Ordered Set Insertion Neighbor Label Tool

Description

Locate a new element in a strictly increasing string members list and return insertion index and neighboring strings, using empty strings at absent edges.

A finite set records membership, while a multiset also records multiplicity. An ordered set adds an ordering rule, and an interval adds endpoint-closure choices. A witness for one element, a count budget, and equality of complete sets establish different facts.

Locate a new element in a strictly increasing string members list and return insertion index and neighboring strings, using empty strings at absent edges.

When to use this tool

Use Ordered Set Insertion Neighbor Label when you need the stated finite-set, interval, multiplicity, membership, or ordering operation under the given equality convention.

How to use the tool and how it works

Enter members, element. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read index, predecessor, successor. Use the output convention below.

Locate a new element in a strictly increasing string members list and return insertion index and neighboring strings, using empty strings at absent edges. Reject existing membership.^[1]

Input field	Meaning and units	Accepted input
members	Members	Required. Array of text; maximum UTF-16 length 8192; maximum items 256.
element	Element	Required. Text; maximum UTF-16 length 8192.

Output field	Interpretation	Returned shape
index	Zero-based index unless the mechanics explicitly state otherwise.	Required. Safe integer.
predecessor	String neighbor or empty edge value; use index and the original list to interpret.	Required. Text; maximum UTF-16 length 8192.
successor	String neighbor or empty edge value.	Required. Text; maximum UTF-16 length 8192.

json

{
  "input": {
    "members": [
      "a",
      "c"
    ],
    "element": "b"
  },
  "output": {
    "index": 1,
    "predecessor": "a",
    "successor": "c"
  }
}

Limitations and assumptions

Order is JavaScript string comparison, not locale collation. An empty-string neighbor can be a real member, so interpret edge availability from index and the original list.
The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.

Alternative or Complementary methods

Use a full set operation when one element or count cannot establish the required relation. Preserve the distinction between strings, typed scalar atoms, nested sets, ordered lists, and multisets.

References

Calculation and input contract: set/ordered-set-insertion-neighbor-label — tool.io

Similar or alternative tools

Ordered Set Neighbor Insertion Rank
Locate a new value in a strictly increasing numeric sorted list and return zero-based insertion rank, predecessor, successor, and presence flags.
Finite Set Rank After One Insertion
Return newRank=oldRank+1 only when the element was not already present and insertedRank<=oldRank.