Description
Return vertices-rootCount as expectedParentEdges and subtract parentEdges for deficit.
A rooted tree organizes vertices by parent, children, and distance from a root. Root status changes local degree relationships, and height or leaf formulas assume the supplied structure really satisfies the tree model.
Return vertices-rootCount as expectedParentEdges and subtract parentEdges for deficit.
When to use this tool
Use Tree Parent Edge Deficit when you need a local rooted-tree count or bound from supplied structural facts.
How to use the tool and how it works
- Enter vertices, parentEdges, rootCount. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read expectedParentEdges, deficit. Use the output convention below.
Require nonnegative integer vertices and parentEdges and rootCount within vertices. Return vertices-rootCount as expectedParentEdges and subtract parentEdges for deficit.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| vertices | Vertices | Required. Safe integer; minimum 0. |
| parentEdges | Parent Edges | Required. Safe integer; minimum 0. |
| rootCount | Root Count | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| expectedParentEdges | Expected Parent Edges | Required. Safe integer. |
| deficit | Deficit | Required. Safe integer. |
{
"input": {
"vertices": 10,
"parentEdges": 7,
"rootCount": 1
},
"output": {
"expectedParentEdges": 9,
"deficit": 2
}
}Limitations and assumptions
- This is a supplied forest edge budget; zero deficit does not prove acyclicity, connectivity within components, valid parent assignments, or the actual root count.
- 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
Traverse a verified tree to derive parent, depth, and leaf data directly. A formula using claimed degrees or depths cannot independently establish connectedness, acyclicity, or a valid root.
References
Similar or alternative tools
- Rooted Tree Preorder Parent Interval Check
Return nested for non-strict containment and proper only when nested and parentStart is strictly earlier.
- Tree Root Depth Parent Step
Return zero for a root or parentDepth+1 otherwise.