FilesExpand file tree

master

/

integer_partition.py

Copy path

Blame

More file actions

Blame

More file actions

Latest commit

 

History

History

History

45 lines (38 loc) · 1.06 KB

master

/

integer_partition.py

Copy path

Top

File metadata and controls

• Code
• Blame

45 lines (38 loc) · 1.06 KB

Raw

Copy raw file

Download raw file

Open symbols panel

Edit and raw actions

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

from __future__ import print_function

try:

xrange #Python 2

except NameError:

xrange = range #Python 3

try:

raw_input #Python 2

except NameError:

raw_input = input #Python 3

'''

The number of partitions of a number n into at least k parts equals the number of partitions into exactly k parts

plus the number of partitions into at least k-1 parts. Subtracting 1 from each part of a partition of n into k parts

gives a partition of n-k into k parts. These two facts together are used for this algorithm.

'''

def partition(m):

memo = [[0 for _ in xrange(m)] for _ in xrange(m+1)]

for i in xrange(m+1):

memo[i][0] = 1

for n in xrange(m+1):

for k in xrange(1, m):

memo[n][k] += memo[n][k-1]

if n-k > 0:

memo[n][k] += memo[n-k-1][k]

return memo[m][m-1]

if __name__ == '__main__':

import sys

if len(sys.argv) == 1:

try:

n = int(raw_input('Enter a number: '))

print(partition(n))

except ValueError:

print('Please enter a number.')

else:

try:

n = int(sys.argv[1])

print(partition(n))

except ValueError:

print('Please pass a number.')