Output_Dense_13.txt

Randomly generating 10000 unique keys from 100000 to 200000
Number of keys generated: 10000
Keys generated: [100010, 100013, 100016, 100032, 100041, 100047, 100052, 100055, 100081, 100089, 100096, 100100, 100107, 100110, 100119, 100130, 100139, 100152, 100154, 100172, 100184, 100193, 100200, 100201, 100203, 100204, 100205, 100222, 100230, 100242, 100243, 100278, 100282, 100289, 100297, 100299, 100313, 100315, 100352, 100356, 100358, 100363, 100386, 100394, 100396, 100398, 100402, 100406, 100419, 100423, 100435, 100444, 100448, 100459, 100464, 100476, 100502, 100514, 100516, 100526, 100540, 100545, 100556, 100557, 100563, 100568, 100580, 100581, 100584, 100587, 100588, 100591, 100601, 100632, 100656, 100666, 100682, 100688, 100702, 100715, 100728, 100732, 100738, 100745, 100752, 100753, 100775, 100787, 100807, 100809, 100813, 100816, 100819, 100825, 100837, 100863, 100878, 100886, 100932, 100935, 100944, 100953, 100956, 100970, 100977, 101013, 101015, 101023, 101025, 101044, 101065, 101070, 101075, 101087, 101094, 101095, 101096, 101100, 101107, 101110, 101119, 101122, 101140, 101163, 101178, 101181, 101184, 101186, 101191, 101194, 101197, 101213, 101235, 101242, 101263, 101279, 101283, 101288, 101298, 101308, 101320, 101321, 101323, 101337, 101349, 101358, 101369, 101373, 101374, 101384, 101386, 101409, 101426, 101440, 101447, 101454, 101457, 101463, 101484, 101497, 101511, 101512, 101513, 101528, 101529, 101587, 101588, 101604, 101617, 101619, 101620, 101629, 101634, 101638, 101642, 101665, 101667, 101676, 101680, 101690, 101694, 101701, 101711, 101714, 101719, 101725, 101726, 101728, 101730, 101732, 101735, 101740, 101745, 101751, 101758, 101774, 101818, 101840, 101857, 101862, 101868, 101895, 101902, 101907, 101941, 101955, 101966, 101977, 101982, 101984, 101985, 101997, 102021, 102023, 102025, 102031, 102043, 102057, 102058, 102064, 102091, 102098, 102110, 102122, 102132, 102154, 102184, 102185, 102187, 102190, 102192, 102200, 102241, 102249, 102251, 102256, 102279, 102293, 102301, 102326, 102328, 102331, 102338, 102347, 102352, 102382, 102404, 102405, 102418, 102468, 102471, 102477, 102489, 102492, 102500, 102501, 102503, 102505, 102518, 102522, 102524, 102526, 102556, 102563, 102581, 102618, 102625, 102626, 102635, 102638, 102662, 102663, 102680, 102694, 102696, 102697, 102714, 102720, 102722, 102726, 102728, 102748, 102756, 102775, 102790, 102797, 102798, 102807, 102814, 102829, 102833, 102847, 102859, 102875, 102879, 102885, 102893, 102901, 102910, 102914, 102924, 102930, 102944, 102952, 102956, 102967, 102973, 102977, 102993, 103000, 103002, 103007, 103013, 103015, 103016, 103017, 103021, 103032, 103037, 103044, 103057, 103066, 103083, 103099, 103101, 103107, 103112, 103123, 103138, 103160, 103169, 103172, 103177, 103191, 103197, 103202, 103213, 103237, 103242, 103245, 103248, 103263, 103280, 103283, 103284, 103288, 103296, 103299, 103306, 103310, 103327, 103328, 103348, 103356, 103377, 103384, 103422, 103425, 103430, 103431, 103442, 103447, 103469, 103481, 103489, 103497, 103500, 103504, 103513, 103520, 103536, 103539, 103542, 103566, 103568, 103571, 103573, 103576, 103594, 103606, 103624, 103633, 103639, 103651, 103691, 103712, 103729, 103773, 103794, 103806, 103815, 103819, 103834, 103853, 103864, 103882, 103889, 103898, 103903, 103910, 103912, 103935, 103952, 103955, 103961, 103965, 103970, 103971, 103973, 103982, 103993, 104011, 104037, 104044, 104050, 104073, 104090, 104103, 104110, 104111, 104125, 104133, 104144, 104147, 104151, 104155, 104157, 104162, 104174, 104177, 104186, 104193, 104203, 104206, 104222, 104230, 104241, 104263, 104288, 104290, 104297, 104301, 104308, 104319, 104321, 104329, 104332, 104333, 104349, 104360, 104361, 104375, 104383, 104387, 104406, 104434, 104438, 104447, 104451, 104468, 104486, 104508, 104510, 104516, 104530, 104543, 104547, 104550, 104573, 104575, 104591, 104597, 104625, 104639, 104641, 104651, 104653, 104673, 104680, 104700, 104703, 104709, 104737, 104738, 104741, 104745, 104748, 104751, 104754, 104762, 104769, 104774, 104816, 104822, 104839, 104878, 104887, 104889, 104950, 104992, 105001, 105003, 105012, 105013, 105015, 105024, 105029, 105037, 105041, 105050, 105054, 105069, 105073, 105095, 105107, 105113, 105120, 105127, 105135, 105143, 105145, 105217, 105218, 105224, 105233, 105265, 105270, 105279, 105294, 105300, 105304, 105318, 105336, 105359, 105360, 105371, 105378, 105381, 105386, 105391, 105400, 105411, 105414, 105422, 105429, 105435, 105461, 105463, 105473, 105479, 105487, 105488, 105506, 105527, 105529, 105541, 105546, 105556, 105561, 105562, 105575, 105576, 105596, 105618, 105621, 105630, 105646, 105698, 105720, 105728, 105752, 105763, 105767, 105771, 105776, 105782, 105785, 105791, 105827, 105836, 105837, 105862, 105873, 105876, 105910, 105912, 105930, 105935, 105942, 105953, 105962, 105972, 105973, 105979, 105998, 106006, 106024, 106043, 106055, 106072, 106080, 106082, 106091, 106117, 106125, 106131, 106136, 106149, 106150, 106156, 106175, 106179, 106213, 106219, 106225, 106247, 106251, 106253, 106255, 106275, 106290, 106298, 106304, 106308, 106317, 106321, 106330, 106346, 106354, 106367, 106369, 106409, 106410, 106417, 106422, 106424, 106447, 106449, 106454, 106465, 106473, 106484, 106514, 106543, 106562, 106573, 106574, 106592, 106595, 106601, 106612, 106632, 106646, 106647, 106671, 106678, 106688, 106694, 106700, 106712, 106713, 106730, 106732, 106734, 106739, 106741, 106744, 106746, 106753, 106754, 106762, 106764, 106776, 106781, 106783, 106788, 106791, 106802, 106827, 106833, 106861, 106868, 106870, 106875, 106880, 106885, 106890, 106902, 106909, 106911, 106926, 106950, 106951, 106979, 106980, 107015, 107043, 107045, 107059, 107074, 107091, 107099, 107107, 107110, 107113, 107114, 107128, 107166, 107177, 107182, 107184, 107195, 107196, 107203, 107215, 107218, 107229, 107233, 107234, 107241, 107257, 107270, 107277, 107283, 107302, 107304, 107308, 107312, 107336, 107351, 107354, 107369, 107386, 107391, 107414, 107423, 107435, 107436, 107443, 107454, 107456, 107457, 107460, 107463, 107464, 107468, 107480, 107482, 107490, 107491, 107492, 107495, 107501, 107515, 107519, 107523, 107558, 107562, 107592, 107594, 107615, 107619, 107625, 107629, 107638, 107640, 107642, 107647, 107648, 107667, 107679, 107702, 107706, 107726, 107738, 107758, 107760, 107782, 107787, 107796, 107821, 107829, 107849, 107863, 107865, 107893, 107906, 107907, 107914, 107915, 107916, 107920, 107922, 107927, 107978, 107989, 107990, 107993, 107995, 108015, 108021, 108026, 108028, 108029, 108038, 108054, 108056, 108074, 108076, 108080, 108084, 108088, 108089, 108090, 108100, 108118, 108129, 108139, 108148, 108150, 108151, 108164, 108170, 108173, 108193, 108205, 108217, 108241, 108282, 108295, 108298, 108300, 108303, 108311, 108313, 108361, 108365, 108366, 108375, 108397, 108400, 108412, 108416, 108433, 108445, 108454, 108469, 108481, 108495, 108498, 108500, 108519, 108536, 108537, 108551, 108576, 108588, 108589, 108597, 108598, 108614, 108616, 108617, 108640, 108642, 108660, 108661, 108670, 108682, 108687, 108689, 108693, 108704, 108705, 108710, 108721, 108723, 108725, 108731, 108758, 108763, 108766, 108778, 108779, 108783, 108788, 108794, 108796, 108798, 108806, 108818, 108848, 108849, 108863, 108870, 108874, 108875, 108888, 108889, 108898, 108907, 108914, 108916, 108921, 108940, 108944, 108955, 108977, 109000, 109011, 109015, 109021, 109024, 109036, 109040, 109044, 109065, 109068, 109077, 109082, 109104, 109119, 109123, 109149, 109152, 109181, 109214, 109220, 109222, 109223, 109228, 109234, 109240, 109249, 109253, 109255, 109270, 109271, 109280, 109281, 109290, 109292, 109304, 109305, 109337, 109351, 109353, 109355, 109356, 109392, 109401, 109404, 109418, 109423, 109433, 109452, 109474, 109475, 109486, 109488, 109502, 109518, 109520, 109525, 109544, 109557, 109567, 109617, 109630, 109638, 109646, 109666, 109672, 109675, 109708, 109724, 109744, 109749, 109766, 109767, 109782, 109792, 109798, 109802, 109804, 109819, 109829, 109830, 109836, 109852, 109875, 109877, 109884, 109893, 109898, 109923, 109936, 109945, 109949, 109951, 109957, 109966, 109975, 109980, 109981, 110011, 110014, 110025, 110049, 110071, 110079, 110089, 110092, 110111, 110117, 110119, 110132, 110157, 110175, 110181, 110192, 110205, 110206, 110212, 110216, 110223, 110246, 110260, 110266, 110268, 110270, 110277, 110300, 110306, 110318, 110323, 110325, 110327, 110334, 110378, 110385, 110397, 110401, 110433, 110441, 110462, 110465, 110467, 110470, 110473, 110484, 110504, 110511, 110517, 110521, 110535, 110537, 110538, 110541, 110542, 110558, 110560, 110562, 110577, 110582, 110585, 110590, 110591, 110592, 110600, 110603, 110615, 110616, 110623, 110644, 110645, 110655, 110670, 110677, 110682, 110683, 110688, 110694, 110705, 110709, 110711, 110713, 110714, 110715, 110741, 110742, 110749, 110755, 110761, 110801, 110807, 110817, 110844, 110852, 110853, 110861, 110866, 110875, 110877, 110888, 110890, 110914, 110924, 110928, 110943, 110944, 110954, 110963, 110964, 110966, 110976, 110982, 110990, 110992, 111008, 111042, 111071, 111082, 111101, 111109, 111128, 111135, 111153, 111161, 111182, 111192, 111197, 111202, 111215, 111217, 111220, 111256, 111271, 111284, 111304, 111315, 111321, 111325, 111326, 111327, 111330, 111358, 111360, 111367, 111368, 111370, 111372, 111376, 111395, 111397, 111402, 111403, 111406, 111438, 111456, 111458, 111496, 111510, 111516, 111519, 111520, 111524, 111535, 111537, 111540, 111543, 111553, 111554, 111558, 111560, 111573, 111574, 111585, 111615, 111636, 111647, 111654, 111660, 111661, 111666, 111709, 111720, 111727, 111737, 111743, 111756, 111791, 111803, 111825, 111826, 111856, 111862, 111870, 111901, 111904, 111915, 111917, 111921, 111927, 111938, 111940, 111945, 111960, 111964, 112008, 112010, 112025, 112026, 112028, 112029, 112073, 112074, 112076, 112091, 112095, 112104, 112110, 112130, 112136, 112142, 112144, 112148, 112160, 112162, 112170, 112177, 112180, 112182, 112186, 112197, 112213, 112216, 112227, 112229, 112236, 112240, 112259, 112268, 112275, 112301, 112307, 112310, 112329, 112344, 112347, 112348, 112349, 112354, 112358, 112366, 112367, 112384, 112402, 112420, 112474, 112484, 112498, 112500, 112503, 112507, 112546, 112548, 112567, 112581, 112598, 112602, 112614, 112620, 112628, 112629, 112634, 112637, 112639, 112644, 112649, 112652, 112665, 112673, 112686, 112707, 112735, 112741, 112746, 112756, 112770, 112773, 112804, 112812, 112818, 112843, 112848, 112855, 112858, 112865, 112868, 112878, 112880, 112881, 112883, 112900, 112908, 112909, 112920, 112930, 112934, 112965, 112974, 112984, 112989, 112996, 113019, 113028, 113033, 113039, 113067, 113068, 113074, 113078, 113084, 113086, 113087, 113092, 113101, 113108, 113110, 113126, 113133, 113135, 113164, 113172, 113182, 113206, 113207, 113212, 113222, 113246, 113259, 113296, 113304, 113306, 113321, 113327, 113338, 113342, 113356, 113360, 113380, 113391, 113429, 113434, 113447, 113453, 113474, 113476, 113478, 113485, 113487, 113491, 113515, 113538, 113569, 113572, 113580, 113592, 113593, 113599, 113602, 113608, 113611, 113613, 113622, 113635, 113636, 113639, 113642, 113645, 113665, 113689, 113692, 113695, 113699, 113724, 113726, 113733, 113742, 113746, 113760, 113765, 113767, 113775, 113783, 113789, 113809, 113813, 113827, 113842, 113846, 113849, 113853, 113855, 113858, 113870, 113872, 113874, 113881, 113883, 113884, 113921, 113953, 113965, 113973, 113977, 113978, 113986, 113988, 114004, 114010, 114013, 114014, 114016, 114021, 114029, 114052, 114063, 114064, 114065, 114069, 114075, 114088, 114102, 114132, 114138, 114160, 114176, 114214, 114226, 114235, 114241, 114253, 114291, 114294, 114295, 114303, 114314, 114323, 114333, 114346, 114361, 114370, 114378, 114383, 114415, 114417, 114440, 114468, 114472, 114484, 114492, 114513, 114519, 114526, 114531, 114543, 114549, 114566, 114592, 114599, 114609, 114618, 114624, 114641, 114646, 114648, 114651, 114664, 114682, 114684, 114685, 114703, 114718, 114720, 114734, 114739, 114746, 114752, 114758, 114769, 114790, 114794, 114796, 114801, 114809, 114815, 114818, 114834, 114858, 114860, 114861, 114867, 114875, 114882, 114885, 114894, 114904, 114929, 114990, 115005, 115043, 115045, 115076, 115091, 115094, 115108, 115129, 115130, 115132, 115134, 115137, 115139, 115145, 115156, 115168, 115171, 115174, 115175, 115187, 115191, 115199, 115200, 115208, 115212, 115214, 115219, 115224, 115230, 115233, 115236, 115238, 115249, 115250, 115261, 115265, 115275, 115277, 115280, 115312, 115313, 115334, 115338, 115352, 115356, 115359, 115365, 115371, 115380, 115402, 115416, 115431, 115441, 115449, 115502, 115510, 115520, 115529, 115530, 115536, 115539, 115546, 115566, 115576, 115578, 115589, 115604, 115614, 115623, 115637, 115644, 115648, 115661, 115667, 115669, 115672, 115674, 115675, 115679, 115690, 115712, 115714, 115727, 115729, 115730, 115744, 115755, 115765, 115794, 115796, 115808, 115814, 115824, 115853, 115862, 115879, 115889, 115890, 115891, 115901, 115907, 115910, 115925, 115953, 115962, 115967, 115974, 115994, 116016, 116032, 116038, 116049, 116066, 116085, 116104, 116111, 116115, 116119, 116139, 116140, 116145, 116155, 116172, 116174, 116180, 116192, 116210, 116229, 116243, 116244, 116250, 116254, 116266, 116273, 116304, 116308, 116338, 116349, 116370, 116373, 116380, 116382, 116384, 116405, 116406, 116411, 116443, 116445, 116447, 116494, 116510, 116519, 116521, 116529, 116552, 116568, 116573, 116584, 116593, 116607, 116612, 116623, 116650, 116667, 116671, 116677, 116683, 116699, 116700, 116704, 116719, 116728, 116742, 116802, 116803, 116804, 116817, 116821, 116826, 116827, 116835, 116847, 116862, 116870, 116899, 116920, 116926, 116934, 116935, 116936, 116939, 116949, 116964, 116966, 116972, 116974, 116981, 117018, 117026, 117044, 117056, 117065, 117066, 117075, 117076, 117103, 117107, 117111, 117126, 117150, 117156, 117162, 117185, 117193, 117237, 117297, 117309, 117314, 117318, 117323, 117332, 117352, 117369, 117375, 117387, 117390, 117400, 117414, 117422, 117427, 117434, 117448, 117473, 117492, 117495, 117497, 117503, 117513, 117526, 117528, 117532, 117537, 117561, 117582, 117589, 117598, 117599, 117611, 117615, 117643, 117660, 117670, 117671, 117674, 117679, 117680, 117682, 117687, 117713, 117723, 117724, 117730, 117737, 117741, 117745, 117755, 117770, 117777, 117780, 117781, 117795, 117802, 117814, 117817, 117821, 117824, 117833, 117858, 117860, 117862, 117874, 117890, 117893, 117901, 117902, 117904, 117911, 117920, 117921, 117929, 117931, 117938, 117946, 117948, 117953, 117954, 117960, 117962, 117969, 117986, 117990, 118012, 118016, 118018, 118021, 118038, 118045, 118046, 118089, 118114, 118120, 118131, 118140, 118173, 118192, 118200, 118201, 118209, 118217, 118228, 118233, 118239, 118257, 118260, 118283, 118310, 118311, 118315, 118327, 118331, 118343, 118348, 118358, 118385, 118386, 118396, 118400, 118412, 118446, 118455, 118470, 118475, 118484, 118495, 118508, 118520, 118533, 118535, 118549, 118551, 118552, 118562, 118579, 118580, 118587, 118606, 118607, 118634, 118643, 118670, 118695, 118711, 118723, 118733, 118739, 118746, 118791, 118813, 118825, 118827, 118868, 118885, 118897, 118900, 118910, 118914, 118940, 118999, 119000, 119001, 119003, 119006, 119014, 119026, 119036, 119037, 119071, 119072, 119074, 119090, 119094, 119097, 119110, 119154, 119180, 119188, 119192, 119215, 119234, 119240, 119246, 119255, 119264, 119267, 119283, 119284, 119291, 119294, 119296, 119306, 119308, 119310, 119313, 119316, 119339, 119342, 119346, 119349, 119354, 119356, 119369, 119385, 119394, 119397, 119402, 119407, 119416, 119420, 119433, 119441, 119452, 119457, 119461, 119471, 119479, 119495, 119507, 119509, 119511, 119516, 119517, 119532, 119536, 119538, 119539, 119541, 119544, 119557, 119580, 119582, 119588, 119592, 119605, 119611, 119632, 119639, 119651, 119671, 119674, 119683, 119732, 119741, 119756, 119780, 119809, 119815, 119855, 119858, 119878, 119894, 119899, 119906, 119912, 119917, 119937, 119952, 119962, 119964, 119965, 119973, 119984, 119986, 119987, 120051, 120058, 120061, 120065, 120066, 120069, 120100, 120113, 120122, 120166, 120170, 120181, 120188, 120194, 120218, 120222, 120235, 120238, 120251, 120257, 120263, 120276, 120286, 120292, 120299, 120319, 120328, 120341, 120343, 120344, 120346, 120349, 120364, 120365, 120374, 120409, 120415, 120418, 120421, 120426, 120438, 120466, 120470, 120474, 120497, 120503, 120506, 120507, 120513, 120521, 120530, 120536, 120537, 120545, 120569, 120583, 120592, 120595, 120597, 120602, 120606, 120615, 120617, 120638, 120649, 120660, 120667, 120672, 120681, 120683, 120686, 120689, 120690, 120692, 120694, 120700, 120767, 120773, 120775, 120778, 120788, 120807, 120808, 120818, 120839, 120893, 120896, 120900, 120914, 120916, 120924, 120930, 120934, 120940, 120951, 120977, 120978, 120980, 120996, 120999, 121015, 121041, 121054, 121067, 121068, 121073, 121076, 121095, 121108, 121138, 121145, 121151, 121159, 121167, 121177, 121189, 121199, 121200, 121206, 121240, 121246, 121287, 121295, 121296, 121308, 121309, 121318, 121322, 121325, 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199989, 199994]
Creating dense tree of order: 13
Printing dense tree. The nodes are printed in DFS format.
Root Node:[100010, 122147, 143922, 165690]
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[182888, 182909, 182929, 182939, 182947, 182973, 182979, 182985, 182991, 182995, 183009, 183020, 183024]
[183028, 183039, 183042, 183046, 183050, 183068, 183074, 183100, 183110, 183116, 183125, 183126, 183127]
[183131, 183132, 183133, 183142, 183146, 183161, 183165, 183177, 183184, 183193, 183209, 183231, 183248]
[183270, 183303, 183312, 183314, 183324, 183333, 183340, 183342, 183346, 183352, 183353, 183368, 183375]
[183386, 183388, 183392, 183407, 183411, 183414, 183423, 183430, 183444, 183454, 183469, 183491, 183494]
[183499, 183502, 183538, 183543, 183553, 183566, 183578, 183584, 183594, 183619, 183623, 183632, 183637]
[183657, 183667, 183671, 183685, 183691, 183696, 183705, 183715, 183722, 183725, 183727, 183732, 183749]
[183755, 183761, 183763, 183764, 183772, 183786, 183797, 183806, 183807, 183809, 183812, 183816, 183823]
[183867, 183882, 183910, 183933, 183940, 183941, 183952, 183957, 183966, 183981, 184005, 184016, 184026]
[184066, 184067, 184084, 184087, 184101, 184129, 184130, 184139, 184140, 184149, 184150, 184152, 184158]
[184168, 184170, 184178, 184198, 184201, 184206, 184214, 184218, 184236, 184244, 184279, 184285, 184291]
[184303, 184310, 184312, 184321, 184328, 184334, 184345, 184351, 184353, 184364, 184390, 184393, 184394]
[184407, 184514, 184631, 184738, 184843, 185045, 185197, 185310, 185470, 185637, 185779, 185917, 186046]
[184407, 184409, 184412, 184419, 184425, 184426, 184435, 184447, 184453, 184455, 184468, 184474, 184499]
[184514, 184527, 184547, 184551, 184564, 184592, 184594, 184598, 184610, 184613, 184616, 184619, 184625]
[184631, 184632, 184633, 184640, 184647, 184655, 184656, 184659, 184669, 184682, 184708, 184720, 184736]
[184738, 184743, 184770, 184774, 184781, 184782, 184789, 184792, 184803, 184810, 184817, 184820, 184822]
[184843, 184864, 184917, 184930, 184931, 184936, 184942, 184988, 184995, 185013, 185023, 185025, 185027]
[185045, 185052, 185053, 185069, 185104, 185114, 185115, 185116, 185127, 185143, 185163, 185183, 185194]
[185197, 185226, 185231, 185233, 185237, 185245, 185255, 185263, 185281, 185283, 185291, 185300, 185303]
[185310, 185340, 185341, 185346, 185369, 185372, 185418, 185440, 185446, 185447, 185449, 185463, 185466]
[185470, 185478, 185481, 185487, 185496, 185497, 185509, 185512, 185525, 185563, 185581, 185599, 185615]
[185637, 185638, 185639, 185641, 185647, 185649, 185662, 185677, 185685, 185703, 185708, 185716, 185736]
[185779, 185786, 185788, 185790, 185793, 185802, 185845, 185857, 185863, 185867, 185893, 185901, 185902]
[185917, 185928, 185930, 185932, 185935, 185937, 185939, 185962, 185981, 185985, 185991, 186002, 186033]
[186046, 186053, 186084, 186095, 186098, 186101, 186119, 186153, 186166, 186179, 186188, 186197, 186204]
[186205, 186377, 186486, 186602, 186706, 186814, 186919, 187092, 187214, 187323, 187454, 187615, 187687]
[186205, 186234, 186237, 186242, 186245, 186260, 186278, 186286, 186299, 186300, 186347, 186357, 186367]
[186377, 186378, 186386, 186412, 186414, 186423, 186429, 186432, 186434, 186438, 186451, 186455, 186476]
[186486, 186487, 186513, 186525, 186529, 186534, 186542, 186547, 186553, 186556, 186569, 186600, 186601]
[186602, 186609, 186614, 186619, 186627, 186628, 186637, 186643, 186657, 186664, 186671, 186679, 186681]
[186706, 186740, 186742, 186750, 186757, 186764, 186769, 186787, 186800, 186804, 186808, 186809, 186812]
[186814, 186841, 186846, 186853, 186855, 186861, 186875, 186878, 186883, 186904, 186910, 186911, 186912]
[186919, 186936, 186956, 186980, 186989, 187010, 187022, 187038, 187045, 187056, 187060, 187069, 187090]
[187092, 187100, 187102, 187115, 187117, 187129, 187147, 187150, 187157, 187172, 187195, 187202, 187207]
[187214, 187218, 187222, 187225, 187231, 187241, 187244, 187267, 187276, 187279, 187282, 187313, 187319]
[187323, 187333, 187334, 187351, 187357, 187383, 187385, 187394, 187403, 187413, 187415, 187422, 187452]
[187454, 187461, 187475, 187484, 187485, 187507, 187536, 187565, 187580, 187585, 187593, 187606, 187611]
[187615, 187617, 187621, 187623, 187637, 187645, 187646, 187662, 187665, 187666, 187671, 187675, 187683]
[187687, 187702, 187705, 187707, 187720, 187722, 187725, 187733, 187736, 187737, 187751, 187753, 187756]
**********************************


Experimentation
1. Generating random numbers for experimentation
Random numbers generated: [116753, 116557, 107733, 112522, 163273, 113547, 198117, 132478, 134191, 186661, 150371, 105442, 199590, 196609]
**********************************


2. Performing two random insert operations 
Inserting: 116753
Searching key 116753 in the tree to see if it already exists.
Searching: 116753
Traversing the tree from root node to leaf:
[100010, 122147, 143922, 165690]
[100010, 101619, 103242, 105037, 106791, 108454, 110117, 111661, 113391, 115134, 116827, 118549, 120374]
[115134, 115208, 115275, 115402, 115566, 115672, 115794, 115910, 116104, 116229, 116380, 116529, 116683]
[116683, 116699, 116700, 116704, 116719, 116728, 116742, 116802, 116803, 116804, 116817, 116821, 116826]
Key 116753 does not exist in the tree
The key 116753 that you want to insert is not already in the B+ tree.
Inserting it
Traversing the tree to insert key 
Root Node: [100010, 122147, 143922, 165690]
Level1: [100010, 101619, 103242, 105037, 106791, 108454, 110117, 111661, 113391, 115134, 116827, 118549, 120374]
Level2: [115134, 115208, 115275, 115402, 115566, 115672, 115794, 115910, 116104, 116229, 116380, 116529, 116683]
Level3: [116683, 116699, 116700, 116704, 116719, 116728, 116742, 116802, 116803, 116804, 116817, 116821, 116826]
Inserting 116753 in leaf node [116683, 116699, 116700, 116704, 116719, 116728, 116742, 116802, 116803, 116804, 116817, 116821, 116826]
After inserting: [116683, 116699, 116700, 116704, 116719, 116728, 116742, 116753, 116802, 116803, 116804, 116817, 116821, 116826]
116753 has been inserted in the tree.
Leaf node is full after insertion. Splitting leaf node to accomodate future keys
Splitting leaf node: [116683, 116699, 116700, 116704, 116719, 116728, 116742, 116753, 116802, 116803, 116804, 116817, 116821, 116826]
Leaf node before splitting: [116683, 116699, 116700, 116704, 116719, 116728, 116742, 116753, 116802, 116803, 116804, 116817, 116821, 116826]

Leaf node after splitting
Left Split keys: [116683, 116699, 116700, 116704, 116719, 116728]
Right split keys: [116742, 116753, 116802, 116803, 116804, 116817, 116821, 116826]

Restructuring parent(internal) nodes
Merging Nodes: [115134, 115208, 115275, 115402, 115566, 115672, 115794, 115910, 116104, 116229, 116380, 116529, 116683] and [116742]
Merged Node: [115134, 115208, 115275, 115402, 115566, 115672, 115794, 115910, 116104, 116229, 116380, 116529, 116683, 116742]

Merged internal node is full. Splitting the node: [115134, 115208, 115275, 115402, 115566, 115672, 115794, 115910, 116104, 116229, 116380, 116529, 116683, 116742]
Merged node after splitting
Left Split keys: [115134, 115208, 115275, 115402, 115566, 115672]
Right Split keys: [115794, 115910, 116104, 116229, 116380, 116529, 116683, 116742]

Restructuring parent(internal) nodes
Merging Nodes: [100010, 101619, 103242, 105037, 106791, 108454, 110117, 111661, 113391, 115134, 116827, 118549, 120374] and [115794]
Merged Node: [100010, 101619, 103242, 105037, 106791, 108454, 110117, 111661, 113391, 115134, 115794, 116827, 118549, 120374]

Merged internal node is full. Splitting the node: [100010, 101619, 103242, 105037, 106791, 108454, 110117, 111661, 113391, 115134, 115794, 116827, 118549, 120374]
Merged node after splitting
Left Split keys: [100010, 101619, 103242, 105037, 106791, 108454]
Right Split keys: [110117, 111661, 113391, 115134, 115794, 116827, 118549, 120374]

Restructuring parent(internal) nodes
Merging Nodes: [100010, 122147, 143922, 165690] and [110117]
Merged Node: [100010, 110117, 122147, 143922, 165690]

**********************************


**********************************


Inserting: 116557
Searching key 116557 in the tree to see if it already exists.
Searching: 116557
Traversing the tree from root node to leaf:
[100010, 110117, 122147, 143922, 165690]
[110117, 111661, 113391, 115134, 115794, 116827, 118549, 120374]
[115794, 115910, 116104, 116229, 116380, 116529, 116683, 116742]
[116529, 116552, 116568, 116573, 116584, 116593, 116607, 116612, 116623, 116650, 116667, 116671, 116677]
Key 116557 does not exist in the tree
The key 116557 that you want to insert is not already in the B+ tree.
Inserting it
Traversing the tree to insert key 
Root Node: [100010, 110117, 122147, 143922, 165690]
Level1: [110117, 111661, 113391, 115134, 115794, 116827, 118549, 120374]
Level2: [115794, 115910, 116104, 116229, 116380, 116529, 116683, 116742]
Level3: [116529, 116552, 116568, 116573, 116584, 116593, 116607, 116612, 116623, 116650, 116667, 116671, 116677]
Inserting 116557 in leaf node [116529, 116552, 116568, 116573, 116584, 116593, 116607, 116612, 116623, 116650, 116667, 116671, 116677]
After inserting: [116529, 116552, 116557, 116568, 116573, 116584, 116593, 116607, 116612, 116623, 116650, 116667, 116671, 116677]
116557 has been inserted in the tree.
Leaf node is full after insertion. Splitting leaf node to accomodate future keys
Splitting leaf node: [116529, 116552, 116557, 116568, 116573, 116584, 116593, 116607, 116612, 116623, 116650, 116667, 116671, 116677]
Leaf node before splitting: [116529, 116552, 116557, 116568, 116573, 116584, 116593, 116607, 116612, 116623, 116650, 116667, 116671, 116677]

Leaf node after splitting
Left Split keys: [116529, 116552, 116557, 116568, 116573, 116584]
Right split keys: [116593, 116607, 116612, 116623, 116650, 116667, 116671, 116677]

Restructuring parent(internal) nodes
Merging Nodes: [115794, 115910, 116104, 116229, 116380, 116529, 116683, 116742] and [116593]
Merged Node: [115794, 115910, 116104, 116229, 116380, 116529, 116593, 116683, 116742]

**********************************


**********************************


3. Performing random delete operations 
Deleting key: 107733
The key107733 that you want to delete does not exist in the tree
**********************************


Deleting key: 112522
The key112522 that you want to delete does not exist in the tree
**********************************


4. Performing random insert/deletion operations 
Inserting: 163273
Searching key 163273 in the tree to see if it already exists.
Searching: 163273
Traversing the tree from root node to leaf:
[100010, 110117, 122147, 143922, 165690]
[143922, 145495, 147300, 149235, 150934, 152383, 154185, 155848, 157213, 158967, 160590, 162163, 163706]
[162163, 162323, 162443, 162533, 162633, 162749, 162896, 162984, 163163, 163294, 163380, 163516, 163617]
[163163, 163181, 163189, 163191, 163198, 163208, 163215, 163218, 163227, 163235, 163250, 163280, 163282]
Key 163273 does not exist in the tree
The key 163273 that you want to insert is not already in the B+ tree.
Inserting it
Traversing the tree to insert key 
Root Node: [100010, 110117, 122147, 143922, 165690]
Level1: [143922, 145495, 147300, 149235, 150934, 152383, 154185, 155848, 157213, 158967, 160590, 162163, 163706]
Level2: [162163, 162323, 162443, 162533, 162633, 162749, 162896, 162984, 163163, 163294, 163380, 163516, 163617]
Level3: [163163, 163181, 163189, 163191, 163198, 163208, 163215, 163218, 163227, 163235, 163250, 163280, 163282]
Inserting 163273 in leaf node [163163, 163181, 163189, 163191, 163198, 163208, 163215, 163218, 163227, 163235, 163250, 163280, 163282]
After inserting: [163163, 163181, 163189, 163191, 163198, 163208, 163215, 163218, 163227, 163235, 163250, 163273, 163280, 163282]
163273 has been inserted in the tree.
Leaf node is full after insertion. Splitting leaf node to accomodate future keys
Splitting leaf node: [163163, 163181, 163189, 163191, 163198, 163208, 163215, 163218, 163227, 163235, 163250, 163273, 163280, 163282]
Leaf node before splitting: [163163, 163181, 163189, 163191, 163198, 163208, 163215, 163218, 163227, 163235, 163250, 163273, 163280, 163282]

Leaf node after splitting
Left Split keys: [163163, 163181, 163189, 163191, 163198, 163208]
Right split keys: [163215, 163218, 163227, 163235, 163250, 163273, 163280, 163282]

Restructuring parent(internal) nodes
Merging Nodes: [162163, 162323, 162443, 162533, 162633, 162749, 162896, 162984, 163163, 163294, 163380, 163516, 163617] and [163215]
Merged Node: [162163, 162323, 162443, 162533, 162633, 162749, 162896, 162984, 163163, 163215, 163294, 163380, 163516, 163617]

Merged internal node is full. Splitting the node: [162163, 162323, 162443, 162533, 162633, 162749, 162896, 162984, 163163, 163215, 163294, 163380, 163516, 163617]
Merged node after splitting
Left Split keys: [162163, 162323, 162443, 162533, 162633, 162749]
Right Split keys: [162896, 162984, 163163, 163215, 163294, 163380, 163516, 163617]

Restructuring parent(internal) nodes
Merging Nodes: [143922, 145495, 147300, 149235, 150934, 152383, 154185, 155848, 157213, 158967, 160590, 162163, 163706] and [162896]
Merged Node: [143922, 145495, 147300, 149235, 150934, 152383, 154185, 155848, 157213, 158967, 160590, 162163, 162896, 163706]

Merged internal node is full. Splitting the node: [143922, 145495, 147300, 149235, 150934, 152383, 154185, 155848, 157213, 158967, 160590, 162163, 162896, 163706]
Merged node after splitting
Left Split keys: [143922, 145495, 147300, 149235, 150934, 152383]
Right Split keys: [154185, 155848, 157213, 158967, 160590, 162163, 162896, 163706]

Restructuring parent(internal) nodes
Merging Nodes: [100010, 110117, 122147, 143922, 165690] and [154185]
Merged Node: [100010, 110117, 122147, 143922, 154185, 165690]

**********************************


**********************************


Deleting key: 113547
The key113547 that you want to delete does not exist in the tree
**********************************


Inserting: 198117
Searching key 198117 in the tree to see if it already exists.
Searching: 198117
Traversing the tree from root node to leaf:
[100010, 110117, 122147, 143922, 154185, 165690]
[165690, 167412, 169181, 170937, 172772, 174376, 176084, 177616, 179333, 181107, 182767, 184407, 186205]
[186205, 186377, 186486, 186602, 186706, 186814, 186919, 187092, 187214, 187323, 187454, 187615, 187687]
[187687, 187702, 187705, 187707, 187720, 187722, 187725, 187733, 187736, 187737, 187751, 187753, 187756]
Key 198117 does not exist in the tree
The key 198117 that you want to insert is not already in the B+ tree.
Inserting it
Traversing the tree to insert key 
Root Node: [100010, 110117, 122147, 143922, 154185, 165690]
Level1: [165690, 167412, 169181, 170937, 172772, 174376, 176084, 177616, 179333, 181107, 182767, 184407, 186205]
Level2: [186205, 186377, 186486, 186602, 186706, 186814, 186919, 187092, 187214, 187323, 187454, 187615, 187687]
Level3: [187687, 187702, 187705, 187707, 187720, 187722, 187725, 187733, 187736, 187737, 187751, 187753, 187756]
Inserting 198117 in leaf node [187687, 187702, 187705, 187707, 187720, 187722, 187725, 187733, 187736, 187737, 187751, 187753, 187756]
After inserting: [187687, 187702, 187705, 187707, 187720, 187722, 187725, 187733, 187736, 187737, 187751, 187753, 187756, 198117]
198117 has been inserted in the tree.
Leaf node is full after insertion. Splitting leaf node to accomodate future keys
Splitting leaf node: [187687, 187702, 187705, 187707, 187720, 187722, 187725, 187733, 187736, 187737, 187751, 187753, 187756, 198117]
Leaf node before splitting: [187687, 187702, 187705, 187707, 187720, 187722, 187725, 187733, 187736, 187737, 187751, 187753, 187756, 198117]

Leaf node after splitting
Left Split keys: [187687, 187702, 187705, 187707, 187720, 187722]
Right split keys: [187725, 187733, 187736, 187737, 187751, 187753, 187756, 198117]

Restructuring parent(internal) nodes
Merging Nodes: [186205, 186377, 186486, 186602, 186706, 186814, 186919, 187092, 187214, 187323, 187454, 187615, 187687] and [187725]
Merged Node: [186205, 186377, 186486, 186602, 186706, 186814, 186919, 187092, 187214, 187323, 187454, 187615, 187687, 187725]

Merged internal node is full. Splitting the node: [186205, 186377, 186486, 186602, 186706, 186814, 186919, 187092, 187214, 187323, 187454, 187615, 187687, 187725]
Merged node after splitting
Left Split keys: [186205, 186377, 186486, 186602, 186706, 186814]
Right Split keys: [186919, 187092, 187214, 187323, 187454, 187615, 187687, 187725]

Restructuring parent(internal) nodes
Merging Nodes: [165690, 167412, 169181, 170937, 172772, 174376, 176084, 177616, 179333, 181107, 182767, 184407, 186205] and [186919]
Merged Node: [165690, 167412, 169181, 170937, 172772, 174376, 176084, 177616, 179333, 181107, 182767, 184407, 186205, 186919]

Merged internal node is full. Splitting the node: [165690, 167412, 169181, 170937, 172772, 174376, 176084, 177616, 179333, 181107, 182767, 184407, 186205, 186919]
Merged node after splitting
Left Split keys: [165690, 167412, 169181, 170937, 172772, 174376]
Right Split keys: [176084, 177616, 179333, 181107, 182767, 184407, 186205, 186919]

Restructuring parent(internal) nodes
Merging Nodes: [100010, 110117, 122147, 143922, 154185, 165690] and [176084]
Merged Node: [100010, 110117, 122147, 143922, 154185, 165690, 176084]

**********************************


**********************************


Deleting key: 132478
The key132478 that you want to delete does not exist in the tree
**********************************


Inserting: 134191
Searching key 134191 in the tree to see if it already exists.
Searching: 134191
Traversing the tree from root node to leaf:
[100010, 110117, 122147, 143922, 154185, 165690, 176084]
[122147, 123736, 125341, 126906, 128581, 130210, 131762, 133625, 135373, 136942, 138559, 140236, 141956]
[133625, 133763, 133914, 134069, 134202, 134311, 134429, 134645, 134753, 134850, 135001, 135105, 135236]
[134069, 134092, 134093, 134099, 134105, 134108, 134124, 134128, 134137, 134140, 134146, 134175, 134201]
Key 134191 does not exist in the tree
The key 134191 that you want to insert is not already in the B+ tree.
Inserting it
Traversing the tree to insert key 
Root Node: [100010, 110117, 122147, 143922, 154185, 165690, 176084]
Level1: [122147, 123736, 125341, 126906, 128581, 130210, 131762, 133625, 135373, 136942, 138559, 140236, 141956]
Level2: [133625, 133763, 133914, 134069, 134202, 134311, 134429, 134645, 134753, 134850, 135001, 135105, 135236]
Level3: [134069, 134092, 134093, 134099, 134105, 134108, 134124, 134128, 134137, 134140, 134146, 134175, 134201]
Inserting 134191 in leaf node [134069, 134092, 134093, 134099, 134105, 134108, 134124, 134128, 134137, 134140, 134146, 134175, 134201]
After inserting: [134069, 134092, 134093, 134099, 134105, 134108, 134124, 134128, 134137, 134140, 134146, 134175, 134191, 134201]
134191 has been inserted in the tree.
Leaf node is full after insertion. Splitting leaf node to accomodate future keys
Splitting leaf node: [134069, 134092, 134093, 134099, 134105, 134108, 134124, 134128, 134137, 134140, 134146, 134175, 134191, 134201]
Leaf node before splitting: [134069, 134092, 134093, 134099, 134105, 134108, 134124, 134128, 134137, 134140, 134146, 134175, 134191, 134201]

Leaf node after splitting
Left Split keys: [134069, 134092, 134093, 134099, 134105, 134108]
Right split keys: [134124, 134128, 134137, 134140, 134146, 134175, 134191, 134201]

Restructuring parent(internal) nodes
Merging Nodes: [133625, 133763, 133914, 134069, 134202, 134311, 134429, 134645, 134753, 134850, 135001, 135105, 135236] and [134124]
Merged Node: [133625, 133763, 133914, 134069, 134124, 134202, 134311, 134429, 134645, 134753, 134850, 135001, 135105, 135236]

Merged internal node is full. Splitting the node: [133625, 133763, 133914, 134069, 134124, 134202, 134311, 134429, 134645, 134753, 134850, 135001, 135105, 135236]
Merged node after splitting
Left Split keys: [133625, 133763, 133914, 134069, 134124, 134202]
Right Split keys: [134311, 134429, 134645, 134753, 134850, 135001, 135105, 135236]

Restructuring parent(internal) nodes
Merging Nodes: [122147, 123736, 125341, 126906, 128581, 130210, 131762, 133625, 135373, 136942, 138559, 140236, 141956] and [134311]
Merged Node: [122147, 123736, 125341, 126906, 128581, 130210, 131762, 133625, 134311, 135373, 136942, 138559, 140236, 141956]

Merged internal node is full. Splitting the node: [122147, 123736, 125341, 126906, 128581, 130210, 131762, 133625, 134311, 135373, 136942, 138559, 140236, 141956]
Merged node after splitting
Left Split keys: [122147, 123736, 125341, 126906, 128581, 130210]
Right Split keys: [131762, 133625, 134311, 135373, 136942, 138559, 140236, 141956]

Restructuring parent(internal) nodes
Merging Nodes: [100010, 110117, 122147, 143922, 154185, 165690, 176084] and [131762]
Merged Node: [100010, 110117, 122147, 131762, 143922, 154185, 165690, 176084]

**********************************


**********************************


5. Performing random search operations 
Searching: 186661
Traversing the tree from root node to leaf:
[100010, 110117, 122147, 131762, 143922, 154185, 165690, 176084]
[176084, 177616, 179333, 181107, 182767, 184407, 186205, 186919]
[186205, 186377, 186486, 186602, 186706, 186814]
[186602, 186609, 186614, 186619, 186627, 186628, 186637, 186643, 186657, 186664, 186671, 186679, 186681]
Key 186661 does not exist in the tree
**********************************

Searching: 150371
Traversing the tree from root node to leaf:
[100010, 110117, 122147, 131762, 143922, 154185, 165690, 176084]
[143922, 145495, 147300, 149235, 150934, 152383]
[149235, 149404, 149573, 149688, 149851, 149948, 150111, 150244, 150398, 150503, 150614, 150722, 150832]
[150244, 150261, 150263, 150281, 150283, 150297, 150334, 150338, 150342, 150360, 150362, 150368, 150380]
Key 150371 does not exist in the tree
**********************************

Searching: 105442
Traversing the tree from root node to leaf:
[100010, 110117, 122147, 131762, 143922, 154185, 165690, 176084]
[100010, 101619, 103242, 105037, 106791, 108454]
[105037, 105145, 105359, 105461, 105562, 105767, 105912, 106055, 106179, 106317, 106449, 106612, 106734]
[105359, 105360, 105371, 105378, 105381, 105386, 105391, 105400, 105411, 105414, 105422, 105429, 105435]
Key 105442 does not exist in the tree
**********************************

Searching: 199590
Traversing the tree from root node to leaf:
[100010, 110117, 122147, 131762, 143922, 154185, 165690, 176084]
[176084, 177616, 179333, 181107, 182767, 184407, 186205, 186919]
[186919, 187092, 187214, 187323, 187454, 187615, 187687, 187725]
[187725, 187733, 187736, 187737, 187751, 187753, 187756, 198117]
Key 199590 does not exist in the tree
**********************************

Searching: 196609
Traversing the tree from root node to leaf:
[100010, 110117, 122147, 131762, 143922, 154185, 165690, 176084]
[176084, 177616, 179333, 181107, 182767, 184407, 186205, 186919]
[186919, 187092, 187214, 187323, 187454, 187615, 187687, 187725]
[187725, 187733, 187736, 187737, 187751, 187753, 187756, 198117]
Key 196609 does not exist in the tree
**********************************


6. Performing two random range search operations 
Searching in the range: 12616, 472558
Keys within the range: 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199953,199979,


Searching in the range: 113838, 174767
Keys within the range: 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1023,171035,171045,171050,171051,171066,171070,171094,171096,171101,171119,171141,171143,171145,171156,171157,171163,171166,171198,171209,171215,171220,171223,171238,171244,171256,171265,171266,171270,171273,171280,171293,171302,171305,171319,171338,171368,171370,171378,171408,171437,171443,171445,171456,171473,171474,171499,171512,171515,171519,171526,171545,171567,171594,171595,171605,171620,171624,171627,171633,171637,171640,171647,171657,171660,171697,171700,171710,171717,171718,171735,171747,171755,171757,171778,171785,171799,171806,171810,171820,171832,171835,171904,171905,171913,171920,171945,171949,171950,171961,172009,172011,172012,172028,172031,172034,172040,172063,172064,172074,172088,172094,172105,172107,172113,172120,172151,172153,172178,172179,172184,172237,172248,172253,172256,172260,172267,172273,172277,172289,172321,172329,172354,172360,172386,172400,172407,172433,172434,172444,172450,172451,172457,172485,172491,172495,172496,172510,172511,172525,172527,172539,172542,172547,172557,172575,172609,172620,172628,172630,172633,172666,172671,172715,172727,172752,172758,172772,172774,172775,172777,172787,172820,172823,172835,172839,172840,172844,172863,172881,172884,172886,172905,172908,172912,172930,172932,172945,172966,172977,172979,172984,172995,172997,173001,173004,173006,173016,173025,173030,173033,173039,173041,173049,173052,173061,173064,173066,173079,173082,173094,173117,173123,173136,173152,173177,173189,173202,173206,173225,173232,173265,173269,173281,173290,173299,173300,173320,173326,173334,173338,173356,173364,173387,173388,173406,173407,173412,173413,173417,173442,173456,173466,173477,173483,173503,173521,173527,173528,173534,173536,173550,173595,173603,173616,173631,173637,173641,173688,173690,173693,173694,173704,173716,173719,173734,173738,173740,173742,173748,173751,173753,173754,173758,173797,173798,173802,173816,173825,173826,173840,173845,173857,173861,173870,173891,173906,173907,173925,173931,173937,173939,173943,173948,173979,173986,174003,174012,174013,174045,174053,174065,174071,174085,174088,174106,174108,174111,174131,174136,174138,174143,174150,174154,174158,174180,174184,174193,174212,174216,174228,174230,174232,174242,174260,174266,174268,174281,174306,174315,174316,174322,174324,174338,174353,174361,174376,174389,174390,174409,174411,174418,174428,174444,174453,174460,174463,174466,174471,174482,174494,174497,174533,174535,174548,174572,174587,174614,174624,174628,174647,174666,174698,174710,174714,174722,174743,174762,


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More Experimentation
Generating a random number
Random number generated: [156438]
1.1. Inserting: 156438
Inserting: 156438
Searching key 156438 in the tree to see if it already exists.
Searching: 156438
Traversing the tree from root node to leaf:
[100010, 110117, 122147, 131762, 143922, 154185, 165690, 176084]
[154185, 155848, 157213, 158967, 160590, 162163, 162896, 163706]
[155848, 155907, 156009, 156143, 156259, 156341, 156450, 156582, 156684, 156793, 156913, 157047, 157129]
[156341, 156344, 156360, 156367, 156379, 156390, 156397, 156426, 156430, 156440, 156441, 156444, 156448]
Key 156438 does not exist in the tree
The key 156438 that you want to insert is not already in the B+ tree.
Inserting it
Traversing the tree to insert key 
Root Node: [100010, 110117, 122147, 131762, 143922, 154185, 165690, 176084]
Level1: [154185, 155848, 157213, 158967, 160590, 162163, 162896, 163706]
Level2: [155848, 155907, 156009, 156143, 156259, 156341, 156450, 156582, 156684, 156793, 156913, 157047, 157129]
Level3: [156341, 156344, 156360, 156367, 156379, 156390, 156397, 156426, 156430, 156440, 156441, 156444, 156448]
Inserting 156438 in leaf node [156341, 156344, 156360, 156367, 156379, 156390, 156397, 156426, 156430, 156440, 156441, 156444, 156448]
After inserting: [156341, 156344, 156360, 156367, 156379, 156390, 156397, 156426, 156430, 156438, 156440, 156441, 156444, 156448]
156438 has been inserted in the tree.
Leaf node is full after insertion. Splitting leaf node to accomodate future keys
Splitting leaf node: [156341, 156344, 156360, 156367, 156379, 156390, 156397, 156426, 156430, 156438, 156440, 156441, 156444, 156448]
Leaf node before splitting: [156341, 156344, 156360, 156367, 156379, 156390, 156397, 156426, 156430, 156438, 156440, 156441, 156444, 156448]

Leaf node after splitting
Left Split keys: [156341, 156344, 156360, 156367, 156379, 156390]
Right split keys: [156397, 156426, 156430, 156438, 156440, 156441, 156444, 156448]

Restructuring parent(internal) nodes
Merging Nodes: [155848, 155907, 156009, 156143, 156259, 156341, 156450, 156582, 156684, 156793, 156913, 157047, 157129] and [156397]
Merged Node: [155848, 155907, 156009, 156143, 156259, 156341, 156397, 156450, 156582, 156684, 156793, 156913, 157047, 157129]

Merged internal node is full. Splitting the node: [155848, 155907, 156009, 156143, 156259, 156341, 156397, 156450, 156582, 156684, 156793, 156913, 157047, 157129]
Merged node after splitting
Left Split keys: [155848, 155907, 156009, 156143, 156259, 156341]
Right Split keys: [156397, 156450, 156582, 156684, 156793, 156913, 157047, 157129]

Restructuring parent(internal) nodes
Merging Nodes: [154185, 155848, 157213, 158967, 160590, 162163, 162896, 163706] and [156397]
Merged Node: [154185, 155848, 156397, 157213, 158967, 160590, 162163, 162896, 163706]

**********************************


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1.2. Re - inserting: 156438
Inserting: 156438
Searching key 156438 in the tree to see if it already exists.
Searching: 156438
Traversing the tree from root node to leaf:
[100010, 110117, 122147, 131762, 143922, 154185, 165690, 176084]
[154185, 155848, 156397, 157213, 158967, 160590, 162163, 162896, 163706]
[156397, 156450, 156582, 156684, 156793, 156913, 157047, 157129]
[156397, 156426, 156430, 156438, 156440, 156441, 156444, 156448]
Key 156438 exists in the tree
The key 156438 that you want to insert already exists in the B+ tree.
**********************************


1.3. Searching: 156438
Searching: 156438
Traversing the tree from root node to leaf:
[100010, 110117, 122147, 131762, 143922, 154185, 165690, 176084]
[154185, 155848, 156397, 157213, 158967, 160590, 162163, 162896, 163706]
[156397, 156450, 156582, 156684, 156793, 156913, 157047, 157129]
[156397, 156426, 156430, 156438, 156440, 156441, 156444, 156448]
Key 156438 exists in the tree
**********************************


1.4. Deleting: 156438
Deleting key: 156438
Node before deleting: [156397, 156426, 156430, 156438, 156440, 156441, 156444, 156448]
Node after deleting: [156397, 156426, 156430, 156440, 156441, 156444, 156448]
Key deletion completed
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Deletion operation complete.
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