In number theory and combinatorics, a partition of a positive integer N, also named an integer partition, is a manner of write N as a sum of positive integers. They happen in a number of branches of mathematics and physics, including the survey of symmetric polynomials and of the symmetric group and in group representation theory in general.
""" 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 range(m)] for _ in range(m + 1)] for i in range(m + 1): memo[i] = 1 for n in range(m + 1): for k in range(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(input("Enter a number: ").strip()) print(partition(n)) except ValueError: print("Please enter a number.") else: try: n = int(sys.argv) print(partition(n)) except ValueError: print("Please pass a number.")