Edit:正如评论中所讨论的，为了解决更新中提到的问题，我们可以使用dense_rank将student_id每次转换为广义序列id，执行步骤1到3（使用student列），然后使用join进行转换student在每一个time回到他们原来的样子学生卡。见下文Step-0 and Step-4。如果一个 timeUnit 中的教授少于 4 名，则 Numpy 端的维度将调整为 4（使用 np_vstack() 和 np_zeros()），请参阅更新后的函数find_assigned.
你可以试试pandas_udf http://spark.apache.org/docs/latest/api/python/pyspark.sql.html#pyspark.sql.GroupedData.apply and scipy.optimize.线性总和分配 https://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.optimize.linear_sum_assignment.html（注意：后端方法是匈牙利算法，如@cronoik在主要评论中），见下文：
from pyspark.sql.functions import pandas_udf, PandasUDFType, first, expr, dense_rank
from pyspark.sql.types import StructType
from scipy.optimize import linear_sum_assignment
from pyspark.sql import Window
import numpy as np
df = spark.createDataFrame([
('1596048041', 'p1', 's1', 0.7), ('1596048041', 'p1', 's2', 0.5), ('1596048041', 'p1', 's3', 0.3),
('1596048041', 'p1', 's4', 0.2), ('1596048041', 'p2', 's1', 0.9), ('1596048041', 'p2', 's2', 0.1),
('1596048041', 'p2', 's3', 0.15), ('1596048041', 'p2', 's4', 0.2), ('1596048041', 'p3', 's1', 0.2),
('1596048041', 'p3', 's2', 0.3), ('1596048041', 'p3', 's3', 0.4), ('1596048041', 'p3', 's4', 0.8),
('1596048041', 'p4', 's1', 0.2), ('1596048041', 'p4', 's2', 0.3), ('1596048041', 'p4', 's3', 0.35),
('1596048041', 'p4', 's4', 0.4)
] , ['time', 'professor_id', 'student_id', 'score'])
N = 4
cols_student = [*range(1,N+1)]
Step-0:添加额外的列student，并使用所有独特的组合创建一个新的数据框 df3time + student_id + student.
w1 = Window.partitionBy('time').orderBy('student_id')
df = df.withColumn('student', dense_rank().over(w1))
+----------+------------+----------+-----+-------+
| time|professor_id|student_id|score|student|
+----------+------------+----------+-----+-------+
|1596048041| p1| s1| 0.7| 1|
|1596048041| p2| s1| 0.9| 1|
|1596048041| p3| s1| 0.2| 1|
|1596048041| p4| s1| 0.2| 1|
|1596048041| p1| s2| 0.5| 2|
|1596048041| p2| s2| 0.1| 2|
|1596048041| p3| s2| 0.3| 2|
|1596048041| p4| s2| 0.3| 2|
|1596048041| p1| s3| 0.3| 3|
|1596048041| p2| s3| 0.15| 3|
|1596048041| p3| s3| 0.4| 3|
|1596048041| p4| s3| 0.35| 3|
|1596048041| p1| s4| 0.2| 4|
|1596048041| p2| s4| 0.2| 4|
|1596048041| p3| s4| 0.8| 4|
|1596048041| p4| s4| 0.4| 4|
+----------+------------+----------+-----+-------+
df3 = df.select('time','student_id','student').dropDuplicates()
+----------+----------+-------+
| time|student_id|student|
+----------+----------+-------+
|1596048041| s1| 1|
|1596048041| s2| 2|
|1596048041| s3| 3|
|1596048041| s4| 4|
+----------+----------+-------+
Step-1:使用pivot来找到教授与学生的矩阵，注意我们将分数的负数设置为pivot的值，以便我们可以使用scipy.optimize.linear_sum_assignment来找到作业问题的最小成本：
df1 = df.groupby('time','professor_id').pivot('student', cols_student).agg(-first('score'))
+----------+------------+----+----+-----+----+
| time|professor_id| 1| 2| 3| 4|
+----------+------------+----+----+-----+----+
|1596048041| p4|-0.2|-0.3|-0.35|-0.4|
|1596048041| p2|-0.9|-0.1|-0.15|-0.2|
|1596048041| p1|-0.7|-0.5| -0.3|-0.2|
|1596048041| p3|-0.2|-0.3| -0.4|-0.8|
+----------+------------+----+----+-----+----+
Step-2:使用 pandas_udf 和 scipy.optimize.linear_sum_assignment 获取列索引，然后将相应的列名称分配给新列assigned:
# returnSchema contains one more StringType column `assigned` than schema from the input pdf:
schema = StructType.fromJson(df1.schema.jsonValue()).add('assigned', 'string')
# since the # of students are always N, we can use np.vstack to set the N*N matrix
# below `n` is the number of professors/rows in pdf
# sz is the size of input Matrix, sz=4 in this example
def __find_assigned(pdf, sz):
cols = pdf.columns[2:]
n = pdf.shape[0]
n1 = pdf.iloc[:,2:].fillna(0).values
_, idx = linear_sum_assignment(np.vstack((n1,np.zeros((sz-n,sz)))))
return pdf.assign(assigned=[cols[i] for i in idx][:n])
find_assigned = pandas_udf(lambda x: __find_assigned(x,N), schema, PandasUDFType.GROUPED_MAP)
df2 = df1.groupby('time').apply(find_assigned)
+----------+------------+----+----+-----+----+--------+
| time|professor_id| 1| 2| 3| 4|assigned|
+----------+------------+----+----+-----+----+--------+
|1596048041| p4|-0.2|-0.3|-0.35|-0.4| 3|
|1596048041| p2|-0.9|-0.1|-0.15|-0.2| 1|
|1596048041| p1|-0.7|-0.5| -0.3|-0.2| 2|
|1596048041| p3|-0.2|-0.3| -0.4|-0.8| 4|
+----------+------------+----+----+-----+----+--------+
Note:根据建议@OluwafemiSule，我们可以使用参数maximize而不是否定分数值。该参数可用SciPy 1.4.0+ https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linear_sum_assignment.html:
_, idx = linear_sum_assignment(np.vstack((n1,np.zeros((N-n,N)))), maximize=True)
Step-3:使用 SparkSQLstack https://spark.apache.org/docs/latest/api/sql/index.html#stack函数对上述 df2 进行归一化，对分数值取反并过滤分数为 NULL 的行。所需is_match列应该有assigned==student:
df_new = df2.selectExpr(
'time',
'professor_id',
'assigned',
'stack({},{}) as (student, score)'.format(len(cols_student), ','.join("int('{0}'), -`{0}`".format(c) for c in cols_student))
) \
.filter("score is not NULL") \
.withColumn('is_match', expr("assigned=student"))
df_new.show()
+----------+------------+--------+-------+-----+--------+
| time|professor_id|assigned|student|score|is_match|
+----------+------------+--------+-------+-----+--------+
|1596048041| p4| 3| 1| 0.2| false|
|1596048041| p4| 3| 2| 0.3| false|
|1596048041| p4| 3| 3| 0.35| true|
|1596048041| p4| 3| 4| 0.4| false|
|1596048041| p2| 1| 1| 0.9| true|
|1596048041| p2| 1| 2| 0.1| false|
|1596048041| p2| 1| 3| 0.15| false|
|1596048041| p2| 1| 4| 0.2| false|
|1596048041| p1| 2| 1| 0.7| false|
|1596048041| p1| 2| 2| 0.5| true|
|1596048041| p1| 2| 3| 0.3| false|
|1596048041| p1| 2| 4| 0.2| false|
|1596048041| p3| 4| 1| 0.2| false|
|1596048041| p3| 4| 2| 0.3| false|
|1596048041| p3| 4| 3| 0.4| false|
|1596048041| p3| 4| 4| 0.8| true|
+----------+------------+--------+-------+-----+--------+
Step-4:使用 join 将student转换回student_id（如果可能，请使用广播连接）：
df_new = df_new.join(df3, on=["time", "student"])
+----------+-------+------------+--------+-----+--------+----------+
| time|student|professor_id|assigned|score|is_match|student_id|
+----------+-------+------------+--------+-----+--------+----------+
|1596048041| 1| p1| 2| 0.7| false| s1|
|1596048041| 2| p1| 2| 0.5| true| s2|
|1596048041| 3| p1| 2| 0.3| false| s3|
|1596048041| 4| p1| 2| 0.2| false| s4|
|1596048041| 1| p2| 1| 0.9| true| s1|
|1596048041| 2| p2| 1| 0.1| false| s2|
|1596048041| 3| p2| 1| 0.15| false| s3|
|1596048041| 4| p2| 1| 0.2| false| s4|
|1596048041| 1| p3| 4| 0.2| false| s1|
|1596048041| 2| p3| 4| 0.3| false| s2|
|1596048041| 3| p3| 4| 0.4| false| s3|
|1596048041| 4| p3| 4| 0.8| true| s4|
|1596048041| 1| p4| 3| 0.2| false| s1|
|1596048041| 2| p4| 3| 0.3| false| s2|
|1596048041| 3| p4| 3| 0.35| true| s3|
|1596048041| 4| p4| 3| 0.4| false| s4|
+----------+-------+------------+--------+-----+--------+----------+
df_new = df_new.drop("student", "assigned")
