明天,咱们将探讨如何在 Python 的 Pandas 库中创立 GroupBy 对象以及该对象的工作原理。咱们将具体理解分组过程的每个步骤,能够将哪些办法利用于 GroupBy 对象上,以及咱们能够从中提取哪些有用信息
不要再张望了,一起学起来吧
应用 Groupby 三个步骤
首先文末要晓得,任何 groupby 过程都波及以下 3 个步骤的某种组合:
- 依据定义的规范将原始对象分成组
- 对每个组利用某些函数
- 整合后果
让我先来大抵浏览下明天用到的测试数据集
import pandas as pd
import numpy as np
pd.set_option('max_columns', None)
df = pd.read_csv('complete.csv')
df = df[['awardYear', 'category', 'prizeAmount', 'prizeAmountAdjusted', 'name', 'gender', 'birth_continent']]
df.head()
Output:
awardYear category prizeAmount prizeAmountAdjusted name gender birth_continent
0 2001 Economic Sciences 10000000 12295082 A. Michael Spence male North America
1 1975 Physics 630000 3404179 Aage N. Bohr male Europe
2 2004 Chemistry 10000000 11762861 Aaron Ciechanover male Asia
3 1982 Chemistry 1150000 3102518 Aaron Klug male Europe
4 1979 Physics 800000 2988048 Abdus Salam male Asia
将原始对象拆分为组
在这个阶段,咱们调用 pandas DataFrame.groupby() 函数。咱们应用它依据预约义的规范将数据分组,沿行(默认状况下,axis=0)或列(axis=1)。换句话说,此函数将标签映射到组的名称。
例如,在咱们的案例中,咱们能够按奖项类别对诺贝尔奖的数据进行分组:
grouped = df.groupby('category')
也能够应用多个列来执行数据分组,传递一个列列表即可。让咱们首先按奖项类别对咱们的数据进行分组,而后在每个创立的组中,咱们将依据获奖年份利用额定的分组:
grouped_category_year = df.groupby(['category', 'awardYear'])
当初,如果咱们尝试打印刚刚创立的两个 GroupBy 对象之一,咱们实际上将看不到任何组:
print(grouped)
Output:
<pandas.core.groupby.generic.DataFrameGroupBy object at 0x0000026083789DF0>
咱们要留神的是,创立 GroupBy 对象胜利与否,只查看咱们是否通过了正确的映射;在咱们显式地对该对象应用某些办法或提取其某些属性之前,都不会真正执行拆分 - 利用 - 组合链的任何操作
为了简要查看生成的 GroupBy 对象并检查组的拆分形式,咱们能够从中提取组或索引属性。它们都返回一个字典,其中键是创立的组,值是原始 DataFrame 中每个组的实例的轴标签列表(对于组属性)或索引(对于索引属性):
grouped.indices
Output:
{'Chemistry': array([ 2, 3, 7, 9, 10, 11, 13, 14, 15, 17, 19, 39, 62,
64, 66, 71, 75, 80, 81, 86, 92, 104, 107, 112, 129, 135,
153, 169, 175, 178, 181, 188, 197, 199, 203, 210, 215, 223, 227,
239, 247, 249, 258, 264, 265, 268, 272, 274, 280, 282, 284, 289,
296, 298, 310, 311, 317, 318, 337, 341, 343, 348, 352, 357, 362,
365, 366, 372, 374, 384, 394, 395, 396, 415, 416, 419, 434, 440,
442, 444, 446, 448, 450, 455, 456, 459, 461, 463, 465, 469, 475,
504, 505, 508, 518, 522, 523, 524, 539, 549, 558, 559, 563, 567,
571, 572, 585, 591, 596, 599, 627, 630, 632, 641, 643, 644, 648,
659, 661, 666, 667, 668, 671, 673, 679, 681, 686, 713, 715, 717,
719, 720, 722, 723, 725, 726, 729, 732, 738, 742, 744, 746, 751,
756, 759, 763, 766, 773, 776, 798, 810, 813, 814, 817, 827, 828,
829, 832, 839, 848, 853, 855, 862, 866, 880, 885, 886, 888, 889,
892, 894, 897, 902, 904, 914, 915, 920, 921, 922, 940, 941, 943,
946, 947], dtype=int64),
'Economic Sciences': array([ 0, 5, 45, 46, 58, 90, 96, 139, 140, 145, 152, 156, 157,
180, 187, 193, 207, 219, 231, 232, 246, 250, 269, 279, 283, 295,
305, 324, 346, 369, 418, 422, 425, 426, 430, 432, 438, 458, 467,
476, 485, 510, 525, 527, 537, 538, 546, 580, 594, 595, 605, 611,
636, 637, 657, 669, 670, 678, 700, 708, 716, 724, 734, 737, 739,
745, 747, 749, 750, 753, 758, 767, 800, 805, 854, 856, 860, 864,
871, 882, 896, 912, 916, 924], dtype=int64),
'Literature': array([ 21, 31, 40, 49, 52, 98, 100, 101, 102, 111, 115, 142, 149,
159, 170, 177, 201, 202, 220, 221, 233, 235, 237, 253, 257, 259,
275, 277, 278, 286, 312, 315, 316, 321, 326, 333, 345, 347, 350,
355, 359, 364, 370, 373, 385, 397, 400, 403, 406, 411, 435, 439,
441, 454, 468, 479, 480, 482, 483, 492, 501, 506, 511, 516, 556,
569, 581, 602, 604, 606, 613, 614, 618, 631, 633, 635, 640, 652,
653, 655, 656, 665, 675, 683, 699, 761, 765, 771, 774, 777, 779,
780, 784, 786, 788, 796, 799, 803, 836, 840, 842, 850, 861, 867,
868, 878, 881, 883, 910, 917, 919, 927, 928, 929, 930, 936],
dtype=int64),
'Peace': array([ 6, 12, 16, 25, 26, 27, 34, 36, 44, 47, 48, 54, 61,
65, 72, 78, 79, 82, 95, 99, 116, 119, 120, 126, 137, 146,
151, 166, 167, 171, 200, 204, 205, 206, 209, 213, 225, 236, 240,
244, 255, 260, 266, 267, 270, 287, 303, 320, 329, 356, 360, 361,
377, 386, 387, 388, 389, 390, 391, 392, 393, 433, 447, 449, 471,
477, 481, 489, 491, 500, 512, 514, 517, 528, 529, 530, 533, 534,
540, 542, 544, 545, 547, 553, 555, 560, 562, 574, 578, 590, 593,
603, 607, 608, 609, 612, 615, 616, 617, 619, 620, 628, 634, 639,
642, 664, 677, 688, 697, 703, 705, 710, 727, 736, 787, 793, 795,
806, 823, 846, 847, 852, 865, 875, 876, 877, 895, 926, 934, 935,
937, 944, 948, 949], dtype=int64),
'Physics': array([ 1, 4, 8, 20, 23, 24, 30, 32, 38, 51, 59, 60, 67,
68, 69, 70, 74, 84, 89, 97, 103, 105, 108, 109, 114, 117,
118, 122, 125, 127, 128, 130, 133, 141, 143, 144, 155, 162, 163,
164, 165, 168, 173, 174, 176, 179, 183, 195, 212, 214, 216, 222,
224, 228, 230, 234, 238, 241, 243, 251, 256, 263, 271, 276, 291,
292, 297, 301, 306, 307, 308, 323, 327, 328, 330, 335, 336, 338,
349, 351, 353, 354, 363, 367, 375, 376, 378, 381, 382, 398, 399,
402, 404, 405, 408, 410, 412, 413, 420, 421, 424, 428, 429, 436,
445, 451, 453, 457, 460, 462, 470, 472, 487, 495, 498, 499, 509,
513, 515, 521, 526, 532, 535, 536, 541, 548, 550, 552, 557, 561,
564, 565, 566, 573, 576, 577, 579, 583, 586, 588, 592, 601, 610,
621, 622, 623, 629, 647, 650, 651, 654, 658, 674, 676, 682, 684,
690, 691, 693, 694, 695, 696, 698, 702, 707, 711, 714, 721, 730,
731, 735, 743, 752, 755, 770, 772, 775, 781, 785, 790, 792, 797,
801, 802, 808, 822, 833, 834, 835, 844, 851, 870, 872, 879, 884,
887, 890, 893, 900, 901, 903, 905, 907, 908, 909, 913, 925, 931,
932, 933, 938, 942, 945], dtype=int64),
'Physiology or Medicine': array([ 18, 22, 28, 29, 33, 35, 37, 41, 42, 43, 50, 53, 55,
56, 57, 63, 73, 76, 77, 83, 85, 87, 88, 91, 93, 94,
106, 110, 113, 121, 123, 124, 131, 132, 134, 136, 138, 147, 148,
150, 154, 158, 160, 161, 172, 182, 184, 185, 186, 189, 190, 191,
192, 194, 196, 198, 208, 211, 217, 218, 226, 229, 242, 245, 248,
252, 254, 261, 262, 273, 281, 285, 288, 290, 293, 294, 299, 300,
302, 304, 309, 313, 314, 319, 322, 325, 331, 332, 334, 339, 340,
342, 344, 358, 368, 371, 379, 380, 383, 401, 407, 409, 414, 417,
423, 427, 431, 437, 443, 452, 464, 466, 473, 474, 478, 484, 486,
488, 490, 493, 494, 496, 497, 502, 503, 507, 519, 520, 531, 543,
551, 554, 568, 570, 575, 582, 584, 587, 589, 597, 598, 600, 624,
625, 626, 638, 645, 646, 649, 660, 662, 663, 672, 680, 685, 687,
689, 692, 701, 704, 706, 709, 712, 718, 728, 733, 740, 741, 748,
754, 757, 760, 762, 764, 768, 769, 778, 782, 783, 789, 791, 794,
804, 807, 809, 811, 812, 815, 816, 818, 819, 820, 821, 824, 825,
826, 830, 831, 837, 838, 841, 843, 845, 849, 857, 858, 859, 863,
869, 873, 874, 891, 898, 899, 906, 911, 918, 923, 939], dtype=int64)}
要查找 GroupBy 对象中的组数,咱们能够从中提取 ngroups 属性或调用 Python 规范库的 len 函数:
print(grouped.ngroups)
print(len(grouped))
Output:
6
6
如果咱们须要可视化每个组的所有或局部条目,那么能够遍历 GroupBy 对象:
for name, entries in grouped:
print(f'First 2 entries for the"{name}"category:')
print(30*'-')
print(entries.head(2), '\n\n')
Output:
First 2 entries for the "Chemistry" category:
------------------------------
awardYear category prizeAmount prizeAmountAdjusted name \
2 2004 Chemistry 10000000 11762861 Aaron Ciechanover
3 1982 Chemistry 1150000 3102518 Aaron Klug
gender birth_continent
2 male Asia
3 male Europe
First 2 entries for the "Economic Sciences" category:
------------------------------
awardYear category prizeAmount prizeAmountAdjusted \
0 2001 Economic Sciences 10000000 12295082
5 2019 Economic Sciences 9000000 9000000
name gender birth_continent
0 A. Michael Spence male North America
5 Abhijit Banerjee male Asia
First 2 entries for the "Literature" category:
------------------------------
awardYear category prizeAmount prizeAmountAdjusted \
21 1957 Literature 208629 2697789
31 1970 Literature 400000 3177966
name gender birth_continent
21 Albert Camus male Africa
31 Alexandr Solzhenitsyn male Europe
First 2 entries for the "Peace" category:
------------------------------
awardYear category prizeAmount prizeAmountAdjusted \
6 2019 Peace 9000000 9000000
12 1980 Peace 880000 2889667
name gender birth_continent
6 Abiy Ahmed Ali male Africa
12 Adolfo Pérez Esquivel male South America
First 2 entries for the "Physics" category:
------------------------------
awardYear category prizeAmount prizeAmountAdjusted name gender \
1 1975 Physics 630000 3404179 Aage N. Bohr male
4 1979 Physics 800000 2988048 Abdus Salam male
birth_continent
1 Europe
4 Asia
First 2 entries for the "Physiology or Medicine" category:
------------------------------
awardYear category prizeAmount prizeAmountAdjusted \
18 1963 Physiology or Medicine 265000 2839286
22 1974 Physiology or Medicine 550000 3263449
name gender birth_continent
18 Alan Hodgkin male Europe
22 Albert Claude male Europe
相同,如果咱们想以 DataFrame 的模式抉择单个组,咱们应该在 GroupBy 对象上应用 get_group()
办法:
grouped.get_group('Economic Sciences')
Output:
awardYear category prizeAmount prizeAmountAdjusted name gender birth_continent
0 2001 Economic Sciences 10000000 12295082 A. Michael Spence male North America
5 2019 Economic Sciences 9000000 9000000 Abhijit Banerjee male Asia
45 2012 Economic Sciences 8000000 8361204 Alvin E. Roth male North America
46 1998 Economic Sciences 7600000 9713701 Amartya Sen male Asia
58 2015 Economic Sciences 8000000 8384572 Angus Deaton male Europe
… … … … … … … …
882 2002 Economic Sciences 10000000 12034660 Vernon L. Smith male North America
896 1973 Economic Sciences 510000 3331882 Wassily Leontief male Europe
912 2018 Economic Sciences 9000000 9000000 William D. Nordhaus male North America
916 1990 Economic Sciences 4000000 6329114 William F. Sharpe male North America
924 1996 Economic Sciences 7400000 9490424 William Vickrey male North America
按组利用函数
在拆分原始数据并查看后果组之后,咱们能够对每个组执行以下操作之一或其组合:
- Aggregation(聚合):计算每个组的汇总统计量(例如,组大小、平均值、中位数或总和)并为许多数据点输入单个数字
- Transformation(变换):按组进行一些操作,例如计算每个组的 z -score
- Filtration(过滤):依据预约义的条件回绝某些组,例如组大小、平均值、中位数或总和,还能够包含从每个组中过滤掉特定的行
Aggregation
要聚合 GroupBy 对象的数据(即按组计算汇总统计量),咱们能够在对象上应用 agg()
办法:
# Showing only 1 decimal for all float numbers
pd.options.display.float_format = '{:.1f}'.format
grouped.agg(np.mean)
Output:
awardYear prizeAmount prizeAmountAdjusted
category
Chemistry 1972.3 3629279.4 6257868.1
Economic Sciences 1996.1 6105845.2 7837779.2
Literature 1960.9 2493811.2 5598256.3
Peace 1964.5 3124879.2 6163906.9
Physics 1971.1 3407938.6 6086978.2
Physiology or Medicine 1970.4 3072972.9 5738300.7
下面的代码生成一个 DataFrame,其中组名作为其新索引,每个数字列的平均值作为分组
咱们能够间接在 GroupBy 对象上利用其余相应的 Pandas 办法,而不仅仅是应用 agg()
办法。最罕用的办法是 mean()
、median()
、mode()
、sum()
、size()
、count()
、min()
、max()
、std()
、var()
(计算每个的方差 group)、describe()
(按组输入描述性统计信息)和 nunique()
(给出每个组中惟一值的数量)
grouped.sum()
Output:
awardYear prizeAmount prizeAmountAdjusted
category
Chemistry 362912 667787418 1151447726
Economic Sciences 167674 512891000 658373449
Literature 227468 289282102 649397731
Peace 263248 418733807 825963521
Physics 419837 725890928 1296526352
Physiology or Medicine 431508 672981066 1256687857
通常状况下咱们只对某些特定列或列的统计信息感兴趣,因而咱们须要指定它们。在下面的例子中,咱们相对不想总结所有年份,相应的咱们可能心愿按奖品类别对奖品价值求和。为此咱们能够抉择 GroupBy 对象的 PrizeAmountAdjusted 列,就像咱们抉择 DataFrame 的列,而后对其利用 sum() 函数:
grouped['prizeAmountAdjusted'].sum()
Output:
category
Chemistry 1151447726
Economic Sciences 658373449
Literature 649397731
Peace 825963521
Physics 1296526352
Physiology or Medicine 1256687857
Name: prizeAmountAdjusted, dtype: int64
对于下面的代码片段,咱们能够在抉择必要的列之前应用对 GroupBy 对象利用函数的等效语法:grouped.sum()['prizeAmountAdjusted']
。然而后面的语法更可取,因为它的性能更好,尤其是在大型数据集上,成果更为显著
如果咱们须要聚合两列或更多列的数据,咱们应用单方括号:
grouped[['prizeAmount', 'prizeAmountAdjusted']].sum()
Output:
prizeAmount prizeAmountAdjusted
category
Chemistry 667787418 1151447726
Economic Sciences 512891000 658373449
Literature 289282102 649397731
Peace 418733807 825963521
Physics 725890928 1296526352
Physiology or Medicine 672981066 1256687857
能够一次将多个函数利用于 GroupBy 对象的一列或多列。为此咱们再次须要 agg()
办法和感兴趣的函数列表:
grouped[['prizeAmount', 'prizeAmountAdjusted']].agg([np.sum, np.mean, np.std])
Output:
prizeAmount prizeAmountAdjusted
sum mean std sum mean std
category
Chemistry 667787418 3629279.4 4070588.4 1151447726 6257868.1 3276027.2
Economic Sciences 512891000 6105845.2 3787630.1 658373449 7837779.2 3313153.2
Literature 289282102 2493811.2 3653734.0 649397731 5598256.3 3029512.1
Peace 418733807 3124879.2 3934390.9 825963521 6163906.9 3189886.1
Physics 725890928 3407938.6 4013073.0 1296526352 6086978.2 3294268.5
Physiology or Medicine 672981066 3072972.9 3898539.3 1256687857 5738300.7 3241781.0
此外,咱们能够思考通过传递字典将不同的聚合函数利用于 GroupBy 对象的不同列:
grouped.agg({'prizeAmount': [np.sum, np.size], 'prizeAmountAdjusted': np.mean})
Output:
prizeAmount prizeAmountAdjusted
sum size mean
category
Chemistry 667787418 184 6257868.1
Economic Sciences 512891000 84 7837779.2
Literature 289282102 116 5598256.3
Peace 418733807 134 6163906.9
Physics 725890928 213 6086978.2
Physiology or Medicine 672981066 219 5738300.7
Transformation
与聚合办法不同,转换方法返回一个新的 DataFrame,其形态和索引与原始 DataFrame 雷同,但具备转换后的各个值。这里须要留神的是,transformation 肯定不能批改原始 DataFrame 中的任何值,也就是这些操作不能原地执行
转换 GroupBy 对象数据的最常见的 Pandas 办法是 transform()
。例如它能够帮忙计算每个组的 z-score:
grouped[['prizeAmount', 'prizeAmountAdjusted']].transform(lambda x: (x - x.mean()) / x.std())
Output:
prizeAmount prizeAmountAdjusted
0 1.0 1.3
1 -0.7 -0.8
2 1.6 1.7
3 -0.6 -1.0
4 -0.6 -0.9
… … …
945 -0.7 -0.8
946 -0.8 -1.1
947 -0.9 0.3
948 -0.5 -1.0
949 -0.7 -1.0
应用转换方法,咱们还能够用组均值、中位数、众数或任何其余值替换缺失数据:
grouped['gender'].transform(lambda x: x.fillna(x.mode()[0]))
Output:
0 male
1 male
2 male
3 male
4 male
...
945 male
946 male
947 female
948 male
949 male
Name: gender, Length: 950, dtype: object
咱们当然还能够应用其余一些 Pandas 办法来转换 GroupBy 对象的数据:bfill()
、ffill()
、diff()
、pct_change()
、rank()
、shift()
、quantile()
等
Filtration
过滤办法依据预约义的条件从每个组中抛弃组或特定行,并返回原始数据的子集。例如咱们可能心愿只保留所有组中某个列的值,其中该列的组均值大于预约义值。在咱们的 DataFrame 的状况下,让咱们过滤掉所有组均值小于 7,000,000 的 prizeAmountAdjusted 列,并在输入中仅保留该列:
grouped['prizeAmountAdjusted'].filter(lambda x: x.mean() > 7000000)
Output:
0 12295082
5 9000000
45 8361204
46 9713701
58 8384572
...
882 12034660
896 3331882
912 9000000
916 6329114
924 9490424
Name: prizeAmountAdjusted, Length: 84, dtype: int64
另一个例子是过滤掉具备超过肯定数量元素的组:
grouped['prizeAmountAdjusted'].filter(lambda x: len(x) < 100)
Output:
0 12295082
5 9000000
45 8361204
46 9713701
58 8384572
...
882 12034660
896 3331882
912 9000000
916 6329114
924 9490424
Name: prizeAmountAdjusted, Length: 84, dtype: int64
在上述两个操作中,咱们应用了 filter()
办法,将 lambda
函数作为参数传递。这样的函数,利用于整个组,依据该组与预约义统计条件的比拟后果返回 True
或 False
。换句话说,filter()
办法中的函数决定了哪些组保留在新的 DataFrame 中
除了过滤掉整个组之外,还能够从每个组中抛弃某些行。这里有一些有用的办法是 first()
、last()
和 nth()
。将其中一个利用于 GroupBy 对象会相应地返回每个组的第一个 / 最初一个 / 第 n 个条目:
grouped.last()
Output:
awardYear prizeAmount prizeAmountAdjusted name gender birth_continent
category
Chemistry 1911 140695 7327865 Marie Curie female Europe
Economic Sciences 1996 7400000 9490424 William Vickrey male North America
Literature 1968 350000 3052326 Yasunari Kawabata male Asia
Peace 1963 265000 2839286 International Committee of the Red Cross male Asia
Physics 1972 480000 3345725 John Bardeen male North America
Physiology or Medicine 2016 8000000 8301051 Yoshinori Ohsumi male Asia
对于 nth()
办法,咱们必须传递示意要为每个组返回的条目索引的整数:
grouped.nth(1)
Output:
awardYear prizeAmount prizeAmountAdjusted name gender birth_continent
category
Chemistry 1982 1150000 3102518 Aaron Klug male Europe
Economic Sciences 2019 9000000 9000000 Abhijit Banerjee male Asia
Literature 1970 400000 3177966 Alexandr Solzhenitsyn male Europe
Peace 1980 880000 2889667 Adolfo Pérez Esquivel male South America
Physics 1979 800000 2988048 Abdus Salam male Asia
Physiology or Medicine 1974 550000 3263449 Albert Claude male Europe
下面的代码收集了所有组的第二个条目
另外两个过滤每个组中的行的办法是 head()
和 tail()
,别离返回每个组的第一 / 最初 n 行(默认为 5):
grouped.head(3)
Output:
awardYear category prizeAmount prizeAmountAdjusted name gender birth_continent
0 2001 Economic Sciences 10000000 12295082 A. Michael Spence male North America
1 1975 Physics 630000 3404179 Aage N. Bohr male Europe
2 2004 Chemistry 10000000 11762861 Aaron Ciechanover male Asia
3 1982 Chemistry 1150000 3102518 Aaron Klug male Europe
4 1979 Physics 800000 2988048 Abdus Salam male Asia
5 2019 Economic Sciences 9000000 9000000 Abhijit Banerjee male Asia
6 2019 Peace 9000000 9000000 Abiy Ahmed Ali male Africa
7 2009 Chemistry 10000000 10958504 Ada E. Yonath female Asia
8 2011 Physics 10000000 10545557 Adam G. Riess male North America
12 1980 Peace 880000 2889667 Adolfo Pérez Esquivel male South America
16 2007 Peace 10000000 11301989 Al Gore male North America
18 1963 Physiology or Medicine 265000 2839286 Alan Hodgkin male Europe
21 1957 Literature 208629 2697789 Albert Camus male Africa
22 1974 Physiology or Medicine 550000 3263449 Albert Claude male Europe
28 1937 Physiology or Medicine 158463 4716161 Albert Szent-Györgyi male Europe
31 1970 Literature 400000 3177966 Alexandr Solzhenitsyn male Europe
40 2013 Literature 8000000 8365867 Alice Munro female North America
45 2012 Economic Sciences 8000000 8361204 Alvin E. Roth male North America
整合后果
split-apply-combine 链的最初一个阶段——合并后果——由 Ppandas 在后盾执行。它包含获取在 GroupBy 对象上执行的所有操作的输入并将它们重新组合在一起,生成新的数据结构,例如 Series 或 DataFrame。将此数据结构调配给一个变量,咱们能够用它来解决其余工作
总结
明天咱们介绍了应用 pandas groupby 函数和应用后果对象的许多常识
- 分组过程所包含的步骤
- split-apply-combine 链是如何一步一步工作的
- 如何创立 GroupBy 对象
- 如何简要查看 GroupBy 对象
- GroupBy 对象的属性
- 可利用于 GroupBy 对象的操作
- 如何按组计算汇总统计量以及可用于此目标的办法
- 如何一次将多个函数利用于 GroupBy 对象的一列或多列
- 如何将不同的聚合函数利用于 GroupBy 对象的不同列
- 如何以及为什么要转换原始 DataFrame 中的值
- 如何过滤 GroupBy 对象的组或每个组的特定行
- Pandas 如何组合分组过程的后果
- 分组过程产生的数据结构
好了,这就是明天分享的全部内容,喜爱就点个赞吧~
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