From my perspective, I believe I have a grasp on the requirements outlined here. The main goal is to group items based on multiple predicate functions, allowing for various groupings due to multiple predicates possibly returning true for the same item. The aim is to identify a grouping that minimizes the differences in sizes of the resulting groups.
The provided examples are not particularly convincing to me, so let's consider a different scenario. If we have a list of items like [8, 6, 7, 5, 3, 0, 9], and three predicates: (n) => n < 7, (n) => n > 3, and (n) => n % 2 == 1, then as an example, the number 8 can only belong to the second group (as it's greater than 3 but not less than 7 and not odd). The 6 can be part of either the first or second group, while the 5 has flexibility across all groups, leading to a possible arrangement depicted below:
8 6 7 5 3 0 9
[[1], [0, 1], [1, 2], [0, 1, 2], [0, 2], [0], [1, 2]]
^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^
| | | | | | | | | | | | |
| +--|----|--|----+--|--|----+--|----+----|--|------> Group 0 (n => n < 7)
| | | | | | | | |
+-------+----+--|-------+--|-------|---------+--|------> Group 1 (n > 3)
| | | |
+----------+-------+------------+------> Group 2 (n % 2 == 1)
Considering the combination possibilities according to the constraints, there could be 48 potential partitions. A sample of such partitions is shown below:
[
[ [6, 5, 3, 0], [8, 7, 9], [] ],
[ [6, 5, 3, 0], [8, 7], [9] ],
[ [6, 5, 0], [8, 7, 9], [3] ],
[ [6, 5, 0], [8, 7], [3, 9] ],
// ... (42 rows omitted)
[ [0], [8, 6, 9], [7, 5, 3] ],
[ [0], [8, 6], [7, 5, 3, 9] ]
]
To determine the most optimal partition with minimal size variations, we calculate the statistical variance by summing the squares of the distances of the values from their mean. For instance, considering [[6, 5, 3, 0], [8, 7, 9], []] with lengths 4, 3, and 0; this yields a variance of 8.667. In comparison, the second option has lengths 4, 2, and
1</code, resulting in a variance of <code>4.667
. Ultimately, the ideal solution would consist of
3,
2, and
2 with a variance of
0.667, as exemplified by
[[6, 5, 0], [8, 7], [3, 9]]. It's worth noting that there may be several alternatives exhibiting similar behaviors, and the subsequent determination process primarily selects the initial favorable choice.
If the problem delineation aligns with your expectations, the code snippet below appears to effectively address the scenario at hand:
const range = (lo, hi) => Array .from ({length: hi - lo}, (_, i) => i + lo)
// Additional utility functions, etc.
// Code snippet truncated for brevity
// Final call to specialFunc function
console .log (specialFunc (
[8, 6, 7, 5, 3, 0, 9],
[n => n < 7, n => n > 3, n => n % 2 == 1]
)) //=> [[6, 5, 0], [8, 7], [3, 9]]
.as-console-wrapper {max-height: 100% !important; top: 0}
A detailed explanation of key utility functions and processes involved in the operation is also provided within the response for clarity and comprehension purposes.
1The standard deviation offers a more explicit interpretation, although its calculation essentially involves the square roots of variances, ensuring consistent ordering without necessitating actual root extractions.