Advanced Topics in Inverted Hierarchies 
This section is intended to be read by students with some familiarity with DSPD and with inverting hierarchies, but need to know more about inverting more complex hierarchies. If you are just getting started with the method this section should be skipped.

Even if you are an advanced student, you should consider the possibility of breaking apart complex mappings as separate passes, to avoid having to invert complicated hierarchies.

Partially Inverted Hierarchies 
When using inverted hierarchies to resolve structure clashes in program designs, we do not necessarily invert the entire hierarchy. In the calendar example discussed earlier, we inverted "week" with respect to "day" because the clashing hierarchy--year/quarter/month--also had a "day" level of hierarchy. A "partially inverted" hierarchy is one which is inverted with respect to some "middle" level instead of to the lowest level in the hierarchy. For instance, the diagram which follows shows the year/quarter/month/day hierarchy inverted with respect to "month."

Notice that when partially inverting a hierarchy, the part of the hierarchy above the level you are inverting to follows the normal pattern of inversion. The part of the hierarchy below the level you are inverting to is unaffected by the inversion.

Inverting Structures Containing Alternatives 
Occasionally, it is necessary to invert hierarchies containing alternation. This is easily done if you remember the concurrency operator. For instance, consider the diagram below...

This hierarchy is equivalent to...

In other words, within an attorney, major clients are listed and minor clients are listed, but in no particular order. This is the same as saying that within an attorney, clients are listed, each one of which is either major or minor (the top picture). The two concurrent hierarchies can be inverted as follows...

and then "glued" back together as...

Notice that the levels common to both the major and minor client levels can be "factored up to the left as follows...

This completes the inversion.

Inverting "0,n" Hierarchies (if you really, really have to) 
Note that this topic should be considered VERY advanced, and if you have wandered in here casually you probably should wander right back out again until you have to do this.

Inverting "0,n" repeating levels is a bit different from inverting "1,n" repeating levels. This is due to the relationship of the "0,n" structure and alternation: a "0,n" level is the same as a "1,n" level INSIDE an alternative "0,1". To invert "0,n" levels, we resort to the same kind of strategy just discussed when inverting alternative levels. Consider the following diagram...

We first eliminate the "0,n" levels by translating them into "1,n" levels inside "0,1" alternatives as follows.

This alternative structure is translated to the concurrent form...

Each "leg" of the hierarchy is inverted normally...

Notice that this structure would require three different "types" of ideal records. A record for an inactive company (which would be the only record in the ideal file if the company were inactive), a record for each inactive agent (with no product information), and a record for each product within an active agent. Thus we can "glue" the three concurrent inverted structures back together at the "ideal record" level: the diagram tells us how to process one "ideal record" at a time.