323400 3241793.60 265000 198750 0.322400 3309183.55 270000 202500 0.329400 3376667.85 275000 206250 0.341500 3444244.75 280000 210000 0.346500 3511912.57 285000 213750 0.348500 3579669.67 290000 217500 0.356600 3647514.50 295000 221250 0.368600 3715445.54 300000 225000 0.370400 3783461.33 305000 228750 0.377300 3851560.45 310000 232500 0.385700 3919741.55 315000 236250 0.393600 3988003.29 320000 240000 0.393500 4056344.41 325000 243750 0.400600 4124763.65 330000 247500 0.401600 4193259.82 335000 251250 0.415500 4261831.75 340000 255000 0.424700 4330478.30 345000 258750 0.424600 4399198.40 350000 262500 0.434600 4467990.95 355000 266250 0.442600 4536854.94 360000 270000 0.445600 4605789.35 365000 273750 0.457800 4674793.21 370000 277500 0.458600 4743865.57 375000 281250 0.470600 4813005.49 380000 285000 0.475800 4882212.08 385000 288750 0.482600 4951484.47 390000 292500 0.491800 5020821.79 395000 296250 0.494700 5090223.21 400000 300000 0.499700 5159687.93 405000 303750 0.511600 5229215.15 410000 307500 0.513700 5298804.10 415000 311250 0.524000 5368454.03 420000 315000 0.525500 5438164.20 425000 318750 0.535000 5507933.89 430000 322500 0.545000 5577762.41 435000 326250 0.551000 5647649.07 440000 330000 0.556200 5717593.20 445000 333750 0.562300 5787594.15 450000 337500 0.565300 5857651.29 455000 341250 0.573000 5927763.98 460000 345000 0.583900 5997931.61 465000 348750 0.587700 6068153.60 470000 352500 0.593700 6138429.35 475000 356250 0.603900 6208758.29 480000 360000 0.609900 6279139.86 485000 363750 0.611800 6349573.52 490000 367500 0.623900 6420058.73 495000 371250 0.628900 6490594.96 500000 375000 0.631900 6561181.69 505000 378750 0.635000 6631818.42 510000 382500 0.658000 6702504.66 515000 386250 0.652000 6773239.92 520000 390000 0.660000 6844023.73 525000 393750 0.670900 6914855.61 530000 397500 0.670800 6985735.11 535000 401250 0.688000 7056661.78 540000 405000 0.694900 7127635.19 545000 408750 0.694000 7198654.89 550000 412500 0.694000 7269720.46 555000 416250 0.714000 7340831.48 560000 420000 0.712100 7411987.56 565000 423750 0.722000 7483188.27 570000 427500 0.732000 7554433.23 575000 431250 0.733000 7625722.06 580000 435000 0.757200 7697054.36 585000 438750 0.748000 7768429.77 590000 442500 0.752100 7839847.91 595000 446250 0.760000 7911308.43 600000 450000 0.766100 7982810.96 605000 453750 0.772100 8054355.16 610000 457500 0.781200 8125940.68 615000 461250 0.782200 8197567.19 620000 465000 0.797100 8269234.35 625000 468750 0.802100 8340941.83 630000 472500 0.814200 8412689.31 635000 476250 0.820100 8484476.48 640000 480000 0.817100 8556303.01 645000 483750 0.839400 8628168.61 650000 487500 0.836500 8700072.97 655000 491250 0.851500 8772015.79 660000 495000 0.852000 8843996.78 665000 498750 0.858200 8916015.64 670000 502500 0.864200 8988072.10 675000 506250 0.872300 9060165.88 680000 510000 0.871100 9132296.69 685000 513750 0.883200 9204464.27 690000 517500 0.890400 9276668.34 695000 521250 0.895400 9348908.65 700000 525000 0.905200 9421184.93 705000 528750 0.913200 9493496.92 710000 532500 0.911400 9565844.38 715000 536250 0.931300 9638227.04 720000 540000 0.926400 9710644.67 725000 543750 0.943300 9783097.03 730000 547500 0.946300 9855583.86 735000 551250 0.953500 9928104.95 740000 555000 0.952400 10000660.04 745000 558750 0.975300 10073248.93 750000 562500 0.984600 10145871.36 755000 566250 0.981400 10218527.14 760000 570000 0.978600 10291216.02 765000 573750 1.000400 10363937.80 770000 577500 0.998400 10436692.26 775000 581250 1.009400 10509479.19 780000 585000 1.013400 10582298.37 785000 588750 1.028400 10655149.61 790000 592500 1.038400 10728032.70 795000 596250 1.037500 10800947.43 800000 600000 1.040500 10873893.61 805000 603750 1.044500 10946871.03 810000 607500 1.058300 11019879.52 815000 611250 1.068400 11092918.86 820000 615000 1.067700 11165988.89 825000 618750 1.075600 11239089.40 830000 622500 1.077300 11312220.21 835000 626250 1.093900 11385381.15 840000 630000 1.119000 11458572.02 845000 633750 1.095600 11531792.66 850000 637500 1.107000 11605042.88 855000 641250 1.117000 11678322.52 860000 645000 1.135000 11751631.39 865000 648750 1.130300 11824969.34 870000 652500 1.142500 11898336.19 875000 656250 1.131900 11971731.77 880000 660000 1.161400 12045155.92 885000 663750 1.168600 12118608.49 890000 667500 1.162900 12192089.30 895000 671250 1.177800 12265598.20 900000 675000 1.179600 12339135.04 905000 678750 1.192500 12412699.65 910000 682500 1.194900 12486291.89 915000 686250 1.196800 12559911.60 920000 690000 1.209700 12633558.63 925000 693750 1.223800 12707232.84 930000 697500 1.219800 12780934.07 935000 701250 1.223800 12854662.19 940000 705000 1.235800 12928417.04 945000 708750 1.249800 13002198.50 950000 712500 1.244800 13076006.40 955000 716250 1.259000 13149840.62 960000 720000 1.271900 13223701.02 965000 723750 1.264800 13297587.46 970000 727500 1.280900 13371499.81 975000 731250 1.287800 13445437.93 980000 735000 1.288700 13519401.69 985000 738750 1.298800 13593390.97 990000 742500 1.307800 13667405.62 995000 746250 1.322000 13741445.53 1000000 750000 1.313000 13815510.56