# The algorithm¶

## Details¶

Every date range breaks down in the same way. Here’s an example range

```----: YYYY-MM-DD HH:MM
From: 2017-02-15 12:30
To  : 2017-02-25 04:00
```

Parsing from left to right, the first part of the range is what’s common between the two datetimes: 2017-02. In the query these common parts are ANDed together using equals signs.

```YYYY=2017 AND MM=02
```

The first unit to differ between the two datetimes is DD, with values 15 and 25. This is referred to in the code as the “bridge”. The bridge shows up in the query like this.

```(DD>15 AND DD<25)
```

The other two parts of the query are the entrance to, and exit from, the bridge. Our bridge excludes the two days on the ends, the 15th and the 25th. So the entrance and exit parts must handle them. Here’s the entrance.

```(DD=15 AND HH=12 AND MIN>=30) OR (DD=15 AND HH>12)
```

And the exit.

```(DD=25 AND HH<04)
```

All together, it looks like this.

```(
YYYY=2017 AND MM=02 AND             -- [shared]
(
(DD=15 AND HH=12 AND MIN>=30)  -- [entrance]
OR (DD=15 AND HH>12)              -- [entrance]
OR (DD>15 AND DD<25)              -- [bridge]
OR (DD=25 AND HH<04)              -- [exit]
)
)
```

## Requirements¶

Each date ranges hpdr outputs must be

• Correct. It represent the date range precisely in compilable HQL.
• Minimal. It must be written in the fewest number of characters possible.

Correctness is a necessary condition for hpdr to be worth anything at all, but others are not.

Pretty printing helps hpdr users check the output visually, so they can verify its output.

The minimal requirement deserves a section of its own.

## Minimal¶

### Common sense minimal¶

There’s an infinite number of bad ways to create any given date range. For example, the first 10 days of May 2015 could be written

```YYYY=2015 AND MM=5 AND (DD=1 OR DD=2 OR DD=3 OR DD=4 OR DD=5 OR DD=6 OR DD=7 OR DD=8 OR DD=9 OR DD=10)
```

But this is better

```YYYY=2015 AND MM=5 AND DD<11
```

because it’s minimal.

### Exceptional minimal¶

This should be avoided.

```MM>=6 AND MM<7
```

because this is clearly better,

```MM=6
```

even though the former mirrors the base case.

```MM>=6 AND MM<10
```

### Non-overlapping minimal¶

A hpdr date range can be correct, but can contain overlapping conditions. A stupid example is

```YYYY=2016 OR (YYYY>=2010 AND YYYY <2017)  -- 2016 included twice
```

This is non-minimal and not allowed in hpdr. A suprising number of these were ferreted out by unit tests.

## Questionable¶

I wrote hpdr to scratch an itch at work. I was composing, and was watching other people composing, these massively complex Hive date ranges. Strings turned into milliseconds truncated to seconds turned into Unix timestamps wrapped in timezone-shifting functions. They were unreadable and unmaintainable. I thought I would whip up a nice Python module that would fix it all.

But it turned out to be much harder than I thought. The code I’ve written to build a date range is pretty dense. The line of attack I settled on is indirect. But it was the best I could come up with.

Is there a simpler, recursive algorithm? I didn’t see it.