Nonogram Clue Sum + Gaps Length Check

Audit Nonogram clue sum plus one mandatory gap between runs and explicit exterior empties, including empty clue; preserves signed deficit, not cellwise consistency or uniqueness solving.

Description

A nonogram line needs room for runs and separating empty cells.

A nonogram line needs room for runs and separating empty cells. Caller end padding adds an independent requirement.^[1]

Enter positive integer run lengths, nonnegative integer line length/end padding; an empty run list is allowed. Return minimum occupied span, signed slack and inclusive fit flag.

When to use Nonogram Clue Sum + Gaps Length Check

Use Nonogram Clue Sum + Gaps Length Check when you need to evaluate the supplied records under the calculation and evidence rules below. No placement enumeration, cell evidence or whole-puzzle uniqueness is checked.

Prepare the supplied game state, observations and explicit variant settings. Follow the card, board, coordinate and state conventions in the calculation rules.

How to use Nonogram Clue Sum + Gaps Length Check and understand its results

Prepare the supplied game state, observations and explicit variant settings. Follow the card, board, coordinate and state conventions in the calculation rules.
Enter runLengths, availableLineCells, fixedLeadingEmptyCells, fixedTrailingEmptyCells using the field table and calculation rules, then run the tool.
Read minimumRequiredLineCells, signedRemainingSlackCells, lineLengthFeasible. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
runLengths	Run lengths	list of number	Required
availableLineCells	Available line cells	number	Required
fixedLeadingEmptyCells	Fixed leading empty cells	number	Required
fixedTrailingEmptyCells	Fixed trailing empty cells	number	Required

Enter positive integer run lengths, nonnegative integer line length/end padding; an empty run list is allowed. Return minimum occupied span, signed slack and inclusive fit flag.

minimum=sum(runs)+max(0,runCount−1)+leading+trailing

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
minimumRequiredLineCells	Minimum required line cells	number
signedRemainingSlackCells	Signed remaining slack cells	number
lineLengthFeasible	Line length feasible	boolean

json

{
  "input": {
    "runLengths": [
      3,
      2
    ],
    "availableLineCells": 8,
    "fixedLeadingEmptyCells": 0,
    "fixedTrailingEmptyCells": 0
  },
  "output": {
    "minimumRequiredLineCells": 6,
    "signedRemainingSlackCells": 2,
    "lineLengthFeasible": true
  }
}

Limitations and assumptions

No placement enumeration, cell evidence or whole-puzzle uniqueness is checked.

Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Numeric lists are limited to 10,000 entries; string lists to 128 strings of at most 128 characters each. The rules above may impose smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.

Alternative or Complementary methods

Use SET Card All-Same-or-All-Different Check: A SET has each feature all equal or all different across three cards. Card distinctness is a separate input rule. For a complementary task, use Kakuro Row Sum Distinct Digits Check: A Kakuro run uses distinct digits 1–9. Unknown cells can be checked by enumerating remaining digit combinations.

References

Nonogram Clue Sum + Gaps Length Check — tool.io

Similar or alternative tools

SET Card All-Same-or-All-Different Check
A SET has each feature all equal or all different across three cards. Card distinctness is a separate input rule.
Kakuro Row Sum Distinct Digits Check
A Kakuro run uses distinct digits 1–9. Unknown cells can be checked by enumerating remaining digit combinations.