L10 2

from ucb import trace
#不大于m的数组成n的方法数,m,n都是正整数
@trace
def count_partitions(n, m):
    """Return the number of ways, N, that N can be expressed as the sum of 1, 2, ..., M.

    """
    # assert n>=1,"输入需要是正整数"
    # assert m>=1,"输入需要是正整数"
    # 探索两种可能性或者不可能性
    # 至少使用一个m和不使用一个m
    if n==0:
        return 1
    elif n<0:
        return 0
    elif m==0:
        return 0
    elif m==1:
        return 1
    else:
        with_m = count_partitions(n-m,m)
        without_m = count_partitions(n,m-1)
        return with_m+without_m



print(count_partitions(6,4))

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