How to Efficiently Generate Integer Partitions in Python?

Elegant Python Code for Integer Partitioning

The Integer Partition problem aims to find all possible ways to express an integer as a sum of positive integers. While solving this problem, it's beneficial to implement a clean and efficient code to improve coding style.

One approach is to use a recursive generator function, as demonstrated in the suggested solution:

<code class="python">def partitions(n, I=1):
    yield (n,)
    for i in range(I, n//2 + 1):
        for p in partitions(n-i, i):
            yield (i,) + p</code>

This solution outperforms a previous implementation by Nolen by being significantly faster and more concise, as shown in the provided timeit comparisons. However, it remains less efficient than the accel_asc function.

Other code versions can be found on ActiveState's Generator For Integer Partitions (Python Recipe).

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