mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-25 04:30:15 +00:00
55 lines
1.0 KiB
Python
55 lines
1.0 KiB
Python
"""
|
|
Counting Summations
|
|
Problem 76
|
|
|
|
It is possible to write five as a sum in exactly six different ways:
|
|
|
|
4 + 1
|
|
3 + 2
|
|
3 + 1 + 1
|
|
2 + 2 + 1
|
|
2 + 1 + 1 + 1
|
|
1 + 1 + 1 + 1 + 1
|
|
|
|
How many different ways can one hundred be written as a sum of at least two
|
|
positive integers?
|
|
"""
|
|
|
|
|
|
def partition(m):
|
|
"""Returns the number of different ways one hundred can be written as a sum
|
|
of at least two positive integers.
|
|
|
|
>>> partition(100)
|
|
190569291
|
|
>>> partition(50)
|
|
204225
|
|
>>> partition(30)
|
|
5603
|
|
>>> partition(10)
|
|
41
|
|
>>> partition(5)
|
|
6
|
|
>>> partition(3)
|
|
2
|
|
>>> partition(2)
|
|
1
|
|
>>> partition(1)
|
|
0
|
|
"""
|
|
memo = [[0 for _ in range(m)] for _ in range(m + 1)]
|
|
for i in range(m + 1):
|
|
memo[i][0] = 1
|
|
|
|
for n in range(m + 1):
|
|
for k in range(1, m):
|
|
memo[n][k] += memo[n][k - 1]
|
|
if n > k:
|
|
memo[n][k] += memo[n - k - 1][k]
|
|
|
|
return memo[m][m - 1] - 1
|
|
|
|
|
|
if __name__ == "__main__":
|
|
print(partition(int(str(input()).strip())))
|