Output_Sparse_24.txt

Randomly generating 10000 unique keys from 100000 to 200000
Number of keys generated: 10000
Keys generated: [100002, 100007, 100011, 100024, 100029, 100040, 100050, 100062, 100089, 100096, 100104, 100133, 100144, 100146, 100149, 100154, 100159, 100166, 100186, 100205, 100212, 100214, 100234, 100245, 100248, 100300, 100303, 100314, 100320, 100336, 100353, 100357, 100362, 100383, 100388, 100408, 100411, 100429, 100437, 100446, 100453, 100476, 100497, 100503, 100505, 100521, 100540, 100564, 100574, 100602, 100615, 100623, 100630, 100639, 100647, 100656, 100678, 100681, 100694, 100698, 100699, 100705, 100706, 100710, 100715, 100725, 100756, 100761, 100766, 100767, 100778, 100779, 100780, 100786, 100794, 100799, 100800, 100808, 100817, 100841, 100871, 100901, 100903, 100910, 100957, 100963, 100979, 100985, 100987, 100992, 100995, 100999, 101010, 101016, 101017, 101021, 101042, 101044, 101047, 101073, 101075, 101111, 101125, 101131, 101140, 101158, 101170, 101206, 101208, 101225, 101229, 101231, 101265, 101266, 101267, 101268, 101270, 101274, 101277, 101280, 101282, 101286, 101297, 101304, 101306, 101337, 101343, 101345, 101346, 101358, 101361, 101363, 101377, 101397, 101400, 101410, 101424, 101427, 101439, 101453, 101469, 101483, 101492, 101500, 101501, 101504, 101514, 101537, 101547, 101557, 101563, 101566, 101569, 101591, 101599, 101607, 101609, 101613, 101625, 101629, 101653, 101656, 101675, 101680, 101683, 101689, 101707, 101708, 101717, 101720, 101747, 101750, 101815, 101818, 101822, 101823, 101845, 101854, 101863, 101865, 101870, 101871, 101894, 101898, 101901, 101918, 101922, 101927, 101930, 101952, 101958, 101962, 101973, 101976, 101977, 101983, 101985, 101992, 101994, 102002, 102005, 102012, 102023, 102028, 102033, 102074, 102079, 102099, 102106, 102135, 102145, 102153, 102156, 102174, 102187, 102190, 102191, 102194, 102209, 102217, 102229, 102230, 102241, 102251, 102276, 102294, 102299, 102326, 102331, 102338, 102349, 102355, 102363, 102373, 102375, 102385, 102386, 102389, 102393, 102400, 102401, 102410, 102413, 102425, 102437, 102467, 102474, 102488, 102493, 102508, 102511, 102513, 102516, 102526, 102530, 102539, 102542, 102568, 102577, 102581, 102585, 102586, 102587, 102598, 102602, 102611, 102623, 102638, 102655, 102657, 102659, 102662, 102663, 102683, 102686, 102694, 102701, 102703, 102705, 102709, 102715, 102724, 102757, 102765, 102768, 102784, 102797, 102802, 102805, 102813, 102814, 102819, 102825, 102830, 102856, 102879, 102892, 102919, 102925, 102929, 102934, 102969, 102982, 102997, 103012, 103047, 103049, 103050, 103055, 103056, 103059, 103081, 103090, 103110, 103112, 103114, 103127, 103147, 103162, 103168, 103173, 103176, 103197, 103217, 103224, 103228, 103241, 103247, 103251, 103278, 103293, 103295, 103309, 103328, 103336, 103340, 103349, 103353, 103368, 103372, 103383, 103403, 103412, 103419, 103440, 103448, 103472, 103473, 103500, 103506, 103541, 103549, 103552, 103560, 103563, 103564, 103574, 103577, 103606, 103607, 103618, 103621, 103625, 103634, 103646, 103651, 103653, 103661, 103664, 103677, 103686, 103688, 103690, 103692, 103734, 103750, 103751, 103769, 103770, 103779, 103798, 103805, 103806, 103814, 103842, 103852, 103882, 103885, 103892, 103896, 103918, 103948, 103950, 103959, 103965, 103985, 103989, 103990, 103991, 103992, 104008, 104020, 104025, 104032, 104033, 104066, 104073, 104076, 104077, 104098, 104106, 104118, 104166, 104181, 104192, 104194, 104197, 104206, 104222, 104233, 104238, 104241, 104245, 104257, 104274, 104295, 104307, 104316, 104332, 104334, 104366, 104375, 104376, 104377, 104414, 104436, 104451, 104452, 104478, 104491, 104493, 104496, 104498, 104499, 104502, 104519, 104520, 104531, 104533, 104541, 104553, 104554, 104580, 104594, 104596, 104616, 104675, 104681, 104682, 104691, 104698, 104699, 104710, 104711, 104741, 104743, 104746, 104755, 104777, 104778, 104787, 104804, 104818, 104837, 104841, 104848, 104856, 104878, 104884, 104885, 104892, 104900, 104923, 104928, 104950, 104954, 104967, 104969, 105003, 105019, 105051, 105058, 105059, 105068, 105074, 105082, 105083, 105088, 105093, 105098, 105103, 105104, 105122, 105124, 105137, 105145, 105152, 105162, 105168, 105175, 105225, 105227, 105231, 105236, 105237, 105249, 105262, 105285, 105286, 105291, 105294, 105295, 105303, 105331, 105355, 105361, 105372, 105373, 105376, 105377, 105379, 105393, 105394, 105404, 105406, 105410, 105421, 105425, 105431, 105433, 105456, 105504, 105511, 105519, 105522, 105524, 105528, 105551, 105556, 105568, 105583, 105585, 105590, 105596, 105599, 105606, 105609, 105615, 105634, 105667, 105669, 105676, 105682, 105696, 105713, 105723, 105729, 105744, 105756, 105763, 105782, 105785, 105786, 105791, 105795, 105810, 105816, 105823, 105829, 105843, 105845, 105848, 105870, 105890, 105901, 105912, 105923, 105926, 105934, 105937, 105945, 105946, 105947, 105957, 105968, 105979, 105981, 106009, 106038, 106051, 106071, 106077, 106079, 106081, 106094, 106098, 106102, 106106, 106107, 106115, 106130, 106131, 106137, 106141, 106147, 106149, 106165, 106183, 106201, 106203, 106205, 106209, 106223, 106225, 106237, 106262, 106285, 106322, 106329, 106337, 106340, 106345, 106349, 106354, 106364, 106373, 106379, 106383, 106386, 106391, 106400, 106419, 106421, 106426, 106427, 106451, 106461, 106463, 106471, 106472, 106481, 106494, 106500, 106505, 106511, 106514, 106521, 106539, 106541, 106543, 106559, 106580, 106586, 106614, 106626, 106634, 106641, 106656, 106658, 106660, 106680, 106683, 106684, 106688, 106697, 106698, 106700, 106709, 106710, 106712, 106713, 106727, 106734, 106751, 106758, 106760, 106763, 106769, 106771, 106775, 106776, 106790, 106795, 106797, 106805, 106819, 106820, 106827, 106840, 106847, 106852, 106860, 106871, 106891, 106921, 106941, 106973, 106979, 107007, 107008, 107036, 107049, 107054, 107061, 107072, 107083, 107089, 107105, 107107, 107115, 107119, 107126, 107136, 107141, 107154, 107160, 107165, 107175, 107185, 107189, 107204, 107218, 107219, 107222, 107244, 107271, 107277, 107285, 107297, 107303, 107317, 107340, 107342, 107345, 107348, 107362, 107370, 107372, 107418, 107420, 107423, 107429, 107438, 107442, 107456, 107465, 107471, 107473, 107476, 107481, 107519, 107526, 107527, 107531, 107537, 107549, 107556, 107558, 107575, 107577, 107578, 107614, 107615, 107619, 107623, 107631, 107633, 107639, 107649, 107665, 107679, 107695, 107703, 107720, 107730, 107731, 107734, 107745, 107760, 107770, 107781, 107810, 107816, 107830, 107834, 107842, 107843, 107868, 107878, 107879, 107920, 107926, 107936, 107954, 107955, 107975, 107978, 107980, 107988, 107990, 107992, 107996, 108003, 108005, 108010, 108033, 108035, 108036, 108062, 108067, 108069, 108117, 108121, 108140, 108151, 108156, 108170, 108175, 108177, 108179, 108191, 108196, 108218, 108219, 108230, 108234, 108239, 108243, 108252, 108258, 108275, 108290, 108293, 108304, 108318, 108332, 108345, 108347, 108350, 108356, 108359, 108365, 108366, 108369, 108403, 108410, 108411, 108421, 108428, 108441, 108450, 108472, 108477, 108479, 108481, 108491, 108498, 108523, 108541, 108548, 108561, 108579, 108582, 108591, 108600, 108607, 108611, 108614, 108646, 108648, 108665, 108677, 108702, 108731, 108734, 108758, 108777, 108789, 108814, 108817, 108822, 108823, 108827, 108830, 108843, 108872, 108873, 108882, 108885, 108893, 108926, 108936, 108940, 108942, 108965, 108980, 108981, 108991, 109017, 109026, 109039, 109044, 109046, 109055, 109060, 109064, 109066, 109070, 109072, 109075, 109077, 109092, 109105, 109125, 109131, 109169, 109170, 109177, 109185, 109202, 109203, 109216, 109222, 109249, 109259, 109261, 109266, 109278, 109279, 109282, 109285, 109290, 109295, 109299, 109315, 109324, 109342, 109343, 109345, 109349, 109360, 109362, 109396, 109422, 109434, 109438, 109448, 109456, 109462, 109463, 109472, 109475, 109483, 109485, 109505, 109537, 109544, 109552, 109566, 109573, 109587, 109588, 109591, 109601, 109611, 109614, 109623, 109630, 109650, 109653, 109661, 109682, 109689, 109710, 109715, 109720, 109740, 109757, 109779, 109787, 109788, 109797, 109808, 109826, 109837, 109860, 109862, 109863, 109899, 109905, 109907, 109914, 109924, 109930, 109940, 109946, 109948, 109955, 109958, 109960, 109968, 109973, 109976, 110015, 110017, 110032, 110036, 110043, 110045, 110054, 110062, 110068, 110083, 110089, 110096, 110104, 110106, 110112, 110117, 110128, 110150, 110160, 110162, 110183, 110184, 110191, 110203, 110217, 110224, 110236, 110242, 110245, 110265, 110273, 110275, 110284, 110285, 110289, 110292, 110319, 110322, 110330, 110334, 110344, 110353, 110360, 110368, 110438, 110448, 110449, 110450, 110458, 110467, 110475, 110485, 110490, 110496, 110497, 110501, 110502, 110505, 110512, 110522, 110525, 110534, 110556, 110619, 110626, 110634, 110647, 110649, 110654, 110660, 110666, 110667, 110671, 110675, 110676, 110679, 110685, 110704, 110706, 110741, 110769, 110776, 110788, 110792, 110811, 110826, 110831, 110850, 110854, 110869, 110896, 110909, 110919, 110929, 110947, 110975, 110981, 110985, 110990, 110998, 111007, 111035, 111057, 111070, 111093, 111098, 111102, 111111, 111112, 111128, 111156, 111166, 111197, 111199, 111203, 111208, 111209, 111212, 111214, 111218, 111232, 111234, 111237, 111249, 111271, 111276, 111290, 111314, 111320, 111326, 111332, 111343, 111345, 111347, 111349, 111352, 111363, 111386, 111392, 111393, 111419, 111428, 111443, 111453, 111457, 111458, 111473, 111476, 111499, 111509, 111525, 111526, 111545, 111547, 111557, 111562, 111574, 111577, 111578, 111585, 111590, 111601, 111609, 111611, 111614, 111616, 111621, 111633, 111636, 111641, 111642, 111653, 111661, 111674, 111703, 111706, 111712, 111716, 111731, 111734, 111738, 111740, 111750, 111752, 111762, 111764, 111766, 111777, 111778, 111783, 111789, 111791, 111795, 111809, 111820, 111847, 111855, 111872, 111875, 111876, 111897, 111919, 111924, 111926, 111935, 111953, 111957, 111966, 111995, 112003, 112008, 112012, 112031, 112040, 112084, 112090, 112097, 112111, 112113, 112131, 112147, 112177, 112191, 112201, 112204, 112206, 112209, 112219, 112223, 112254, 112278, 112281, 112300, 112308, 112329, 112340, 112346, 112348, 112376, 112383, 112392, 112406, 112409, 112414, 112433, 112436, 112452, 112454, 112456, 112460, 112463, 112470, 112474, 112479, 112489, 112495, 112519, 112533, 112541, 112547, 112548, 112557, 112583, 112588, 112596, 112603, 112604, 112619, 112632, 112637, 112641, 112653, 112659, 112663, 112664, 112669, 112674, 112675, 112682, 112708, 112720, 112721, 112723, 112725, 112728, 112739, 112749, 112764, 112774, 112787, 112790, 112802, 112806, 112826, 112827, 112836, 112839, 112854, 112860, 112865, 112869, 112873, 112913, 112921, 112924, 112936, 112942, 112967, 112969, 113001, 113004, 113009, 113014, 113017, 113018, 113024, 113058, 113070, 113088, 113089, 113097, 113102, 113108, 113111, 113113, 113130, 113150, 113154, 113159, 113165, 113178, 113184, 113185, 113196, 113204, 113207, 113241, 113254, 113258, 113262, 113265, 113268, 113270, 113273, 113274, 113288, 113291, 113303, 113308, 113309, 113312, 113317, 113319, 113322, 113325, 113332, 113337, 113355, 113371, 113374, 113382, 113385, 113409, 113413, 113417, 113422, 113433, 113435, 113448, 113454, 113455, 113480, 113483, 113484, 113503, 113510, 113525, 113529, 113536, 113548, 113549, 113556, 113577, 113582, 113602, 113619, 113623, 113626, 113635, 113641, 113643, 113666, 113673, 113681, 113682, 113692, 113695, 113700, 113704, 113725, 113747, 113756, 113768, 113778, 113787, 113822, 113826, 113835, 113837, 113843, 113865, 113868, 113901, 113930, 113941, 113976, 113983, 113984, 113987, 113989, 113997, 114012, 114045, 114070, 114080, 114087, 114093, 114095, 114098, 114104, 114111, 114125, 114128, 114151, 114154, 114159, 114170, 114180, 114190, 114191, 114202, 114205, 114206, 114210, 114216, 114227, 114228, 114246, 114257, 114268, 114273, 114285, 114312, 114323, 114327, 114339, 114343, 114346, 114370, 114371, 114374, 114382, 114389, 114407, 114418, 114436, 114440, 114446, 114448, 114464, 114468, 114483, 114505, 114508, 114537, 114539, 114545, 114549, 114550, 114553, 114558, 114598, 114600, 114601, 114619, 114652, 114669, 114681, 114694, 114714, 114768, 114782, 114789, 114793, 114805, 114807, 114809, 114821, 114835, 114849, 114853, 114859, 114862, 114870, 114899, 114900, 114940, 114953, 114958, 114967, 114976, 114979, 114988, 114993, 115017, 115039, 115047, 115048, 115060, 115063, 115069, 115107, 115119, 115125, 115126, 115128, 115135, 115137, 115157, 115181, 115184, 115195, 115211, 115213, 115222, 115227, 115230, 115248, 115257, 115260, 115279, 115283, 115285, 115310, 115323, 115333, 115344, 115352, 115353, 115362, 115365, 115366, 115375, 115390, 115394, 115406, 115411, 115412, 115420, 115425, 115428, 115429, 115433, 115434, 115449, 115456, 115469, 115497, 115510, 115530, 115535, 115536, 115540, 115558, 115562, 115565, 115578, 115590, 115600, 115624, 115628, 115641, 115647, 115656, 115670, 115677, 115701, 115753, 115768, 115769, 115788, 115802, 115805, 115823, 115832, 115833, 115840, 115852, 115853, 115865, 115895, 115901, 115918, 115928, 115937, 115943, 115948, 115959, 115968, 115981, 115999, 116005, 116009, 116010, 116013, 116034, 116059, 116061, 116072, 116076, 116077, 116093, 116108, 116131, 116132, 116146, 116152, 116154, 116165, 116168, 116195, 116203, 116204, 116226, 116242, 116243, 116271, 116305, 116329, 116355, 116379, 116385, 116387, 116388, 116401, 116402, 116403, 116413, 116430, 116457, 116459, 116465, 116483, 116486, 116489, 116497, 116498, 116510, 116523, 116533, 116541, 116566, 116592, 116594, 116595, 116596, 116597, 116602, 116624, 116628, 116630, 116641, 116645, 116664, 116665, 116670, 116671, 116696, 116705, 116708, 116716, 116717, 116725, 116771, 116772, 116776, 116790, 116809, 116814, 116846, 116847, 116849, 116859, 116866, 116867, 116878, 116881, 116885, 116888, 116896, 116898, 116901, 116916, 116937, 116952, 116956, 116961, 116962, 116964, 116978, 116985, 117009, 117014, 117028, 117038, 117052, 117054, 117062, 117068, 117076, 117085, 117105, 117110, 117120, 117155, 117163, 117165, 117170, 117174, 117183, 117187, 117225, 117228, 117229, 117234, 117263, 117266, 117279, 117280, 117286, 117290, 117308, 117314, 117324, 117333, 117336, 117348, 117355, 117374, 117382, 117383, 117384, 117401, 117416, 117430, 117431, 117448, 117462, 117464, 117467, 117490, 117512, 117517, 117519, 117521, 117536, 117541, 117547, 117556, 117561, 117563, 117568, 117584, 117600, 117609, 117615, 117622, 117628, 117644, 117649, 117651, 117704, 117707, 117717, 117726, 117735, 117740, 117771, 117780, 117794, 117811, 117814, 117819, 117820, 117822, 117832, 117839, 117845, 117871, 117889, 117898, 117913, 117940, 117948, 117962, 117964, 117965, 117983, 117987, 117989, 117992, 117993, 117994, 117996, 118002, 118060, 118074, 118086, 118112, 118117, 118123, 118125, 118127, 118153, 118161, 118162, 118201, 118205, 118210, 118214, 118221, 118225, 118238, 118245, 118259, 118269, 118274, 118294, 118362, 118364, 118371, 118378, 118424, 118427, 118440, 118449, 118458, 118460, 118475, 118478, 118502, 118535, 118539, 118542, 118557, 118570, 118593, 118628, 118644, 118650, 118651, 118682, 118683, 118689, 118718, 118719, 118721, 118722, 118738, 118739, 118742, 118747, 118760, 118764, 118765, 118779, 118781, 118783, 118791, 118819, 118820, 118824, 118825, 118830, 118840, 118844, 118846, 118857, 118858, 118860, 118903, 118905, 118908, 118920, 118922, 118926, 118945, 118965, 118967, 118975, 118977, 118981, 119018, 119020, 119025, 119029, 119066, 119076, 119103, 119104, 119115, 119119, 119136, 119140, 119152, 119175, 119176, 119182, 119183, 119193, 119208, 119209, 119218, 119219, 119222, 119233, 119234, 119241, 119270, 119271, 119280, 119318, 119320, 119325, 119329, 119331, 119353, 119369, 119376, 119380, 119402, 119406, 119407, 119410, 119426, 119432, 119434, 119439, 119444, 119448, 119451, 119457, 119490, 119526, 119537, 119545, 119553, 119563, 119567, 119573, 119602, 119607, 119633, 119643, 119644, 119646, 119660, 119661, 119671, 119696, 119697, 119698, 119704, 119708, 119715, 119718, 119723, 119745, 119750, 119759, 119768, 119776, 119778, 119790, 119797, 119811, 119813, 119822, 119825, 119827, 119828, 119829, 119864, 119875, 119891, 119896, 119898, 119900, 119905, 119915, 119934, 119940, 119952, 119962, 119963, 119992, 119998, 120029, 120040, 120075, 120086, 120096, 120101, 120107, 120112, 120117, 120120, 120149, 120153, 120156, 120167, 120178, 120186, 120190, 120214, 120237, 120240, 120246, 120251, 120269, 120295, 120322, 120356, 120365, 120372, 120388, 120394, 120402, 120406, 120424, 120441, 120445, 120457, 120461, 120464, 120466, 120467, 120470, 120498, 120500, 120503, 120504, 120510, 120512, 120528, 120529, 120533, 120541, 120557, 120585, 120594, 120595, 120605, 120611, 120639, 120650, 120663, 120665, 120694, 120710, 120715, 120718, 120724, 120727, 120730, 120731, 120746, 120750, 120761, 120786, 120789, 120791, 120792, 120818, 120820, 120849, 120851, 120860, 120879, 120888, 120899, 120908, 120928, 120939, 120945, 120946, 120953, 120956, 120961, 120982, 120988, 120993, 121006, 121014, 121021, 121030, 121041, 121046, 121052, 121056, 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199995, 199998]
Creating sparse tree of order: 24
Printing sparse tree. The nodes are printed in DFS format.
Root Node:[100002, 117052, 134164, 151609, 169033]
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[180969, 180982, 180983, 180985, 180989, 180993, 181007, 181018, 181032, 181041, 181044, 181068]
[181072, 181076, 181078, 181091, 181092, 181093, 181116, 181125, 181137, 181144, 181157, 181168]
[181195, 181197, 181202, 181204, 181207, 181216, 181220, 181272, 181283, 181297, 181304, 181306]
[181310, 181315, 181318, 181339, 181343, 181354, 181355, 181359, 181363, 181376, 181393, 181403]
[181425, 181426, 181428, 181431, 181438, 181441, 181468, 181474, 181480, 181482, 181491, 181505]
[181509, 181523, 181529, 181532, 181536, 181546, 181550, 181561, 181582, 181583, 181586, 181596]
[181616, 181628, 181635, 181637, 181645, 181664, 181680, 181693, 181695, 181696, 181702, 181708]
[181709, 181718, 181727, 181740, 181758, 181760, 181761, 181769, 181782, 181787, 181793, 181806]
[181807, 181929, 182032, 182133, 182239, 182356, 182466, 182573, 182713, 182812, 182996, 183130]
[181807, 181816, 181829, 181840, 181846, 181849, 181851, 181857, 181876, 181911, 181918, 181920]
[181929, 181935, 181936, 181948, 181968, 181971, 181973, 181991, 182005, 182011, 182020, 182024]
[182032, 182037, 182039, 182063, 182065, 182075, 182082, 182083, 182089, 182095, 182106, 182112]
[182133, 182144, 182146, 182148, 182155, 182158, 182185, 182196, 182204, 182205, 182210, 182213]
[182239, 182246, 182250, 182270, 182275, 182277, 182306, 182334, 182336, 182337, 182349, 182350]
[182356, 182361, 182378, 182380, 182385, 182396, 182400, 182402, 182433, 182436, 182451, 182459]
[182466, 182477, 182478, 182512, 182525, 182527, 182537, 182543, 182547, 182548, 182551, 182557]
[182573, 182574, 182580, 182581, 182591, 182596, 182646, 182653, 182657, 182677, 182694, 182701]
[182713, 182739, 182754, 182758, 182767, 182776, 182783, 182788, 182789, 182800, 182801, 182808]
[182812, 182815, 182829, 182890, 182907, 182913, 182924, 182936, 182953, 182954, 182960, 182981]
[182996, 183001, 183012, 183014, 183016, 183022, 183035, 183040, 183045, 183064, 183101, 183114]
[183130, 183136, 183138, 183139, 183144, 183149, 183187, 183191, 183208, 183212, 183224, 183225]
[183230, 183330, 183439, 183562, 183714, 183778, 183885, 184034, 184128, 184220, 184305, 184411]
[183230, 183242, 183247, 183279, 183283, 183290, 183295, 183302, 183305, 183313, 183317, 183325]
[183330, 183338, 183339, 183347, 183356, 183366, 183373, 183398, 183410, 183415, 183420, 183436]
[183439, 183440, 183455, 183465, 183481, 183495, 183496, 183511, 183539, 183551, 183557, 183558]
[183562, 183567, 183570, 183585, 183590, 183592, 183594, 183640, 183655, 183682, 183686, 183694]
[183714, 183715, 183724, 183727, 183731, 183734, 183738, 183744, 183748, 183759, 183766, 183772]
[183778, 183809, 183815, 183817, 183818, 183823, 183837, 183846, 183856, 183861, 183862, 183868]
[183885, 183898, 183917, 183938, 183940, 183948, 183953, 183965, 184001, 184018, 184027, 184033]
[184034, 184040, 184041, 184042, 184045, 184060, 184063, 184065, 184086, 184088, 184092, 184100]
[184128, 184142, 184144, 184149, 184157, 184165, 184170, 184177, 184178, 184189, 184193, 184207]
[184220, 184232, 184235, 184251, 184253, 184260, 184265, 184272, 184274, 184283, 184298, 184300]
[184305, 184313, 184324, 184325, 184331, 184335, 184343, 184345, 184382, 184392, 184403, 184409]
[184411, 184416, 184420, 184431, 184436, 184455, 184468, 184480, 184490, 184496, 184507, 184519]
[184526, 184652, 184785, 184887, 185041, 185135, 185300, 185378, 185459, 185567, 185715, 185854]
[184526, 184527, 184530, 184544, 184558, 184573, 184574, 184592, 184616, 184620, 184624, 184630]
[184652, 184655, 184658, 184677, 184692, 184708, 184713, 184716, 184723, 184731, 184744, 184775]
[184785, 184796, 184805, 184820, 184823, 184841, 184843, 184847, 184851, 184858, 184876, 184883]
[184887, 184892, 184897, 184903, 184915, 184933, 184937, 184965, 184979, 184991, 185010, 185037]
[185041, 185050, 185051, 185063, 185069, 185074, 185079, 185096, 185097, 185108, 185124, 185127]
[185135, 185138, 185145, 185167, 185196, 185213, 185217, 185224, 185237, 185255, 185276, 185294]
[185300, 185306, 185308, 185309, 185310, 185313, 185329, 185349, 185350, 185368, 185369, 185372]
[185378, 185386, 185401, 185409, 185419, 185422, 185434, 185435, 185438, 185445, 185446, 185450]
[185459, 185475, 185480, 185493, 185502, 185506, 185523, 185532, 185533, 185542, 185556, 185565]
[185567, 185612, 185625, 185635, 185639, 185641, 185658, 185663, 185674, 185686, 185696, 185711]
[185715, 185729, 185736, 185754, 185763, 185764, 185780, 185786, 185799, 185819, 185820, 185842]
[185854, 185860, 185864, 185896, 185915, 185916, 185920, 185922, 185929, 185933, 185988, 185992]
**********************************


Experimentation
1. Generating random numbers for experimentation
Random numbers generated: [106116, 117924, 120392, 126891, 130974, 108776, 106161, 101470, 197596, 148389, 198608, 194193, 122065, 121178]
**********************************


2. Performing two random insert operations 
Inserting: 106116
Searching key 106116 in the tree to see if it already exists.
Searching: 106116
Traversing the tree from root node to leaf:
[100002, 117052, 134164, 151609, 169033]
[100002, 101501, 102805, 104376, 105816, 107119, 108481, 109958, 111393, 112725, 114095, 115536]
[105816, 105934, 106071, 106137, 106237, 106379, 106471, 106559, 106684, 106758, 106820, 107007]
[106071, 106077, 106079, 106081, 106094, 106098, 106102, 106106, 106107, 106115, 106130, 106131]
Key 106116 does not exist in the tree
The key 106116 that you want to insert is not already in the B+ tree.
Inserting it
Traversing the tree to insert key 
Root Node: [100002, 117052, 134164, 151609, 169033]
Level1: [100002, 101501, 102805, 104376, 105816, 107119, 108481, 109958, 111393, 112725, 114095, 115536]
Level2: [105816, 105934, 106071, 106137, 106237, 106379, 106471, 106559, 106684, 106758, 106820, 107007]
Level3: [106071, 106077, 106079, 106081, 106094, 106098, 106102, 106106, 106107, 106115, 106130, 106131]
Inserting 106116 in leaf node [106071, 106077, 106079, 106081, 106094, 106098, 106102, 106106, 106107, 106115, 106130, 106131]
After inserting: [106071, 106077, 106079, 106081, 106094, 106098, 106102, 106106, 106107, 106115, 106116, 106130, 106131]
106116 has been inserted in the tree.
**********************************


Inserting: 117924
Searching key 117924 in the tree to see if it already exists.
Searching: 117924
Traversing the tree from root node to leaf:
[100002, 117052, 134164, 151609, 169033]
[117052, 118650, 119962, 121561, 123000, 124225, 125746, 127220, 128633, 130075, 131450, 132749]
[117052, 117170, 117286, 117384, 117519, 117615, 117771, 117889, 117993, 118153, 118269, 118460]
[117889, 117898, 117913, 117940, 117948, 117962, 117964, 117965, 117983, 117987, 117989, 117992]
Key 117924 does not exist in the tree
The key 117924 that you want to insert is not already in the B+ tree.
Inserting it
Traversing the tree to insert key 
Root Node: [100002, 117052, 134164, 151609, 169033]
Level1: [117052, 118650, 119962, 121561, 123000, 124225, 125746, 127220, 128633, 130075, 131450, 132749]
Level2: [117052, 117170, 117286, 117384, 117519, 117615, 117771, 117889, 117993, 118153, 118269, 118460]
Level3: [117889, 117898, 117913, 117940, 117948, 117962, 117964, 117965, 117983, 117987, 117989, 117992]
Inserting 117924 in leaf node [117889, 117898, 117913, 117940, 117948, 117962, 117964, 117965, 117983, 117987, 117989, 117992]
After inserting: [117889, 117898, 117913, 117924, 117940, 117948, 117962, 117964, 117965, 117983, 117987, 117989, 117992]
117924 has been inserted in the tree.
**********************************


3. Performing random delete operations 
Deleting key: 120392
The key120392 that you want to delete does not exist in the tree
**********************************


Deleting key: 126891
The key126891 that you want to delete does not exist in the tree
**********************************


4. Performing random insert/deletion operations 
Inserting: 130974
Searching key 130974 in the tree to see if it already exists.
Searching: 130974
Traversing the tree from root node to leaf:
[100002, 117052, 134164, 151609, 169033]
[117052, 118650, 119962, 121561, 123000, 124225, 125746, 127220, 128633, 130075, 131450, 132749]
[130075, 130140, 130227, 130361, 130427, 130535, 130703, 130781, 130953, 131074, 131174, 131332]
[130953, 130956, 130960, 130973, 130978, 130987, 131007, 131030, 131036, 131038, 131055, 131058]
Key 130974 does not exist in the tree
The key 130974 that you want to insert is not already in the B+ tree.
Inserting it
Traversing the tree to insert key 
Root Node: [100002, 117052, 134164, 151609, 169033]
Level1: [117052, 118650, 119962, 121561, 123000, 124225, 125746, 127220, 128633, 130075, 131450, 132749]
Level2: [130075, 130140, 130227, 130361, 130427, 130535, 130703, 130781, 130953, 131074, 131174, 131332]
Level3: [130953, 130956, 130960, 130973, 130978, 130987, 131007, 131030, 131036, 131038, 131055, 131058]
Inserting 130974 in leaf node [130953, 130956, 130960, 130973, 130978, 130987, 131007, 131030, 131036, 131038, 131055, 131058]
After inserting: [130953, 130956, 130960, 130973, 130974, 130978, 130987, 131007, 131030, 131036, 131038, 131055, 131058]
130974 has been inserted in the tree.
**********************************


Deleting key: 108776
The key108776 that you want to delete does not exist in the tree
**********************************


Inserting: 106161
Searching key 106161 in the tree to see if it already exists.
Searching: 106161
Traversing the tree from root node to leaf:
[100002, 117052, 134164, 151609, 169033]
[100002, 101501, 102805, 104376, 105816, 107119, 108481, 109958, 111393, 112725, 114095, 115536]
[105816, 105934, 106071, 106137, 106237, 106379, 106471, 106559, 106684, 106758, 106820, 107007]
[106137, 106141, 106147, 106149, 106165, 106183, 106201, 106203, 106205, 106209, 106223, 106225]
Key 106161 does not exist in the tree
The key 106161 that you want to insert is not already in the B+ tree.
Inserting it
Traversing the tree to insert key 
Root Node: [100002, 117052, 134164, 151609, 169033]
Level1: [100002, 101501, 102805, 104376, 105816, 107119, 108481, 109958, 111393, 112725, 114095, 115536]
Level2: [105816, 105934, 106071, 106137, 106237, 106379, 106471, 106559, 106684, 106758, 106820, 107007]
Level3: [106137, 106141, 106147, 106149, 106165, 106183, 106201, 106203, 106205, 106209, 106223, 106225]
Inserting 106161 in leaf node [106137, 106141, 106147, 106149, 106165, 106183, 106201, 106203, 106205, 106209, 106223, 106225]
After inserting: [106137, 106141, 106147, 106149, 106161, 106165, 106183, 106201, 106203, 106205, 106209, 106223, 106225]
106161 has been inserted in the tree.
**********************************


Deleting key: 101470
The key101470 that you want to delete does not exist in the tree
**********************************


Inserting: 197596
Searching key 197596 in the tree to see if it already exists.
Searching: 197596
Traversing the tree from root node to leaf:
[100002, 117052, 134164, 151609, 169033]
[169033, 170565, 171852, 173437, 174969, 176370, 177764, 179043, 180381, 181807, 183230, 184526]
[184526, 184652, 184785, 184887, 185041, 185135, 185300, 185378, 185459, 185567, 185715, 185854]
[185854, 185860, 185864, 185896, 185915, 185916, 185920, 185922, 185929, 185933, 185988, 185992]
Key 197596 does not exist in the tree
The key 197596 that you want to insert is not already in the B+ tree.
Inserting it
Traversing the tree to insert key 
Root Node: [100002, 117052, 134164, 151609, 169033]
Level1: [169033, 170565, 171852, 173437, 174969, 176370, 177764, 179043, 180381, 181807, 183230, 184526]
Level2: [184526, 184652, 184785, 184887, 185041, 185135, 185300, 185378, 185459, 185567, 185715, 185854]
Level3: [185854, 185860, 185864, 185896, 185915, 185916, 185920, 185922, 185929, 185933, 185988, 185992]
Inserting 197596 in leaf node [185854, 185860, 185864, 185896, 185915, 185916, 185920, 185922, 185929, 185933, 185988, 185992]
After inserting: [185854, 185860, 185864, 185896, 185915, 185916, 185920, 185922, 185929, 185933, 185988, 185992, 197596]
197596 has been inserted in the tree.
**********************************


5. Performing random search operations 
Searching: 148389
Traversing the tree from root node to leaf:
[100002, 117052, 134164, 151609, 169033]
[134164, 135552, 137011, 138525, 139834, 141389, 142876, 144260, 145648, 147180, 148679, 150273]
[147180, 147334, 147439, 147564, 147681, 147799, 147902, 148035, 148143, 148227, 148408, 148534]
[148227, 148232, 148252, 148287, 148300, 148310, 148313, 148321, 148326, 148342, 148364, 148368]
Key 148389 does not exist in the tree
**********************************

Searching: 198608
Traversing the tree from root node to leaf:
[100002, 117052, 134164, 151609, 169033]
[169033, 170565, 171852, 173437, 174969, 176370, 177764, 179043, 180381, 181807, 183230, 184526]
[184526, 184652, 184785, 184887, 185041, 185135, 185300, 185378, 185459, 185567, 185715, 185854]
[185854, 185860, 185864, 185896, 185915, 185916, 185920, 185922, 185929, 185933, 185988, 185992, 197596]
Key 198608 does not exist in the tree
**********************************

Searching: 194193
Traversing the tree from root node to leaf:
[100002, 117052, 134164, 151609, 169033]
[169033, 170565, 171852, 173437, 174969, 176370, 177764, 179043, 180381, 181807, 183230, 184526]
[184526, 184652, 184785, 184887, 185041, 185135, 185300, 185378, 185459, 185567, 185715, 185854]
[185854, 185860, 185864, 185896, 185915, 185916, 185920, 185922, 185929, 185933, 185988, 185992, 197596]
Key 194193 does not exist in the tree
**********************************

Searching: 122065
Traversing the tree from root node to leaf:
[100002, 117052, 134164, 151609, 169033]
[117052, 118650, 119962, 121561, 123000, 124225, 125746, 127220, 128633, 130075, 131450, 132749]
[121561, 121663, 121779, 121911, 121986, 122074, 122236, 122362, 122597, 122697, 122773, 122907]
[121986, 121987, 121994, 121998, 122004, 122008, 122019, 122020, 122029, 122047, 122050, 122065]
Key 122065 exists in the tree
**********************************

Searching: 121178
Traversing the tree from root node to leaf:
[100002, 117052, 134164, 151609, 169033]
[117052, 118650, 119962, 121561, 123000, 124225, 125746, 127220, 128633, 130075, 131450, 132749]
[119962, 120117, 120246, 120424, 120504, 120611, 120731, 120860, 120982, 121080, 121239, 121352]
[121080, 121101, 121134, 121139, 121148, 121164, 121172, 121174, 121183, 121195, 121219, 121231]
Key 121178 does not exist in the tree
**********************************


6. Performing two random range search operations 
Searching in the range: 72019, 266303
Keys within the range: 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Searching in the range: 137901, 159620
Keys within the range: 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More Experimentation
Generating random number for experimentation
Random number generated: [174599]
1.1. Inserting: 174599
Inserting: 174599
Searching key 174599 in the tree to see if it already exists.
Searching: 174599
Traversing the tree from root node to leaf:
[100002, 117052, 134164, 151609, 169033]
[169033, 170565, 171852, 173437, 174969, 176370, 177764, 179043, 180381, 181807, 183230, 184526]
[173437, 173536, 173673, 173832, 174001, 174155, 174272, 174451, 174583, 174696, 174770, 174867]
[174583, 174592, 174595, 174618, 174644, 174651, 174661, 174677, 174679, 174683, 174684, 174690]
Key 174599 does not exist in the tree
The key 174599 that you want to insert is not already in the B+ tree.
Inserting it
Traversing the tree to insert key 
Root Node: [100002, 117052, 134164, 151609, 169033]
Level1: [169033, 170565, 171852, 173437, 174969, 176370, 177764, 179043, 180381, 181807, 183230, 184526]
Level2: [173437, 173536, 173673, 173832, 174001, 174155, 174272, 174451, 174583, 174696, 174770, 174867]
Level3: [174583, 174592, 174595, 174618, 174644, 174651, 174661, 174677, 174679, 174683, 174684, 174690]
Inserting 174599 in leaf node [174583, 174592, 174595, 174618, 174644, 174651, 174661, 174677, 174679, 174683, 174684, 174690]
After inserting: [174583, 174592, 174595, 174599, 174618, 174644, 174651, 174661, 174677, 174679, 174683, 174684, 174690]
174599 has been inserted in the tree.
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1.2. Re - inserting: 174599
Inserting: 174599
Searching key 174599 in the tree to see if it already exists.
Searching: 174599
Traversing the tree from root node to leaf:
[100002, 117052, 134164, 151609, 169033]
[169033, 170565, 171852, 173437, 174969, 176370, 177764, 179043, 180381, 181807, 183230, 184526]
[173437, 173536, 173673, 173832, 174001, 174155, 174272, 174451, 174583, 174696, 174770, 174867]
[174583, 174592, 174595, 174599, 174618, 174644, 174651, 174661, 174677, 174679, 174683, 174684, 174690]
Key 174599 exists in the tree
The key 174599 that you want to insert already exists in the B+ tree.
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1.3. Searching: 174599
Searching: 174599
Traversing the tree from root node to leaf:
[100002, 117052, 134164, 151609, 169033]
[169033, 170565, 171852, 173437, 174969, 176370, 177764, 179043, 180381, 181807, 183230, 184526]
[173437, 173536, 173673, 173832, 174001, 174155, 174272, 174451, 174583, 174696, 174770, 174867]
[174583, 174592, 174595, 174599, 174618, 174644, 174651, 174661, 174677, 174679, 174683, 174684, 174690]
Key 174599 exists in the tree
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1.4. Deleting: 174599
Deleting key: 174599
Node before deleting: [174583, 174592, 174595, 174599, 174618, 174644, 174651, 174661, 174677, 174679, 174683, 174684, 174690]
Node after deleting: [174583, 174592, 174595, 174618, 174644, 174651, 174661, 174677, 174679, 174683, 174684, 174690]
Key deletion completed
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Deletion operation complete.
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