The Base-N-Odometer by Phillip P. Fuchs

What if the same principles are applied to a permutation? One could effortlessly answer the concerns presented above. In this case, the odometer is utilized to count generations of N elements within a complete permutation set. Arriving at a solution depends upon the initial list(s) given, the speed of the computer(s), threading, and distribution (by degree). The initial list given directly corresponds to the

Often permutation odometer-style models only display a current combination order as index wheels and fail to record vital information such as a simple generation count (or

As a Computer Science student, one must ask questions such as: If a standalone permutation odometer only registers the current combination order, then is it really an odometer? Can a single odometer reading (as a linear array) exist by itself and be read by other algorithms? Are programmers allowed to create practical odometer functions such as a current generation count,

As stated before, the "Base-N-Odometer" that is promoted on this website easily addresses concerns described above and is highly

The QuickPerm algorithm presented earlier can utilize a countdown process or it can utilize a counting process. The significant difference between a countdown QuickPerm algorithm and a counting QuickPerm algorithm is the initialization of the Base-N-Odometer (coded as the primary controller array p[N]). A countdown process will initialize the controller array to corresponding index values (a maximum digit), whereas a counting process will initialize all values in the controller array to zero. Whether a countdown process or a counting process is utilized is rather debatable. Both counting processes offer similar advantages and only a few minor disadvantages if any.

In any case scenario, the primary controller array p[N] within the QuickPerm algorithm(s) is analogous to an incremental

Before another swap can take place, upper and lower index values must be recalculated based upon values stored in the

This process continues until the upper index attempts to reference an odometer digit beyond the length of the linear permutable target in question.

Presented below is a table that compares common odometer characteristics with various computerized odometer models such as my "Base-N-Odometer", a standard automobile trip odometer, and an odometer-style generator commonly referenced by modern lexicographical (alpha-permutation) algorithms. Each odometer characteristic can have a "Yes" or "No" answer or ??? for an unknown. The third and fourth columns are open for your interpretation. Please provide a sound explanation and corresponding code to support your answer(s). I'll collect the data and compile the results within the table below:

Common Odometer Characteristics:Standalone Odometer ModelsBase N~ Mileage ~LexicogRepresents Current Combination Yes Yes Yes Counts All Generations ("Distance") Yes Yes No Sequentially Linked Digits or Wheels Yes Yes No Expected Duplicate Digits Yes Yes No Standalone and Shareable Readings Yes Yes ??? Defines Upper and Lower Indices at a Glance Yes ??? ??? Able to Set(n) & Distribute Readings Yes ??? ??? Able to Reset() Yes Yes ??? Able to Quickly Rewind(n) Yes ??? ??? Able to Fast-Forward(n) Yes ??? ??? Calculate the Nth Combination Yes ??? ??? Miscellaneous / Other ??? ??? ???

For more information on the

- a core algorithm primarily used to count all generations within a permutation set containing N elements or used as a Big Integer Calculator.
- an algorithm for recording numerous events over time by counting in a sequentially based numbering system.
- an algorithm for counting events within a fixed time period that can be initialized, reset, rewound, or advanced.
- an algorithm for sequentially counting events exceptionally characterized by occurrences of duplicate digits and digit roll-overs.
- an algorithm used to identify valid target elements within a parallel linear list(s) or used to determine a pending event.

- an instrument used to measure distance traveled.
- an instrument for recording an overall distance traveled counting in a universal base 10 numbering system.
- an instrument for measuring a distance traveled between two geographic coordinates. Often referenced as a
*trip-odometer*. - an instrument for measuring distance traveled by a sequential count characterized by occurrences of duplicate digits and digit roll-overs.
- an instrument used to determine a scheduled event or repair.

- an algorithm used to count all generations within a permutation set containing N elements. Also called the
*"Base-N-Odometer"*. - an algorithm for recording unique generations processed by counting in a sequentially based numbering system.
- an algorithm for counting generations over a fixed time period within a permutation set that can be initialized, reset, rewound, or advanced.
- an algorithm for sequentially counting generations exceptionally characterized by occurrences of duplicate digits and digit roll-overs.
- an algorithm used to identify valid target elements to swap within a linear list(s) or used to predict an imminent generation order.