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Versioning with git

Concepts

We are familiar with the concept of revision numbers in a classic source code repository: a single branch tracks a “history” for changes to the source code, each commit corresponds to an improvement in the source code, and there is a separate line for each change.

The history of each change is tracked with its own revision number, but there is no special relationship between changes and their revision number. The idea of a revision number was that it was a “best effort” for numbering changes: any number could be used, but the best effort is the one that is remembered most readily, so the revision number is the one that remembers the most changes.

Each of these concepts can be adapted for versioning.

The whole history of changes is not necessarily part of the same repository. The revision number itself could be available in a separate repository: (early-mid) revision numbers are used for versioning, and (latest) revision numbers are used to refer to the actual history.

A single change can have its own revision number. Since the actual change might still be in other revisions, the change revision can’t be used directly to uniquely identify the source code. The name of the change might uniquely identify the source code instead.

In a versioning system, you can number changes without stating a specific revision number. In the first case, you would just be creating and tracking a change. In the second case, you would just be creating a change. These are two concepts that we can apply to versioning: revision-less versioning, and revision-less coding.

In source code history, the concept of “

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Q:

For a given number X, find the largest prime factor of number X

It seems so simple but I’ve been sitting on this for a long time and I just couldn’t find a solution.

A:

The key to finding the largest prime factor of an integer is factorization theory.
We already know that for a positive integer, the prime factorization is either
$$\prod_i p_i^{a_i}$$
where the $p_i$’s are distinct primes, $a_i$ are positive integers, or
$$\prod_i p_i^n$$
where the $p_i$’s are distinct primes, $n$ is a non-negative integer.
So the prime factorization for
$$X = \prod_i p_i^{a_i}$$
clearly means that
$$a_i \ge 0$$
and
$$\sum a_i = X$$
where we define $0^0=1$ so that
$$X = 1^0 \cdot \prod_i p_i = 1 \cdot \prod_i p_i.$$
Now, as for the factorization of
$$X = \prod_i p_i^n$$
we also have that
$$n \ge 0$$
and
$$\sum n = X$$
where the sum of $n$’s includes the zero.
So, the largest prime factor is just $p_1$ and we have that
$$X = p_1^n.$$
So, we can implement the algorithm by a simple loop:

If the current value of $n$ is $0$, we’ve got the largest prime factor.
If the current value of $n$ is not $0$, and $n \ge 1$, then let $a_i$ be the current value of $i$ (starting with $0$) and decrease the value of $n$ by $1$.
If the current value of $n$ is not $0$ and $n from django
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