Description
Check a candidate rook against supplied occupied rows and columns.
Graph and lattice counts depend on the allowed moves, edges and geometric or incidence assumptions. A necessary count identity or local conflict test may hold even when no valid complete object with the requested structure has been supplied.
Check a candidate rook against supplied occupied rows and columns.
When to use this tool
Use Combinatorics: Rook Placement Cell Conflict when checking one supplied path, tree, matching or rook-placement condition.
How to use the tool and how it works
- Enter existingRows, existingColumns, candidateRow, candidateColumn. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Check a candidate rook against supplied occupied rows and columns. Require aligned arrays and bounded nonnegative integer coordinates; rowConflict/columnConflict use membership and nonattacking requires neither.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| existingRows | Existing Rows | Required. Array of finite number. Implementation limit: 128 items. |
| existingColumns | Existing Columns | Required. Array of finite number. Implementation limit: 128 items. |
| candidateRow | Candidate Row | Required. Safe integer. |
| candidateColumn | Candidate Column | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Returned calculated value or nested object under the stated output convention. | Required. Object. |
| result.rowConflict | Row Conflict | Calculated result member: boolean. |
| result.columnConflict | Column Conflict | Calculated result member: boolean. |
| result.nonattacking | Nonattacking | Calculated result member: boolean. |
{
"input": {
"existingRows": [
0,
2
],
"existingColumns": [
1,
3
],
"candidateRow": 1,
"candidateColumn": 3
},
"output": {
"result": {
"rowConflict": false,
"columnConflict": true,
"nonattacking": false
}
}
}Limitations and assumptions
- Existing rooks need not themselves be nonattacking; no board dimensions or placement count are established.
- Outputs are nested inside result. Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Inspect or construct the complete graph/path and apply all relevant structural constraints for a full validity or counting result.
References
Similar or alternative tools
- Matching Unpaired Vertex Budget
Return unpaired vertices from a supplied matching size.
- Combinatorics: Lattice Path Endpoint Parity Check
Check square-lattice endpoint reachability for an exact step count.