Possible Selections With Repetition.
Imagine being given the opportunity to pick six (6) exercise books
from a book-shop having 10 different brands of exercise books -
Ben 10, Chelsea F.C., Superman, Tottenham F.C.,
Indomitables, Manchester City F.C., Spider Man,
Power Rangers, Liverpool F.C. and Bat Man exercise books.
If you happen to be a big Power Rangers fan, nothing stops you from
selecting all 6 exercise books to be Power Rangers exercise books.
But you can as well decide to pick only 3 Power Rangers exercise books
and make up for the other 3 with any other brands of exercise book.
Code for Repetitive Selection in Python
The algorithm for Selection with Repetition will be a lot similar
to that of combination.
-
Beginning with the first member in the mother set, match it separately with
every member - including itself - until the required Selection group-size (r)
is reached.
-
When every possible Selection with this member is exhausted,
move to the next member in the mother set and repeat Step I.
This is how our Repetitive Selection code in Python will work.
Create a new module file;
Call it Selection.py
.
Type out the adjoining Python code for Selection with Repetition.
Python code for Selection.py Module
class Choice:
def __init__(self):
self.i = 0
def groupSelection(self, candidates, size):
self.words = candidates
self.r = size
self.complete_group = []
self.i = 0
self.recursiveFillUp([])
return self.complete_group
def recursiveFillUp(self, temp):
picked_elements = [[] for k in range(len(self.words))]
j = self.i
while j < len(self.words):
picked_elements[j].extend(temp)
picked_elements[j].append(self.words[j])
if self.i >= len(self.words):
self.i = j
if len(picked_elements[j]) == self.r:
self.complete_group.append(picked_elements[j])
elif len(picked_elements[j]) < self.r:
self.recursiveFillUp(picked_elements[j])
j += 1
j -= 1
if picked_elements[j] != None and len(picked_elements[j]) == self.r:
self.i += 1
Main Class
from Selection import Choice
goods = ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9"]
pick = Choice()
result = pick.groupSelection(goods, 6)
print("\n", pick.words, " selection ", pick.r, ":\n")
i = 0
for group in result:
i += 1
print(i, ": ", group)
print("\n\nNumber of ways is ", len(result), ".\n")