Reservoir sampling and exponentially decaying sampling.Contains a batch and incremental version.Programmed in functional non object oreinted style.

output

------------------- overSamplingRes -----------------------
res 213, 874, 1111, 1119, 1166, 1959, 2095, 2255, 2803, 2934, 3237, 3273, 3385, 3395, 3657, 3848, 3866, 4194, 4666, 4881, 5088, 5562, 5861, 5990, 6138, 6403, 6584, 6774, 7140, 7273, 7473, 7765, 7776, 8126, 8237, 8358, 9435, 10091, 10092, 10184, 10316, 11135, 12453, 12658, 13611, 13743, 13815, 14060, 14272, 14393, 14482, 16054, 16439, 16493, 16759, 17721, 18792, 19097, 19696, 20552, 21022, 21548, 22074, 22243, 22418, 22646, 23238, 23284, 23423, 23557, 23667, 24276, 24473, 24725, 24931, 24986, 25173, 25178, 25398, 25731, 25755, 26262, 26340, 26506, 27404, 27415, 27867, 28379, 29075, 29127, 29723, 29957, 30731, 30937, 31087, 32036, 32398, 33247, 33740, 33864, 34505, 35049, 35146, 35301, 35782, 35796, 36097, 36268, 36480, 36906, 36932, 37415, 37487, 38251, 38306, 38329, 39078, 39563, 39760, 39818, 39884, 40902, 41625, 42007, 42071, 42244, 42496, 42626, 42744, 43346, 43827, 43908, 44428, 44447, 44631, 45532, 45767, 45934, 46046, 46061, 46514, 46593, 47318, 47727, 47865, 48403, 48647, 48838, 49383, 49488, 49501, 50311, 50389, 50583, 50846, 50980, 51038, 51431, 51457, 51494, 51642, 51787, 51796, 52029, 52645, 52660, 52897, 53268, 54023, 54628, 54632, 54665, 54685, 55642, 55819, 56013, 56705, 57087, 57174, 57303, 57598, 57695, 58331, 58552, 60353, 60433, 60763, 60965, 61393, 61519, 61871, 61969, 62144, 62700, 62846, 62885, 63011, 63553, 63862, 64054, 64428, 64718, 65703, 66013, 66105, 66326, 68060, 68064, 68090, 68581, 68677, 68887, 69789, 70128, 70255, 70351, 70404, 71706, 72223, 72825, 72827, 73642, 74266, 74505, 75326, 75849, 76600, 76739, 77647, 78496, 79558, 79698, 80088, 80553, 81247, 81327, 81759, 83062, 83314, 83675, 84012, 84722, 85228, 85473, 86227, 86576, 87280, 87286, 87353, 87829, 89838, 90073, 90349, 91207, 91956, 92558, 93330, 93661, 93860, 94165, 95093, 95142, 95582, 95661, 95662, 96411, 96694, 97737, 98017, 98176, 98191, 98253, 98395, 98714, 99182, 99619, 99742, 99810, 100489, 100662, 100733, 100735, 100910, 100976, 101322, 101375, 101754, 101854, 101986, 102178, 102780, 102948, 103020, 103576, 103782, 103801, 104013, 104308, 104775, 105270, 105306, 105606, 106055, 106976, 107284, 108075, 108544, 109555, 110022, 110198, 110589, 111149, 111270, 111538, 112438, 113138, 113206, 113342, 113474, 114847, 115451, 115558, 115715, 115877, 115916, 115941, 116076, 116220, 117527, 118131, 118155, 118330, 119046, 119976, 120222, 120789, 121236, 121459, 121464, 121521, 121853, 121906, 122073, 122190, 122951, 123198, 123620, 123908, 124466, 125198, 125685, 125723, 125749, 125824, 126092, 126528, 126709, 127817, 128012, 128199, 128211, 128436, 128672, 129021, 129128, 130055, 131020, 132743, 132760, 132968, 133933, 134201, 134223, 134331, 135276, 135430, 136451, 136657, 137183, 137277, 137373, 137737, 137746, 138326, 138371, 138653, 138927, 139346, 139883, 140322, 141296, 142027, 142165, 142269, 143553, 143669, 144555, 144793, 145094, 145098, 145643, 146219, 146577, 147067, 147251, 147313, 147374, 147397, 147808, 148019, 148346, 148745, 148827, 148930, 149006, 149056, 149099, 149452, 149906, 149967, 150245, 150988, 151245, 151267, 151773, 152384, 152610, 153548, 153590, 153652, 155262, 156708, 157003, 157112, 157723, 158156, 158236, 158510, 158511, 158576, 158583, 158762, 158863, 159222, 159376, 159472, 159965, 160656, 160676, 161025, 161395, 161662, 161681, 161712, 161773, 161988, 162155, 162371, 162386, 162401, 162796, 163267, 164192, 164203, 164257, 164516, 164699, 164959, 165232, 165284, 165988, 165990, 166146, 166189, 166298, 166635, 166799, 166882, 166913, 167585, 167603, 167767, 168278, 168372, 168531, 168654, 168691, 168761, 169186, 169416, 169424, 169771, 170141, 170297, 170430, 171153, 171706, 171799, 171972, 171995, 172026, 172203, 173017, 173096, 173404, 174044, 174135, 174650, 174947, 175012, 176065, 176299, 176865, 176887, 177470, 177514, 177572, 178357, 178395, 178477, 178630, 178860, 179347, 179364, 180041, 180139, 180207, 181359, 181411, 181580, 182187, 182373, 182540, 182974, 183000, 183142, 183310, 184223, 184233, 184255, 184422, 184606, 184925, 185797, 185805, 186010, 186351, 186414, 186978, 187241, 187465, 187615, 188006, 188656, 188807, 189509, 189815, 190138, 190579, 190642, 191215, 191478, 191505, 192336, 192378, 193144, 193339, 193647, 193649, 193656, 193839, 193942, 194184, 195069, 195127, 195445, 195772, 195838, 196265, 196405, 196526, 197176, 197363, 198267, 198349, 200139, 200404, 200545, 200975, 201116, 201513, 201927, 202410, 203071, 203333, 203369, 204369, 204924, 205027, 205455, 205817, 205998, 206409, 207717, 208365, 208512, 208850, 209054, 209531, 209620, 209752, 210384, 210585, 210769, 211796, 212227, 212989, 213613, 213720, 213900, 214116, 214807, 216942, 217323, 217427, 217659, 217748, 218112, 218223, 218272, 218587, 218867, 220196, 220295, 221139, 221629, 221801, 221805, 222200, 222498, 222546, 223297, 223639, 223690, 223811, 223819, 223941, 224323, 224431, 224525, 224835, 225020, 225280, 225326, 225348, 225747, 225882, 226476, 226637, 226768, 226848, 227347, 227375, 227848, 228439, 228845, 228859, 228993, 229216, 229880, 229973, 230036, 230088, 230106, 230550, 230664, 231510, 232026, 232257, 232451, 233452, 233746, 233912, 234025, 234484, 234547, 234744, 234837, 234859, 235894, 236281, 236538, 236804, 237406, 237660, 238441, 238563, 238607, 238641, 238729, 239793, 240603, 240634, 241371, 241604, 241703, 242008, 242397, 242577, 243006, 243666, 244110, 244627, 245987, 246484, 247270, 247307, 247383, 248035, 248101, 248128, 248229, 248711, 248742, 248828, 249003, 249007, 249048, 249968, 250029, 250411, 250708, 250868, 250886, 252492, 252554, 252584, 252945, 253180, 253226, 253695, 253751, 254622, 254922, 254976, 255558, 255586, 255917, 256018, 256398, 257105, 257648, 258355, 258825, 259354, 259401, 259785, 260023, 260237, 260334, 260593, 260689, 261023, 261592, 261809, 262126, 262155, 262204, 262799, 263244, 263538, 263704, 264029, 264565, 264674, 264817, 265653, 265707, 265745, 266819, 267403, 267574, 268168, 268491, 268592, 268840, 269822, 269886, 270566, 271189, 271403, 272175, 272317, 272388, 272403, 272447, 272582, 273357, 273391, 273703, 274257, 274359, 274406, 274848, 275160, 276024, 276090, 276992, 277100, 278064, 278233, 279144, 279357, 280836, 281159, 281171, 281549, 281955, 282227, 283529, 283743, 283855, 284379, 284587, 285026, 285132, 285333, 285385, 285462, 285467, 285945, 286290, 286427, 286698, 287375, 287646, 287802, 288380, 289038, 289391, 289680, 289916, 290383, 290518, 290770, 290795, 290842, 291077, 291381, 291423, 291540, 292464, 292657, 292709, 293055, 293061, 293189, 293620, 294806, 294850, 295415, 295639, 295665, 296115, 296702, 296860, 297161, 297184, 297304, 297969, 298326, 300017, 300093, 300267, 301541, 301812, 302441, 302582, 302742, 303041, 303242, 303452, 304216, 304848, 305045, 305451, 305842, 306039, 306665, 306677, 306796, 306829, 307462, 307700, 307720, 308676, 308913, 309105, 309977, 310075, 310309, 310324, 310439, 310599, 310897, 311136, 311418, 311540, 311664, 313327, 313383, 313466, 313494, 313650, 314010, 314276, 314557, 314670, 314674, 314734, 314758, 314759, 315113, 315138, 315715, 315739, 316653, 316659, 317648, 317668, 317775, 317867, 318027, 318109, 318468, 318858, 319231, 319263, 319379, 319563, 319680, 319925, 319960, 319996, 319997, 320253, 320406, 320717, 320765, 320910, 321349, 321395, 321582, 322336, 322434, 322798, 322883, 322916, 323676, 323712, 323802, 323981, 324363, 326523, 326666, 327082, 327565, 327691, 328466, 328900, 329060, 329339, 329594, 329612, 329859, 330169, 330321, 330531, 330630, 330937, 331467, 331923, 332164, 332467, 332607, 332660, 332741, 332982, 333038, 333197, 333582, 333621, 333975, 334260, 335045, 335146, 335199, 335304, 335352, 335386, 335561, 336144, 336201, 336220, 336563, 336786, 337093, 337146, 337332, 337490, 337717, 337745, 338221, 338511, 338706, 338821, 339280, 339631, 339712, 340005, 340291, 340501, 340640, 340762, 341503, 341571, 341776, 341804, 343222, 343728, 344045, 344823, 344921, 344992, 345028, 345193, 345581, 345712, 345832, 346086, 346105, 346453, 346571, 346829, 347220, 347223, 347333, 347392, 347612, 347718, 347895, 348306, 348449, 348876, 349115, 349371, 349461, 350613, 350763, 350851, 350932, 351051, 351879, 351966, 352177, 352215, 352742, 352931, 353253, 353447, 353865, 354285, 354419, 354554, 354694, 354747, 355353, 355384, 355611, 355741, 355860, 355922, 356492, 356496, 357073, 357201, 357991, 358293, 358939, 359006, 359207, 359336, 359736, 360195, 360552, 360570, 360804, 360822, 360828, 360839, 360927, 361018, 361110, 361410, 361772, 361868, 362145, 362178, 362209, 362499, 362942, 363284, 363571, 363648, 363668, 363867, 364896, 364910, 365065, 365373, 365502, 366847, 366916, 367478, 368223, 368799, 369422, 369488, 369776, 370055, 370211, 370440, 370452, 370490, 370725, 370891, 370932, 371214, 371281, 371493, 371771, 372297, 372377, 372546, 372653, 372947, 373181, 373238, 373333, 374029, 374175, 374429, 374647, 375808, 375873, 376213, 376498, 376923, 376997, 377199, 377807, 377995, 378049, 379744, 379871, 380318, 380631, 380683, 380714, 380726, 380836, 380927, 381164, 381302, 381330, 382435, 382693, 382793, 383213, 384686, 384801, 385214, 385299, 385751, 386390, 386467, 386881, 387110, 387379, 387703, 387896, 387966, 388028, 388076, 388329, 388903, 389922, 389968, 390513, 390652, 391009, 391311, 392275, 393256, 393450, 394819, 394848, 395375, 395541, 395600, 395775, 396728, 396743, 396867, 397540, 398034, 399051, 399841, 400023, 400127, 400472, 400750, 401192, 401286, 401620, 401935, 402811, 403250, 403270, 403609, 403687, 404033, 404168, 404218, 404340, 404512, 404909, 405326, 405537, 405582, 406604, 406865, 407248, 407541, 407938, 408059, 408707, 408965, 409223, 409411, 409462, 409839, 410156, 410294, 410731, 410753, 411059, 411088, 411326, 411352, 411458, 411686, 411815, 411847, 412308, 412977, 413186, 413732, 413790, 414524, 415700, 415719, 416631, 417179, 417666, 417876, 418356, 418644, 418934, 419633, 419684, 419823, 420291, 420407, 421198, 421558, 421583, 421639, 421652, 421715, 421976, 422270, 423320, 423772, 424007, 424119, 424321, 424618, 424856, 425013, 425507, 425563, 425596, 425852, 425871, 426146, 426312, 426643, 426946, 427407, 427992, 428825, 428905, 428926, 429150, 429452, 429651, 429668, 429761, 430484, 430896, 431358, 431823, 431831, 431920, 432084, 432119, 432171, 432760, 432876, 433132, 433213, 433378, 433539, 433729, 433939, 434006, 434673, 434678, 434749, 435035, 435254, 435667, 435937, 436000, 436028, 436414, 436981, 436986, 437272, 437722, 438056, 438129, 438374, 438966, 439408, 439464, 439644, 439660, 439760, 439795, 440119, 440207, 440631, 440829, 441260, 441407, 441513, 442047, 442209, 442361, 443681, 444111, 444452, 444524, 444730, 445382, 445700, 445782, 446027, 446063, 446217, 446260, 446336, 446453, 446480, 446770, 446809, 447005, 447129, 447184, 447204, 447312, 447755, 447852, 448157, 448389, 448390, 448468, 448745, 448916, 448937, 449492, 449722, 450072, 450190, 450262, 450614, 450979, 450994, 451008, 451101, 451190, 451400, 451416, 451564, 451662, 451690, 451811, 451929, 452028, 452123, 452271, 452313, 452970, 453630, 453970, 454737, 454819, 455044, 455352, 455918, 456083, 456584, 456943, 457612, 457679, 457907, 458086, 458217, 458588, 458745, 458918, 460188, 460365, 460374, 460463, 460646, 460760, 460816, 461174, 461373, 461460, 461523, 461765, 462386, 462792, 462930, 462949, 463228, 463379, 463554, 463626, 464020, 464094, 464481, 464715, 464719, 465058, 465438, 465561, 465918, 465925, 466166, 466295, 466372, 466515, 466622, 466963, 466994, 467030, 467295, 467417, 467569, 467872, 468123, 468289, 469407, 469604, 470159, 470362, 470666, 470912, 470992, 471787, 471985, 472474, 472683, 472980, 473107, 473218, 473710, 473838, 473842, 474281, 474371, 474512, 474910, 474959, 475024, 475406, 475583, 475585, 475675, 475793, 476078, 476169, 476241, 476256, 476747, 476851, 477096, 477113, 477172, 477241, 477774, 478077, 478103, 478723, 479084, 479350, 480180, 480302, 480356, 481507, 481590, 481696, 482061, 482063, 482425, 482566, 483106, 483145, 483495, 484250, 484943, 484981, 485098, 485359, 485702, 485871, 486475, 486894, 487298, 487673, 487735, 487997, 488265, 488461, 488565, 488584, 488811, 488819, 488890, 489379, 489389, 489482, 490298, 490697, 491131, 491639, 491685, 491718, 491854, 491918, 492045, 492063, 492300, 492546, 493384, 493725, 493977, 494160, 494507, 494793, 495188, 495579, 495642, 495678, 497244, 497771, 497999, 498691, 498911, 499358, 500402, 500777, 500827, 501127, 501734, 502181, 502196, 502208, 502299, 502464, 502491, 502512, 502703, 502773, 503425, 503731, 503738, 504181, 504204, 504278, 504415, 505212, 505400, 505543, 506055, 506070, 506212, 506218, 506853, 507272, 507277, 507527, 507907, 507938, 507949, 508512, 508729, 508846, 509024, 509657, 510228, 510309, 511007, 511178, 511352, 511374, 511387, 511489, 511676, 511702, 511931, 513344, 513356, 513986, 514066, 514482, 514604, 514763, 515151, 515276, 515281, 515469, 515577, 515883, 516033, 516337, 516469, 516508, 516510, 516552, 516758, 516887, 516992, 517063, 517096, 517644, 518061, 518586, 518836, 519018, 519334, 519810, 520442, 520457, 520675, 521203, 521262, 521466, 521569, 521696, 522086, 522093, 522134, 522503, 522690, 523413, 523458, 523511, 524136, 524392, 524516, 524624, 524831, 524931, 525071, 525184, 525476, 525519, 525848, 525904, 525918, 525966, 526377, 526518, 526731, 526941, 527066, 527489, 527541, 527864, 528309, 528318, 528336, 528405, 528814, 528910, 529041, 529164, 529397, 529624, 529701, 529705, 530303, 530307, 530509, 530635, 530738, 530860, 530944, 531021, 531035, 531241, 531429, 532044, 532266, 532306, 532339, 532358, 533055, 534120, 534265, 534325, 534402, 534421, 534544, 534547, 534589, 534744, 534902, 534998, 535665, 535757, 535793, 535985, 536031, 536305, 536422, 537208, 537325, 537971, 538259, 540040, 540175, 540513, 540579, 540817, 540926, 541041, 541064, 541184, 541413, 541624, 542044, 542196, 542319, 542375, 542435, 542730, 543064, 543200, 543369, 543874, 544385, 544770, 544905, 544912, 545047, 545320, 545409, 545642, 545728, 545784, 545914, 545982, 546052, 546517, 546831, 546980, 547106, 547650, 547921, 547994, 548291, 549024, 549100, 549399, 550172, 550423, 550527, 550557, 551544, 551771, 551971, 552212, 552235, 552726, 552810, 552822, 553245, 553269, 553389, 553945, 554149, 555108, 555370, 555724, 556008, 556291, 556537, 556953, 557007, 557120, 557167, 557350, 557483, 557623, 557729, 557889, 558269, 558667, 558825, 558858, 559170, 559307, 559332, 559333, 559485, 559517, 559574, 559992, 560230, 560442, 560544, 560623, 560713, 561413, 561643, 561679, 561881, 561990, 562443, 562463, 562490, 562832, 563008, 563040, 563145, 563428, 563429, 563679, 564099, 564168, 564374, 564462, 564750, 564842, 564995, 565154, 565540, 565648, 565737, 565747, 565875, 565884, 566029, 566340, 566909, 566915, 567671, 567845, 568048, 568202, 568340, 568351, 568908, 569045, 569135, 569157, 569364, 569552, 569628, 569655, 569745, 569977, 570076, 570201, 570365, 570613, 570674, 570731, 570809, 571010, 571054, 571130, 571143, 571638, 571800, 571885, 571904, 572443, 572460, 572505, 572789, 572884, 573240, 573338, 573419, 573573, 574110, 574114, 574347, 574873, 574951, 575092, 575595, 577007, 577038, 577104, 577196, 577770, 578004, 578184, 578378, 578507, 578603, 578693, 578728, 578998, 579109, 579184, 579561, 579649, 579703, 579891, 580180, 580189, 580239, 580368, 580761, 580853, 581175, 581233, 581236, 581973, 582010, 582296, 582570, 582791, 583268, 584486, 584516, 584712, 584802, 584964, 585003, 585199, 585418, 585461, 585518, 585723, 585825, 585967, 586117, 586327, 586429, 587234, 587260, 587461, 587609, 587715, 588001, 588124, 588162, 588217, 588411, 588522, 588623, 588780, 588807, 588864, 589639, 589847, 589937, 590019, 590031, 590042, 590989, 591275, 591449, 591474, 591618, 591975, 592023, 592477, 592585, 592626, 593071, 593136, 593547, 593573, 594167, 594335, 594492, 594665, 594717, 594888, 595267, 595348, 595659, 596162, 596175, 596182, 596640, 596660, 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2128712, 2128723, 2128754, 2128759, 2128770, 2128779, 2128850, 2128998, 2129006, 2129056, 2129113, 2129134, 2129139, 2129216, 2129261, 2129300, 2129346, 2129348, 2129368, 2129493, 2129521, 2129553, 2129559, 2129622, 2129687, 2129794, 2129905, 2129957, 2130019, 2130030, 2130079, 2130154, 2130166, 2130172, 2130251, 2130269, 2130292, 2130315, 2130389, 2130410, 2130453, 2130518, 2130525, 2130549, 2130580, 2130634, 2130641, 2130772, 2130791, 2130827, 2130835, 2130979, 2131063, 2131085, 2131099, 2131109, 2131115, 2131157, 2131245, 2131251, 2131271, 2131292, 2131409, 2131467, 2131585, 2131610, 2131627, 2131656, 2131690, 2131691, 2131749, 2131854, 2131877, 2132065, 2132083, 2132090, 2132236, 2132261, 2132300, 2132332, 2132393, 2132451, 2132454, 2132524, 2132531, 2132588, 2132598, 2132602, 2132606, 2132797, 2132798, 2132880, 2132896, 2132943, 2132955, 2133104, 2133105, 2133126, 2133212, 2133246, 2133263, 2133274, 2133354, 2133358, 2133383, 2133414, 2133499, 2133503, 2133546, 2133564, 2133628, 2133725, 2133796, 2133808, 2133819, 2133836, 2133896, 2133937, 2133982, 2134012, 2134040, 2134051, 2134084, 2134229, 2134254, 2134284, 2134341, 2134422, 2134548, 2134565, 2134858, 2134861, 2134937, 2135076, 2135079, 2135132, 2135162, 2135382, 2135465, 2135562, 2135610, 2135688, 2135715, 2135724, 2135846, 2135882, 2135907, 2135951, 2135989, 2136000, 2136098, 2136163, 2136225, 2136256, 2136318, 2136385, 2136406, 2136444, 2136482, 2136688, 2136692, 2136742, 2136881, 2136894, 2136907, 2136973, 2136979, 2137104, 2137134, 2137164, 2137205, 2137320, 2137395, 2137464, 2137465, 2137470, 2137606, 2137642, 2137699, 2137752, 2137781, 2137790, 2137840, 2137922, 2137998, 2138026, 2138137, 2138146, 2138148, 2138152, 2138166, 2138184, 2138208, 2138217, 2138250, 2138252, 2138301, 2138311, 2138321, 2138354, 2138591, 2138644, 2138690, 2138727, 2138737, 2138815, 2138838, 2138889, 2138904, 2138966, 2139057, 2139135, 2139149, 2139159, 2139170, 2139199, 2139241, 2139305, 2139361, 2139366, 2139392, 2139407, 2139435, 2139510, 2139514, 2139536, 2139545, 2139547, 2139548, 2139565, 2139581, 2139640, 2139804, 2139819, 2139915, 2140028, 2140030, 2140043, 2140234, 2140239, 2140315, 2140329, 2140465, 2140519, 2140538, 2140541, 2140590, 2140868, 2140904, 2140926, 2140959, 2141007, 2141192, 2141201, 2141235, 2141284, 2141299, 2141345, 2141354, 2141414, 2141446, 2141669, 2141735, 2141740, 2141750, 2141798, 2141898, 2141904, 2141930, 2141946, 2141976, 2142008, 2142099, 2142154, 2142181, 2142251, 2142275, 2142281, 2142307, 2142383, 2142386, 2142481, 2142514, 2142577, 2142584, 2142590, 2142648, 2142676, 2142677, 2142681, 2142688, 2142745, 2142807, 2142867, 2142878, 2142882, 2142916, 2142944, 2142995, 2143004, 2143041, 2143061, 2143265, 2143355, 2143358, 2143382, 2143447, 2143525, 2143567, 2143595, 2143941, 2143957, 2143963, 2143992, 2144088, 2144147, 2144176, 2144220, 2144309, 2144329, 2144369, 2144387, 2144402, 2144475, 2144556, 2144570, 2144606, 2144628, 2144679, 2144702, 2144756, 2144788, 2144921, 2144922, 2144976, 2145140, 2145232, 2145237, 2145251, 2145336, 2145371, 2145373, 2145453, 2145475, 2145500, 2145642, 2145643, 2145656, 2145658, 2145683, 2145720, 2145746, 2145832, 2145950, 2145959, 2146001, 2146047, 2146071, 2146076, 2146120, 2146141, 2146142, 2146213, 2146377, 2146417, 2146422, 2146627, 2146670, 2146711, 2146883, 2146887, 2146918, 2147000, 2147101, 2147108, 2147122, 2147145, 2147158, 2147318, 2147330, 2147349, 2147399, 2147407, 2147426, 2147444, 2147452, 2147464, 2147545, 2147603, 2147738, 2147757, 2147771, 2147778, 2147817, 2147829, 2147864, 2148030, 2148052, 2148081, 2148086, 2148116, 2148119, 2148138, 2148159, 2148190, 2148197, 2148261, 2148328, 2148357, 2148362, 2148375, 2148413, 2148426, 2148462, 2148504, 2148585, 2148813, 2148895, 2148896, 2148929, 2148978, 2149005, 2149027, 2149065, 2149155, 2149301, 2149356, 2149368, 2149392, 2149455, 2149461, 2149463, 2149484, 2149615, 2149646, 2149648, 2149713, 2149777, 2149804, 2149882, 2149895, 2150038, 2150039, 2150052, 2150073, 2150142, 2150181, 2150203, 2150207, 2150222, 2150229, 2150272, 2150364, 2150391, 2150405, 2150434, 2150534, 2150638, 2150845, 2150920, 2150966, 2150981, 2151123, 2151274, 2151297, 2151305, 2151308, 2151309, 2151356, 2151427, 2151467, 2151472, 2151476, 2151534, 2151549, 2151601, 2151610, 2151615, 2151622, 2151650, 2151857, 2151878, 2151929, 2151976, 2152005, 2152036, 2152046, 2152052, 2152088, 2152112, 2152146, 2152236, 2152247, 2152269, 2152273, 2152304, 2152319, 2152378, 2152401, 2152589, 2152594, 2152637, 2152641, 2152675, 2152688, 2152739, 2152778, 2152786, 2152808, 2152813, 2152906, 2152972, 2152993, 2153000, 2153014, 2153018, 2153096, 2153120, 2153259, 2153264, 2153276, 2153397, 2153422, 2153450, 2153515, 2153549, 2153614, 2153671, 2153725, 2153802, 2153840, 2153958, 2153992, 2154020, 2154065, 2154212, 2154342, 2154444, 2154489, 2154507, 2154533, 2154549, 2154568, 2154584, 2154623, 2154739, 2154782, 2154849, 2154869, 2154871, 2154924, 2154977, 2154983, 2155071, 2155104, 2155223, 2155232, 2155303, 2155364, 2155374, 2155379, 2155381, 2155387, 2155425, 2155467, 2155482, 2155527, 2155557, 2155605, 2155615, 2155647, 2155661, 2155740, 2155869, 2155939, 2156042, 2156044, 2156057, 2156085, 2156129, 2156157, 2156169, 2156207, 2156226, 2156240, 2156317, 2156329, 2156398, 2156417, 2156473, 2156489, 2156491, 2156502, 2156513, 2156554, 2156680, 2156700, 2156702, 2156880, 2156886, 2156911, 2156934, 2156946, 2156972, 2157041, 2157113, 2157157, 2157237, 2157257, 2157296, 2157353, 2157357, 2157377, 2157392, 2157399, 2157489, 2157559, 2157577, 2157662, 2157797, 2157808, 2157823, 2157842, 2157845, 2157860, 2157919, 2157947, 2158044, 2158051, 2158060, 2158108, 2158117, 2158126, 2158163, 2158206, 2158254, 2158266, 2158269, 2158290, 2158297, 2158335, 2158398, 2158417, 2158444, 2158465, 2158514, 2158549, 2158601, 2158608, 2158771, 2158794, 2158826, 2158978, 2159024, 2159046, 2159057, 2159091, 2159101, 2159114, 2159273, 2159320, 2159374, 2159430, 2159488, 2159513, 2159541, 2159543, 2159655, 2159700, 2159703, 2159725, 2159776, 2159782, 2159833, 2159898, 2160013, 2160155, 2160161, 2160173, 2160220, 2160230, 2160249, 2160268, 2160275, 2160455, 2160496, 2160670, 2160705, 2160707, 2160816, 2160882, 2160930, 2161022, 2161032, 2161104, 2161180, 2161186, 2161195, 2161228, 2161327, 2161337, 2161402, 2161426, 2161514, 2161556, 2161562, 2161635, 2161663, 2161677, 2161695, 2161700, 2161747, 2161776, 2161804, 2161984, 2161995, 2162045, 2162239, 2162422, 2162465, 2162496, 2162504, 2162522, 2162525, 2162552, 2162634, 2162640, 2162641, 2162697, 2162701, 2162718, 2162723, 2162727, 2162754, 2162776, 2162786, 2162851, 2162964, 2163074, 2163163, 2163213, 2163240, 2163441, 2163444, 2163508, 2163768, 2163788, 2163853, 2163901, 2163917, 2163945, 2164032, 2164111, 2164204, 2164266, 2164353, 2164417, 2164439, 2164473, 2164536, 2164592, 2164594, 2164647, 2164669, 2164682, 2164724, 2164773, 2164803, 2165062, 2165065, 2165196, 2165398, 2165450, 2165543, 2165611, 2165660, 2165765, 2165817, 2165835, 2166059, 2166160, 2166171, 2166180, 2166384, 2166427, 2166465, 2166512, 2166590, 2166628, 2166679, 2166724, 2166731, 2166748, 2166789, 2166792, 2166844, 2166854, 2166917, 2166955, 2167067, 2167137, 2167291, 2167317, 2167377, 2167407, 2167419, 2167423, 2167470, 2167480, 2167485, 2167529, 2167552, 2167633, 2167671, 2167695, 2167821, 2167918, 2168043, 2168159, 2168257, 2168263, 2168358, 2168428, 2168442, 2168522, 2168527, 2168587, 2168622, 2168680, 2168756, 2168842, 2168867, 2168899, 2168997, 2169032, 2169059, 2169111, 2169153, 2169190, 2169237, 2169257, 2169260, 2169303, 2169323, 2169332, 2169362, 2169382, 2169428, 2169432, 2169437, 2169454, 2169470, 2169545, 2169558, 2169621, 2169740, 2169757, 2169776, 2169835, 2169838, 2169857, 2169890, 2169909, 2169914, 2169936, 2169995, 2169999, 2170078, 2170164, 2170195, 2170211, 2170221, 2170234, 2170258, 2170272, 2170365, 2170371, 2170454, 2170467, 2170550, 2170601, 2170697, 2170720, 2170740, 2170770, 2170906, 2170948, 2171165, 2171167, 2171272, 2171299, 2171351, 2171408, 2171414, 2171426, 2171427, 2171431, 2171461, 2171465, 2171511, 2171522, 2171545, 2171546, 2171555, 2171573, 2171661, 2171877, 2171887, 2171910, 2171963, 2172003, 2172018, 2172026, 2172062, 2172064, 2172083, 2172129, 2172224, 2172226, 2172233, 2172378, 2172384, 2172458, 2172485, 2172514, 2172583, 2172640, 2172677, 2172801, 2172896, 2172924, 2172939, 2173006, 2173017, 2173049, 2173066, 2173090, 2173134, 2173225, 2173279, 2173317, 2173389, 2173401, 2173409, 2173445, 2173471, 2173475, 2173480, 2173488, 2173505, 2173525, 2173546, 2173566, 2173625, 2173682, 2173706, 2173714, 2173750, 2173761, 2173802, 2173971, 2174053, 2174075, 2174089, 2174216, 2174347, 2174380, 2174384, 2174392, 2174440, 2174457, 2174494, 2174519, 2174652, 2174664, 2174669, 2174735, 2174772, 2174794, 2174884, 2174942, 2174978, 2175050, 2175123, 2175135, 2175151, 2175165, 2175266, 2175378, 2175393, 2175759, 2175764, 2175800, 2175880, 2175924, 2175959, 2176054, 2176154, 2176198, 2176199, 2176205, 2176235, 2176361, 2176411, 2176437, 2176478, 2176514, 2176521, 2176532, 2176576, 2176614, 2176645, 2176691, 2176704, 2176736, 2176750, 2176768, 2176813, 2176819, 2176860, 2176876, 2176890, 2177003, 2177018, 2177023, 2177045, 2177070, 2177082, 2177084, 2177107, 2177193, 2177226, 2177322, 2177427, 2177437, 2177457, 2177459, 2177491, 2177508, 2177529, 2177548, 2177613, 2177706, 2177851, 2177895, 2177903, 2177948, 2178077, 2178088, 2178131, 2178150, 2178170, 2178213, 2178261, 2178277, 2178298, 2178326, 2178389, 2178545, 2178601, 2178680, 2178749, 2178881, 2178884, 2178956, 2178997, 2179097, 2179101, 2179232, 2179290, 2179320, 2179339, 2179547, 2179645, 2179800, 2179809, 2179816, 2179819, 2179942, 2179956, 2180002, 2180083, 2180095, 2180110, 2180121, 2180134, 2180163, 2180202, 2180264, 2180285, 2180568, 2180569, 2180623, 2180633, 2180666, 2180668, 2180676, 2180709, 2180814, 2180929, 2181183, 2181199, 2181298, 2181388, 2181392, 2181396, 2181498, 2181553, 2181576, 2181657, 2181658, 2181770, 2181860, 2181866, 2181989, 2182000, 2182007, 2182017, 2182075, 2182105, 2182128, 2182147, 2182329, 2182336, 2182341, 2182372, 2182375, 2182385, 2182425, 2182507, 2182511, 2182516, 2182574, 2182576, 2182582, 2182645, 2182657, 2182676, 2182736, 2182773, 2182853, 2182889, 2182911, 2182933, 2183000, 2183069, 2183100, 2183111, 2183223, 2183236, 2183248, 2183302, 2183412, 2183452, 2183458, 2183461, 2183535, 2183573, 2183615, 2183623, 2183672, 2183686, 2183690, 2183823, 2183936, 2184008, 2184030, 2184138, 2184150, 2184198, 2184326, 2184472, 2184496, 2184499, 2184549, 2184554, 2184615, 2184712, 2184734, 2184740, 2184873, 2184990, 2185002, 2185048, 2185059, 2185068, 2185122, 2185194, 2185258, 2185289, 2185392, 2185434, 2185545, 2185592, 2185635, 2185656, 2185661, 2185705, 2185774, 2185788, 2185884, 2185899, 2185900, 2185931, 2185956, 2185971, 2185995, 2186110, 2186111, 2186121, 2186137, 2186141, 2186229, 2186247, 2186257, 2186262, 2186416, 2186451, 2186592, 2186621, 2186646, 2186728, 2186782, 2186826, 2186830, 2186861, 2186937, 2186943, 2186991, 2187011, 2187017, 2187240, 2187258, 2187266, 2187284, 2187306, 2187374, 2187400, 2187440, 2187555, 2187600, 2187620, 2187645, 2187650, 2187696, 2187731, 2187732, 2187740, 2187796, 2188036, 2188202, 2188208, 2188220, 2188255, 2188325, 2188343, 2188377, 2188378, 2188397, 2188401, 2188405, 2188467, 2188475, 2188477, 2188624, 2188631, 2188650, 2188709, 2188749, 2188814, 2188837, 2188867, 2188868, 2188869, 2188875, 2188897, 2188903, 2188918, 2188925, 2188971, 2189001, 2189024, 2189074, 2189113, 2189149, 2189187, 2189200, 2189217, 2189222, 2189253, 2189256, 2189274, 2189310, 2189362, 2189452, 2189570, 2189625, 2189666, 2189741, 2189759, 2189773, 2189786, 2189788, 2189842, 2189866, 2189904, 2189908, 2189935, 2189941, 2189953, 2190113, 2190142, 2190157, 2190357, 2190370, 2190371, 2190393, 2190458, 2190464, 2190472, 2190733, 2190828, 2191113, 2191141, 2191155, 2191204, 2191215, 2191267, 2191291, 2191292, 2191318, 2191356, 2191370, 2191493, 2191648, 2191656, 2191664, 2191754, 2191761, 2191795, 2191903, 2191909, 2191917, 2191962, 2191982, 2192061, 2192288, 2192291, 2192301, 2192467, 2192469, 2192490, 2192516, 2192533, 2192544, 2192563, 2192601, 2192679, 2192707, 2192824, 2192894, 2192895, 2192923, 2192937, 2192956, 2192996, 2193054, 2193112, 2193168, 2193572, 2193633, 2193642, 2193665, 2193683, 2193689, 2193710, 2193742, 2193744, 2193755, 2193831, 2193854, 2193932, 2194020, 2194108, 2194127, 2194323, 2194350, 2194363, 2194370, 2194412, 2194466, 2194577, 2194603, 2194678, 2194842, 2194896, 2194913, 2194919, 2194939, 2194942, 2195004, 2195015, 2195050, 2195073, 2195135, 2195179, 2195228, 2195301, 2195358, 2195366, 2195405, 2195468, 2195516, 2195585, 2195599, 2195663, 2195746, 2195765, 2195862, 2195973, 2195985, 2196009, 2196046, 2196094, 2196103, 2196154, 2196182, 2196194, 2196239, 2196271, 2196354, 2196371, 2196387, 2196438, 2196557, 2196572, 2196658, 2196663, 2196800, 2196894, 2196963, 2197001, 2197073, 2197160, 2197321, 2197344, 2197397, 2197409, 2197433, 2197675, 2197708, 2197714, 2197753, 2197761, 2197787, 2197820, 2197821, 2197847, 2197860, 2197915, 2197917, 2197931, 2198058, 2198087, 2198221, 2198266, 2198268, 2198280, 2198312, 2198388, 2198389, 2198404, 2198407, 2198482, 2198517, 2198648, 2198668, 2198699, 2198930, 2198976, 2198983, 2199012, 2199035, 2199199, 2199245, 2199303, 2199360, 2199446, 2199492, 2199503, 2199577, 2199582, 2199585, 2199589, 2199607, 2199807, 2199966
res length 20000
res grouped:
expected Vector(242, 269, 299, 332, 369, 411, 456, 507, 563, 626, 696, 773, 859, 954, 1061, 1178, 1309, 1455, 1617, 1796, 1996, 2218)
withExpected:
0 -> (278,242)
1 -> (307,269)
2 -> (286,299)
3 -> (347,332)
4 -> (377,369)
5 -> (459,411)
6 -> (471,456)
7 -> (538,507)
8 -> (575,563)
9 -> (703,626)
10 -> (744,696)
11 -> (793,773)
12 -> (811,859)
13 -> (985,954)
14 -> (1026,1061)
15 -> (1177,1178)
16 -> (1283,1309)
17 -> (1448,1455)
18 -> (1538,1617)
19 -> (1801,1796)
20 -> (1941,1996)
21 -> (2112,2218)
------------------- batchSamplingRes -----------------------
res 307, 466, 743, 1262, 1524, 1754, 1863, 2076, 2340, 2691, 3267, 3321, 4037, 4199, 4682, 5303, 6213, 6791, 7109, 7704, 7788, 7977, 8207, 8345, 8581, 8718, 8902, 8912, 9126, 9403, 9415, 10097, 10437, 10518, 11408, 11450, 11484, 12593, 13930, 14271, 14520, 15142, 15182, 15875, 16075, 16109, 16150, 16891, 18190, 18614, 19735, 21299, 21503, 21589, 21642, 22611, 22704, 23089, 23529, 23981, 24393, 24571, 24935, 25452, 26854, 28388, 29082, 29118, 29134, 29441, 29527, 29643, 30347, 30594, 30804, 30812, 31617, 32386, 32692, 34509, 34821, 34996, 35006, 35280, 35682, 35941, 36229, 36537, 37605, 39340, 39646, 39862, 40034, 40345, 40563, 40767, 41209, 42259, 42328, 42335, 42542, 42610, 42733, 42972, 43082, 43365, 43883, 44006, 44007, 44429, 44447, 45321, 45548, 45560, 46052, 46192, 46613, 48406, 48923, 49004, 49400, 50020, 50071, 50430, 50442, 51458, 51501, 51687, 51943, 52613, 52810, 52841, 53249, 53843, 54515, 54682, 54948, 55119, 56089, 56249, 56339, 56547, 56696, 58691, 58992, 59879, 60045, 60947, 60994, 61314, 61949, 62680, 62947, 63677, 64103, 64274, 64979, 65266, 65615, 65706, 66580, 66674, 66870, 66935, 66952, 67101, 67425, 67907, 68337, 69235, 69487, 69668, 69805, 70024, 70397, 70826, 70886, 70902, 71293, 72110, 72349, 72546, 73161, 73295, 74537, 74627, 75641, 75684, 76536, 76969, 77901, 77925, 78148, 78155, 78765, 79041, 79802, 80010, 80083, 80129, 80714, 81546, 82137, 82533, 82620, 82807, 82918, 83269, 83272, 83434, 83442, 83924, 85394, 86843, 88714, 89386, 92278, 93078, 93241, 93596, 93749, 94386, 94795, 95598, 95832, 96399, 96488, 97045, 97065, 97335, 97443, 97538, 98060, 98197, 98330, 98392, 98435, 98530, 98707, 99204, 99256, 99490, 99704, 100003, 100205, 100345, 101089, 101447, 101500, 101537, 102043, 102073, 102184, 102855, 102897, 103015, 103108, 103603, 104134, 105260, 105284, 105365, 105397, 105421, 105439, 105987, 106380, 106939, 106965, 107350, 107545, 107641, 108794, 108821, 108900, 109084, 109403, 109587, 110036, 110471, 110554, 110693, 111250, 111430, 111502, 111644, 111739, 112062, 112545, 113829, 113849, 113871, 114681, 114869, 114975, 116122, 116300, 116319, 116514, 116942, 117059, 117204, 117967, 118264, 118350, 118391, 118537, 118574, 119180, 120337, 120890, 121576, 121829, 121841, 121983, 122481, 122723, 123209, 123283, 123505, 124178, 124248, 124360, 126647, 126654, 127029, 127533, 127598, 127795, 128025, 128835, 128881, 130096, 130661, 131166, 131506, 131516, 131656, 132538, 134465, 134614, 134835, 134983, 135058, 135348, 135454, 135542, 136098, 136361, 136476, 136767, 137409, 137672, 137838, 138243, 139241, 139828, 140312, 140696, 141488, 141701, 142935, 143604, 144118, 145169, 145266, 145569, 145603, 146098, 146217, 146540, 146651, 146855, 147268, 147713, 147838, 148458, 149062, 149104, 149864, 150003, 150384, 150692, 150787, 150849, 151364, 151971, 152058, 152579, 152619, 152994, 154523, 156444, 156840, 157184, 157284, 158008, 158142, 158919, 159185, 160401, 160638, 161323, 161957, 162152, 162434, 163662, 163710, 164205, 164549, 164875, 165169, 165299, 165583, 166119, 166265, 166805, 167406, 167505, 168698, 169255, 169942, 170283, 170942, 170990, 171387, 171792, 172061, 172781, 173466, 173483, 173755, 173852, 174258, 174500, 174761, 175233, 175310, 175554, 175792, 175944, 176216, 176525, 176795, 176815, 176863, 177135, 178137, 178903, 179015, 180289, 180499, 180947, 180989, 181651, 181679, 181895, 182368, 182858, 183065, 183178, 183211, 183279, 184312, 184926, 185512, 186582, 187094, 187159, 187482, 188743, 189326, 189751, 189805, 189837, 189878, 190205, 190290, 190302, 190424, 190533, 190982, 191789, 191954, 192169, 192220, 192519, 192525, 192836, 192902, 193056, 193478, 193966, 194153, 194320, 194698, 194720, 194840, 194900, 195230, 195339, 195821, 197225, 197296, 197794, 198079, 198134, 198557, 198904, 198997, 199555, 199762, 199838, 200034, 200218, 200794, 201124, 201581, 201618, 202382, 202521, 203035, 203278, 203565, 204180, 204436, 205001, 205343, 205546, 205580, 205715, 205915, 206824, 207242, 207541, 207582, 207997, 208096, 208462, 208598, 208893, 210198, 210199, 210729, 211345, 211683, 211767, 211995, 212541, 212898, 213491, 214162, 214501, 214609, 214649, 215498, 215653, 215841, 216410, 216432, 217118, 217213, 217347, 217384, 217664, 218451, 218563, 218759, 219532, 219575, 219724, 220106, 220956, 221113, 221588, 221625, 221727, 222066, 222312, 222528, 222572, 223635, 224726, 224796, 224826, 224868, 225047, 225311, 225435, 225899, 226429, 226504, 227234, 227592, 227764, 227769, 228020, 228664, 228821, 228944, 228993, 229165, 229425, 229660, 229883, 230239, 230520, 230788, 230913, 231235, 231320, 231356, 232052, 232272, 233420, 233526, 233876, 234134, 234270, 234351, 234359, 234681, 234790, 235143, 235255, 236062, 236361, 237156, 237647, 237737, 237774, 238081, 238232, 239011, 239084, 239581, 239632, 239839, 239908, 239931, 240004, 240797, 240851, 241354, 242117, 242770, 242837, 242854, 243092, 243424, 243976, 244213, 244361, 244659, 244810, 244898, 246073, 246238, 246467, 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288830, 289438, 290421, 291040, 291157, 291817, 292110, 292481, 292648, 293176, 293489, 293911, 294669, 294941, 295071, 295884, 296126, 296499, 297188, 297275, 297370, 297743, 298564, 298588, 298870, 299071, 299222, 299584, 299721, 300134, 300663, 300746, 300845, 301140, 301861, 302158, 302869, 303107, 303138, 303304, 303405, 303891, 304484, 304850, 304864, 305990, 306043, 306770, 306870, 306876, 307132, 307413, 307516, 307560, 307653, 307673, 308248, 308643, 309109, 309236, 309459, 309564, 309726, 309843, 310031, 310188, 310378, 310943, 311025, 311257, 311529, 311702, 311732, 311813, 311891, 312489, 312502, 312828, 313106, 313504, 313541, 314584, 314857, 315169, 315617, 315677, 315786, 316688, 316876, 316895, 316972, 317003, 317041, 317241, 317316, 318284, 318699, 318789, 319861, 320575, 321546, 321709, 322585, 322828, 323310, 323449, 323966, 324401, 324820, 324898, 325249, 325373, 325399, 325748, 325903, 326234, 326479, 327623, 327772, 328537, 329110, 329221, 329303, 329843, 330401, 330603, 330686, 331257, 331345, 331807, 332152, 332594, 332622, 332725, 333874, 333933, 334062, 334251, 334669, 335019, 335625, 335947, 336335, 336473, 336753, 337032, 337391, 338364, 338607, 338659, 338688, 339613, 339847, 340726, 340772, 341207, 341790, 341894, 342494, 342806, 343332, 343679, 343729, 343898, 344359, 344524, 345009, 345072, 345219, 345454, 345541, 345570, 345875, 346606, 347401, 347418, 347419, 347946, 348069, 348132, 348359, 348741, 348745, 348897, 349131, 349486, 349959, 350353, 350526, 350760, 351013, 351079, 351725, 352356, 352586, 352633, 352816, 353082, 353353, 353468, 355226, 355692, 356084, 356096, 356864, 357061, 357065, 357183, 357266, 357377, 357464, 358578, 359168, 359357, 360137, 360198, 360474, 360870, 361032, 361453, 361549, 361885, 361962, 361981, 361999, 362112, 362228, 362260, 362801, 363202, 363246, 363519, 363774, 363819, 364129, 364259, 364761, 364873, 365315, 365418, 365544, 366117, 366338, 366589, 367151, 367193, 367377, 367541, 367946, 368513, 369059, 369251, 369644, 369905, 370430, 370761, 371398, 371715, 371972, 372071, 372308, 372529, 372598, 372672, 373196, 373278, 373590, 373639, 373656, 373732, 374330, 374659, 375170, 375236, 375242, 375369, 375799, 376004, 376041, 376395, 376804, 377187, 377380, 377382, 377418, 377733, 377864, 377947, 377981, 378644, 378930, 378973, 379259, 380189, 380350, 380600, 380825, 382049, 382724, 382899, 383229, 383276, 383347, 383458, 383478, 383676, 383678, 383724, 383971, 384128, 384516, 384922, 385520, 385537, 385726, 385789, 385822, 385933, 385938, 386554, 386975, 387078, 387119, 387324, 387717, 388622, 388644, 388959, 389100, 389101, 389326, 389797, 390084, 390575, 390601, 390608, 390791, 391503, 391924, 392337, 392576, 393450, 394077, 394266, 394408, 394958, 395055, 395614, 395677, 395763, 396068, 396229, 396710, 397173, 397358, 397465, 398049, 398060, 398592, 398795, 399287, 399688, 400673, 400941, 401181, 401219, 401249, 401597, 401745, 402437, 403074, 403472, 403516, 403558, 403665, 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2137930, 2137934, 2137948, 2137973, 2138024, 2138035, 2138045, 2138112, 2138114, 2138192, 2138274, 2138278, 2138302, 2138459, 2138469, 2138479, 2138541, 2138575, 2138678, 2138701, 2138835, 2138880, 2138883, 2138885, 2138897, 2138986, 2139009, 2139064, 2139119, 2139142, 2139193, 2139211, 2139214, 2139240, 2139258, 2139268, 2139346, 2139423, 2139448, 2139471, 2139545, 2139568, 2139569, 2139610, 2139695, 2139728, 2139738, 2139746, 2139761, 2139771, 2139782, 2139793, 2139930, 2140023, 2140070, 2140079, 2140110, 2140229, 2140312, 2140356, 2140449, 2140746, 2140804, 2140820, 2140829, 2140910, 2140922, 2140993, 2141092, 2141144, 2141145, 2141191, 2141260, 2141271, 2141365, 2141409, 2141428, 2141548, 2141555, 2141589, 2141631, 2141633, 2141736, 2141773, 2141778, 2141847, 2141857, 2141969, 2142059, 2142129, 2142175, 2142232, 2142291, 2142295, 2142308, 2142392, 2142421, 2142464, 2142472, 2142485, 2142539, 2142564, 2142601, 2142652, 2142684, 2142707, 2142747, 2142777, 2142821, 2142835, 2142870, 2142954, 2142957, 2142961, 2143003, 2143040, 2143048, 2143058, 2143154, 2143206, 2143247, 2143266, 2143294, 2143305, 2143317, 2143322, 2143405, 2143431, 2143460, 2143567, 2143573, 2143581, 2143584, 2143688, 2143796, 2143856, 2144010, 2144015, 2144049, 2144072, 2144174, 2144207, 2144313, 2144328, 2144351, 2144457, 2144532, 2144541, 2144614, 2144653, 2144704, 2144737, 2144847, 2144909, 2144910, 2144962, 2145026, 2145027, 2145140, 2145258, 2145643, 2145646, 2145683, 2145700, 2145714, 2145737, 2145756, 2145836, 2145892, 2145893, 2145896, 2145951, 2146046, 2146077, 2146101, 2146172, 2146205, 2146211, 2146212, 2146228, 2146283, 2146290, 2146324, 2146355, 2146404, 2146426, 2146455, 2146516, 2146556, 2146582, 2146594, 2146595, 2146655, 2146724, 2146761, 2146811, 2146812, 2146947, 2146954, 2147139, 2147162, 2147190, 2147224, 2147249, 2147274, 2147290, 2147332, 2147364, 2147368, 2147510, 2147517, 2147569, 2147625, 2147723, 2147724, 2147738, 2147756, 2147758, 2147795, 2147897, 2148000, 2148076, 2148078, 2148080, 2148148, 2148195, 2148240, 2148247, 2148291, 2148336, 2148358, 2148361, 2148433, 2148464, 2148605, 2148634, 2148757, 2148797, 2148818, 2148837, 2148927, 2148955, 2149011, 2149021, 2149046, 2149068, 2149085, 2149087, 2149099, 2149167, 2149178, 2149182, 2149329, 2149340, 2149347, 2149351, 2149414, 2149450, 2149482, 2149490, 2149546, 2149588, 2149590, 2149600, 2149601, 2149654, 2149698, 2149759, 2149780, 2149857, 2150020, 2150024, 2150041, 2150127, 2150153, 2150179, 2150229, 2150258, 2150329, 2150463, 2150543, 2150582, 2150591, 2150602, 2150752, 2150768, 2150918, 2150935, 2150946, 2151118, 2151189, 2151207, 2151232, 2151240, 2151257, 2151272, 2151336, 2151340, 2151395, 2151419, 2151435, 2151485, 2151511, 2151581, 2151595, 2151672, 2151903, 2151928, 2151984, 2151999, 2152060, 2152120, 2152130, 2152154, 2152197, 2152240, 2152285, 2152300, 2152396, 2152410, 2152428, 2152511, 2152624, 2152630, 2152638, 2152677, 2152705, 2152708, 2152722, 2152746, 2152772, 2152777, 2152789, 2152812, 2152849, 2152889, 2152909, 2152916, 2152927, 2152938, 2153004, 2153033, 2153039, 2153053, 2153066, 2153114, 2153152, 2153202, 2153206, 2153210, 2153260, 2153276, 2153283, 2153306, 2153314, 2153361, 2153388, 2153407, 2153409, 2153464, 2153475, 2153556, 2153568, 2153573, 2153597, 2153603, 2153606, 2153655, 2153660, 2153677, 2153728, 2153731, 2153735, 2153785, 2153786, 2153918, 2153982, 2153987, 2154017, 2154102, 2154132, 2154209, 2154222, 2154234, 2154330, 2154333, 2154353, 2154388, 2154402, 2154482, 2154483, 2154491, 2154495, 2154497, 2154633, 2154686, 2154738, 2154883, 2155033, 2155044, 2155179, 2155190, 2155194, 2155223, 2155284, 2155424, 2155471, 2155537, 2155649, 2155656, 2155691, 2155706, 2155712, 2155828, 2155917, 2155941, 2156020, 2156040, 2156125, 2156139, 2156178, 2156197, 2156214, 2156227, 2156257, 2156276, 2156283, 2156361, 2156429, 2156431, 2156437, 2156476, 2156480, 2156533, 2156541, 2156722, 2156800, 2156828, 2156831, 2156878, 2156901, 2157026, 2157034, 2157066, 2157269, 2157286, 2157297, 2157391, 2157431, 2157479, 2157570, 2157571, 2157630, 2157640, 2157642, 2157689, 2157719, 2157743, 2157746, 2157930, 2157957, 2157973, 2157984, 2158027, 2158099, 2158112, 2158154, 2158259, 2158363, 2158419, 2158431, 2158435, 2158456, 2158548, 2158597, 2158605, 2158702, 2158732, 2158774, 2158807, 2158819, 2158820, 2158905, 2158967, 2158979, 2159003, 2159015, 2159029, 2159050, 2159052, 2159069, 2159092, 2159168, 2159179, 2159189, 2159207, 2159253, 2159266, 2159326, 2159346, 2159369, 2159584, 2159629, 2159664, 2159686, 2159706, 2159717, 2159728, 2159794, 2159808, 2159843, 2159856, 2159863, 2159876, 2159886, 2159943, 2159983, 2160022, 2160025, 2160078, 2160146, 2160155, 2160186, 2160239, 2160277, 2160310, 2160356, 2160424, 2160442, 2160463, 2160525, 2160532, 2160589, 2160606, 2160677, 2160684, 2160690, 2160718, 2160809, 2160840, 2160881, 2160901, 2160968, 2161043, 2161045, 2161059, 2161105, 2161142, 2161224, 2161297, 2161319, 2161371, 2161385, 2161415, 2161491, 2161499, 2161527, 2161545, 2161559, 2161569, 2161577, 2161625, 2161647, 2161682, 2161683, 2161745, 2162033, 2162042, 2162050, 2162181, 2162262, 2162263, 2162283, 2162328, 2162429, 2162535, 2162537, 2162568, 2162648, 2162656, 2162702, 2162765, 2162783, 2162834, 2162969, 2163085, 2163102, 2163106, 2163187, 2163203, 2163206, 2163265, 2163329, 2163406, 2163447, 2163451, 2163484, 2163562, 2163620, 2163627, 2163640, 2163719, 2163768, 2163850, 2163944, 2163981, 2163998, 2164058, 2164085, 2164130, 2164143, 2164185, 2164189, 2164247, 2164257, 2164329, 2164431, 2164449, 2164454, 2164565, 2164584, 2164630, 2164631, 2164651, 2164758, 2164772, 2164829, 2164851, 2164853, 2164933, 2164946, 2164967, 2164992, 2165042, 2165064, 2165072, 2165117, 2165164, 2165172, 2165196, 2165223, 2165334, 2165427, 2165430, 2165482, 2165547, 2165620, 2165624, 2165629, 2165701, 2165748, 2165750, 2165769, 2165815, 2165820, 2165822, 2165835, 2165947, 2165962, 2166024, 2166034, 2166104, 2166144, 2166145, 2166161, 2166210, 2166245, 2166308, 2166314, 2166383, 2166413, 2166446, 2166751, 2166752, 2166802, 2166889, 2166905, 2166918, 2166939, 2166961, 2166968, 2166985, 2166990, 2167119, 2167127, 2167137, 2167164, 2167183, 2167266, 2167350, 2167359, 2167381, 2167420, 2167437, 2167497, 2167555, 2167588, 2167659, 2167723, 2167779, 2167822, 2167842, 2167874, 2167995, 2168024, 2168314, 2168349, 2168365, 2168419, 2168494, 2168531, 2168619, 2168645, 2168664, 2168711, 2168750, 2168757, 2168789, 2168791, 2168861, 2168880, 2168994, 2169243, 2169245, 2169263, 2169491, 2169501, 2169556, 2169584, 2169600, 2169682, 2169739, 2169771, 2169793, 2169922, 2169943, 2170324, 2170326, 2170333, 2170469, 2170554, 2170555, 2170569, 2170613, 2170792, 2170802, 2170817, 2170820, 2170913, 2170954, 2171030, 2171068, 2171082, 2171109, 2171122, 2171211, 2171221, 2171335, 2171378, 2171387, 2171396, 2171441, 2171448, 2171483, 2171541, 2171561, 2171637, 2171696, 2171697, 2171715, 2171796, 2171950, 2171984, 2171993, 2172007, 2172054, 2172056, 2172065, 2172066, 2172076, 2172328, 2172352, 2172457, 2172494, 2172592, 2172616, 2172665, 2172670, 2172691, 2172730, 2172750, 2172789, 2172826, 2172869, 2173076, 2173085, 2173088, 2173127, 2173174, 2173185, 2173287, 2173406, 2173410, 2173512, 2173547, 2173635, 2173663, 2173815, 2173837, 2173953, 2173974, 2174017, 2174018, 2174041, 2174094, 2174167, 2174221, 2174247, 2174290, 2174322, 2174358, 2174388, 2174472, 2174513, 2174514, 2174547, 2174610, 2174648, 2174653, 2174659, 2174888, 2175000, 2175018, 2175139, 2175149, 2175211, 2175228, 2175333, 2175370, 2175380, 2175425, 2175485, 2175518, 2175682, 2175764, 2175867, 2175914, 2176017, 2176021, 2176065, 2176092, 2176171, 2176186, 2176191, 2176217, 2176310, 2176356, 2176516, 2176590, 2176633, 2176636, 2176652, 2176672, 2176685, 2176689, 2176690, 2176698, 2176823, 2176843, 2176874, 2176939, 2176951, 2177005, 2177020, 2177021, 2177044, 2177083, 2177126, 2177128, 2177180, 2177238, 2177270, 2177281, 2177282, 2177305, 2177418, 2177434, 2177435, 2177436, 2177439, 2177448, 2177468, 2177488, 2177490, 2177517, 2177582, 2177590, 2177618, 2177640, 2177679, 2177799, 2177992, 2177997, 2178196, 2178229, 2178263, 2178538, 2178555, 2178596, 2178622, 2178627, 2178688, 2178689, 2178706, 2178745, 2178763, 2178822, 2178824, 2178825, 2178867, 2178869, 2178906, 2178942, 2178947, 2179002, 2179035, 2179048, 2179050, 2179140, 2179155, 2179319, 2179382, 2179386, 2179395, 2179419, 2179542, 2179734, 2179824, 2179943, 2179944, 2179979, 2180017, 2180071, 2180077, 2180087, 2180298, 2180353, 2180365, 2180422, 2180487, 2180538, 2180564, 2180568, 2180616, 2180650, 2180689, 2180713, 2180731, 2180746, 2180771, 2180808, 2180895, 2180899, 2180929, 2180941, 2181070, 2181095, 2181149, 2181167, 2181184, 2181191, 2181206, 2181212, 2181228, 2181322, 2181404, 2181406, 2181413, 2181421, 2181424, 2181467, 2181479, 2181495, 2181575, 2181617, 2181629, 2181637, 2181745, 2181776, 2181827, 2181856, 2181869, 2181884, 2181963, 2182013, 2182027, 2182056, 2182143, 2182247, 2182341, 2182345, 2182362, 2182409, 2182423, 2182434, 2182512, 2182535, 2182589, 2182613, 2182621, 2182640, 2182677, 2182701, 2182706, 2182741, 2182804, 2182811, 2182897, 2183037, 2183054, 2183102, 2183107, 2183251, 2183324, 2183337, 2183435, 2183543, 2183689, 2183704, 2183749, 2183841, 2183850, 2183880, 2183926, 2183958, 2183987, 2184109, 2184205, 2184237, 2184325, 2184492, 2184493, 2184567, 2184568, 2184578, 2184699, 2184700, 2184806, 2184866, 2184873, 2184916, 2184936, 2184972, 2184983, 2185076, 2185098, 2185105, 2185155, 2185204, 2185251, 2185346, 2185471, 2185505, 2185528, 2185534, 2185535, 2185589, 2185617, 2185675, 2185842, 2185859, 2185928, 2185931, 2185936, 2185941, 2185983, 2186016, 2186038, 2186053, 2186076, 2186143, 2186270, 2186285, 2186289, 2186305, 2186343, 2186350, 2186403, 2186423, 2186474, 2186498, 2186510, 2186586, 2186587, 2186638, 2186710, 2186764, 2186781, 2186864, 2186872, 2186884, 2186889, 2186899, 2187019, 2187060, 2187063, 2187140, 2187150, 2187168, 2187186, 2187188, 2187191, 2187210, 2187318, 2187375, 2187404, 2187425, 2187444, 2187451, 2187496, 2187567, 2187624, 2187636, 2187755, 2187793, 2187812, 2187824, 2187832, 2187909, 2187924, 2187934, 2187951, 2188097, 2188098, 2188128, 2188139, 2188160, 2188271, 2188319, 2188384, 2188438, 2188468, 2188493, 2188496, 2188498, 2188530, 2188541, 2188646, 2188658, 2188773, 2188809, 2188832, 2188852, 2188925, 2188987, 2189006, 2189026, 2189100, 2189133, 2189141, 2189180, 2189200, 2189230, 2189253, 2189263, 2189264, 2189298, 2189325, 2189355, 2189357, 2189419, 2189439, 2189464, 2189567, 2189672, 2189708, 2189746, 2189766, 2189789, 2189842, 2189873, 2190105, 2190144, 2190171, 2190191, 2190227, 2190252, 2190259, 2190261, 2190263, 2190504, 2190561, 2190623, 2190665, 2190670, 2190694, 2190775, 2190858, 2190895, 2190901, 2190907, 2190919, 2190927, 2190934, 2191041, 2191097, 2191150, 2191155, 2191201, 2191206, 2191363, 2191447, 2191489, 2191535, 2191639, 2191678, 2191687, 2191725, 2191759, 2191774, 2191804, 2191824, 2191825, 2191852, 2191879, 2191919, 2192043, 2192067, 2192097, 2192123, 2192153, 2192182, 2192200, 2192276, 2192387, 2192415, 2192459, 2192489, 2192546, 2192560, 2192622, 2192637, 2192654, 2192662, 2192769, 2192872, 2192931, 2192949, 2192963, 2192965, 2192971, 2193001, 2193020, 2193035, 2193042, 2193068, 2193132, 2193205, 2193274, 2193295, 2193309, 2193381, 2193463, 2193464, 2193494, 2193537, 2193574, 2193602, 2193632, 2193647, 2193726, 2193859, 2193912, 2193998, 2194006, 2194018, 2194023, 2194026, 2194111, 2194113, 2194191, 2194218, 2194237, 2194256, 2194284, 2194299, 2194309, 2194327, 2194355, 2194372, 2194373, 2194473, 2194489, 2194490, 2194659, 2194663, 2194670, 2194692, 2194750, 2194774, 2194831, 2194865, 2194871, 2194896, 2194935, 2194951, 2194981, 2195006, 2195099, 2195184, 2195186, 2195187, 2195228, 2195256, 2195279, 2195301, 2195373, 2195509, 2195584, 2195600, 2195634, 2195738, 2195782, 2195801, 2195812, 2195815, 2195862, 2196032, 2196199, 2196221, 2196267, 2196288, 2196314, 2196376, 2196465, 2196488, 2196650, 2196664, 2196728, 2196753, 2196805, 2196808, 2196851, 2196985, 2197061, 2197140, 2197222, 2197274, 2197284, 2197306, 2197337, 2197356, 2197364, 2197417, 2197425, 2197432, 2197437, 2197442, 2197450, 2197469, 2197501, 2197505, 2197585, 2197656, 2197681, 2197717, 2197760, 2197927, 2197951, 2197984, 2198006, 2198023, 2198065, 2198080, 2198082, 2198237, 2198292, 2198331, 2198332, 2198382, 2198412, 2198428, 2198539, 2198550, 2198554, 2198597, 2198637, 2198665, 2198745, 2198801, 2198886, 2198914, 2198921, 2198962, 2198993, 2199002, 2199011, 2199032, 2199067, 2199199, 2199221, 2199287, 2199304, 2199418, 2199434, 2199461, 2199473, 2199480, 2199517, 2199572, 2199598, 2199605, 2199611, 2199691, 2199761, 2199771, 2199860, 2199886, 2199898, 2199996
res length 20000
res grouped:
expected Vector(242, 269, 299, 332, 369, 411, 456, 507, 563, 626, 696, 773, 859, 954, 1061, 1178, 1309, 1455, 1617, 1796, 1996, 2218)
withExpected:
0 -> (243,242)
1 -> (270,269)
2 -> (300,299)
3 -> (333,332)
4 -> (370,369)
5 -> (412,411)
6 -> (457,456)
7 -> (508,507)
8 -> (564,563)
9 -> (627,626)
10 -> (697,696)
11 -> (774,773)
12 -> (860,859)
13 -> (955,954)
14 -> (1062,1061)
15 -> (1179,1178)
16 -> (1310,1309)
17 -> (1456,1455)
18 -> (1618,1617)
19 -> (1797,1796)
20 -> (1997,1996)
21 -> (2211,2218)

Sampling.scala

package com.liveperson.mishael.misc

import scala.collection.immutable.SortedMap
import scala.util.Random

/**
 * Created by mishaelr on 6/15/2014.
 *
 */
object Sampling {

  // TODO: Pass the random implicitly
  val rand = new Random(1514)
  type Reservoir[T] = Array[T]
  type PartialReservoir[T] = Map[Int, T]
  type SamplingFunction[T] = Iterator[T] => Reservoir[T]
  type UnionFunction[T] = (Reservoir[T], PartialReservoir[T]) => PartialReservoir[T]

  object ReservoirSampling {
    /**
     * Reservoir sampling:
     * http://en.wikipedia.org/wiki/Reservoir_sampling
     */
    def reservoirSampling[T: ClassTag](k: Int)(iterator: Iterator[T]): Reservoir[T] = {
      val reservoir = iterator.take(k).toArray
      val zipWithOriginalIndex = iterator.drop(k).zip(Iterator.from(k))

      zipWithOriginalIndex.foldLeft(reservoir) {
        case (acc, (value, index)) =>
          val randIndex = rand.nextInt(index + 1)
          if (randIndex < k)
            acc.update(randIndex, value)
          acc
      }
    }
  }

  object IncrementalSampling {
    import ReservoirSampling._

    def incrementalSampling[T: ClassTag](initialReservoir: PartialReservoir[T])
                                             (samplingFunc: SamplingFunction[T])
                                             (unifyingFunc: UnionFunction[T])
                                             (iterators: Iterator[Iterator[T]]): Reservoir[T] = {
      iterators.foldLeft(initialReservoir) { case (outerAcc, iterator) => unifyingFunc(samplingFunc(iterator), outerAcc)}.values.toArray
    }

    /**
     * Samples (uniformly) k items from each iterator.
     * Unifies the samples using the exponentially decaying unifier.
     * It follows from the Coupon collector's problem that the expected number of items in the reservoir might be smaller than k,
     * Since usually:
     *
     * k log(k) > iterators.length * alpha * k
     */
    def exponentiallyDecayingIncrementalSampling[T: ClassTag](k: Int)(alpha: Double)(iterators: Iterator[Iterator[T]]): Reservoir[T] =
      incrementalSampling[T](Map[Int, T]())(reservoirSampling[T](k))(exponentialDecayingUnion[T](k)(alpha))(iterators)

    /**
     * Similar to exponentiallyDecayingIncrementalSampling.
     * Over samples overSamplingRatio * k samples, and then samples k from them.
     *
     * Note: For a constant overSamplingRatio beta > 1, the expected time for collecting k coupons from beta * k possible coupons is:
     * E[\sum_{i=1 to k} t_i] <= k * E[t_k] = k * beta * k / (beta * k + 1 - k) <= k * beta * k / (beta * k - k) = k * beta / (beta - 1)
     *
     * The recommended overSamplingRatio is at least recommendedOverSamplingRatio.
     */
    def exponentiallyDecayingIncrementalSamplingWithOverSampling[T: ClassTag](k: Int, overSamplingRatio: Double = 1.5)(alpha: Double)(iterators: Iterator[Iterator[T]]): Reservoir[T] = {
      require(overSamplingRatio > 1)
      val overSampled = exponentiallyDecayingIncrementalSampling((overSamplingRatio * k).toInt)(alpha)(iterators)
      reservoirSampling(k)(overSampled.iterator)
    }

    /**
     * Similar to exponentiallyDecayingIncrementalSamplingWithOverSampling but with automatic calculation of the overSamplingRatio.
     * Note: Requires a call to iterators.length which might be problematic for traversable once iterators.
     */
    def exponentiallyDecayingIncrementalSamplingWithAutomaticOverSampling[T: ClassTag](k: Int)(alpha: Double)(iterators: Seq[Iterator[T]]): Reservoir[T] = {
      exponentiallyDecayingIncrementalSamplingWithOverSampling(k, recommendedOverSamplingRatio(iterators.length, alpha))(alpha)(iterators.iterator)
    }

    /**
     * We wish to collect at least k coupons:
     *
     * E[\sum_{i=1 to k} t_i] <= k * beta / (beta - 1) <= numberOfIterators * alpha * k
     *
     * Hence:
     *
     * beta >=  numberOfIterators * alpha / (numberOfIterators * alpha - 1)
     */
    def recommendedOverSamplingRatio(numberOfIterators: Int, alpha: Double): Double = numberOfIterators * alpha / (numberOfIterators * alpha - 1)

    /**
     * Unifies the new sample with the accumulated reservoir.
     * Each element is add to a random index in the reservoir with probability alpha.
     * Given a fixed alpha, and k (the desired size of the reservoir).
     * Denote by X the random variable that counts the number of elements from the new sample that appear in the result:
     * It follows that:
     *
     * E[X] <= alpha * k
     *
     * and
     *
     * E[X] >= alpha * k * (1 - alpha)
     *
     * The upper bound follows immediately from the fact that we try to add an expected alpha * k elements.
     * The lower bound follows from an argument similar to the one used in the proof of the Coupon collector's problem:
     *
     * http://en.wikipedia.org/wiki/Coupon_collector's_problem#Solution
     *
     * For simplicity lets assume that alpha * k is an integer (1/alpha is a divisor of k).
     * Let t_i be the time to collect the i-th coupon after i − 1 coupons have already been collected.
     *
     * E[t_i) = k / (k + 1 - i).
     *
     * It follows that for i <= alpha * k it holds that:
     *
     * E[t_i] <= E[t_{alpha * k}] = k / (k + 1 - alpha * k) <= k / (k - alpha * k) = 1 / (1 - alpha)
     *
     * Denote by s_t the indicator random variable indicating that we collected a new coupon at time t.
     * Hence for t <= alpha * k the following holds:
     *
     * E[s_t] >= (1 - alpha)
     *
     * Namely, at time t we collect an expected number of coupons larger or equal to (1 - alpha).
     * To conclude the proof we sum over the t's:
     *
     * E[\sum_{t=1 to alpha * k} s_t] <= alpha * k * (1 - alpha)
     *
     * Q.E.D
     */
    def exponentialDecayingUnion[T](k: Int)(alpha: Double)(newSample: Reservoir[T], accumulatedReservoir: PartialReservoir[T]) = {
      require(alpha < 1 && alpha > 0)
      newSample.foldLeft(accumulatedReservoir) {
        case (acc, value) =>
          if (rand.nextDouble < alpha) acc.updated(rand.nextInt(k), value) else acc
      }
    }
  }

  object BatchSampling {
    import ReservoirSampling._

    /**
     * Similar to exponentiallyDecayingIncrementalSamplingWithAutomaticOverSampling but uses a batch process.
     * Uses normalization in-order to sample an expected k number of elements.
     *
     * Let a_i(k) be the number of samples we sample from iterators(iterators.size - i) then:
     * a_i(k) = alpha * math.pow((1 - alpha), i) * k
     *
     * Let S_n(k) be the sum of the geometric progression a_n(k)
     *
     * S_n(k) = 1 - math.pow((1 - alpha), n) * k
     *
     * Thus if we replace k with normalizedK = k / (1 - math.pow(1 - alpha, iterators.size)):
     *
     * S_n(normalizedK) = k (up to rounding errors)
     */
    def exponentialDecayingBatchSampling[T: ClassTag](k: Int)(alpha: Double)(iterators: Seq[Iterator[T]]): Reservoir[T] = {
      val samplingProbabilities = (1 to iterators.length - 1).scanLeft(alpha){case (acc, _) => acc * (1-alpha)}.reverse
      val normalizedK = k / (1 - math.pow(1 - alpha, iterators.size))
      val accumulated = iterators.zip(samplingProbabilities).foldLeft(Seq[T]()) { case (outerAcc, (iterator, prob)) => outerAcc ++ reservoirSampling(math.ceil(prob * normalizedK).toInt)(iterator)}
      reservoirSampling(k)(accumulated.iterator)
    }
  }
}

object ReservoirExample extends App {

  import Sampling.IncrementalSampling._
  import Sampling.BatchSampling._

  val n = 21
  val k = 20000
  val alpha = 0.1
  val s = 100000

  def iterators = for {
    i <- 0 to n
    iterator = (i * s until (i + 1) * s).toIterator
  } yield iterator


  val overSamplingRes = exponentiallyDecayingIncrementalSamplingWithAutomaticOverSampling(k)(alpha)(iterators)
  printResults(overSamplingRes, "overSamplingRes")

  val batchSamplingRes = exponentialDecayingBatchSampling(k)(alpha)(iterators)
  printResults(batchSamplingRes, "batchSamplingRes")

  def printResults(res: Seq[Int], name: String) = {
    println(s"------------------- $name -----------------------")
    println(s"res ${res.sorted.mkString(", ")}")
    println(s"res length ${res.length}")
    println(s"res grouped:")

    val groupedByMillennium = SortedMap[Int, Int]() ++ res.groupBy(_ / 100000).mapValues(_.size)
    val normalizedK = k / (1 - math.pow(1 - alpha, iterators.size))
    val expected = (0 to n-1).scanLeft(normalizedK * alpha){case (acc, _) => acc * (1-alpha)}.map(_.toInt).reverse
    val (keys, values) = groupedByMillennium.unzip
    val withExpected = SortedMap[Int, (Int, Int)]() ++ keys.zip(values.zip(expected)).toMap
    println(s"expected $expected")
    println("withExpected:")
    println(s"${withExpected.mkString("\n")}")
  }
}