Description
Return max(0, height-1) as lowerBound and either that same value when allDeepestLeavesRemoved or originalHeight as upperBound.
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 max(0, height-1) as lowerBound and either that same value when allDeepestLeavesRemoved or originalHeight as upperBound.
When to use this tool
Use Tree Pruned Leaf Height Bound when you need a local rooted-tree count or bound from supplied structural facts.
How to use the tool and how it works
- Enter originalHeight, allDeepestLeavesRemoved. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read lowerBound, upperBound. Use the output convention below.
Require nonnegative integer originalHeight. Return max(0, height-1) as lowerBound and either that same value when allDeepestLeavesRemoved or originalHeight as upperBound.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| originalHeight | Original Height | Required. Safe integer; minimum 0. |
| allDeepestLeavesRemoved | All Deepest Leaves Removed | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| lowerBound | Lower Bound | Required. Safe integer. |
| upperBound | Upper Bound | Required. Safe integer. |
{
"input": {
"originalHeight": 4,
"allDeepestLeavesRemoved": true
},
"output": {
"lowerBound": 3,
"upperBound": 3
}
}Limitations and assumptions
- These are caller-model bounds in edge-depth units; actual tree structure, which leaves were removed, and whether any pruning occurred are not verified.
- 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
- Tree Leaf Removal Degree Budget
Subtract one from both degree and vertex count and mark parentBecomesLeaf when the new degree is exactly one.
- Rooted Tree Preorder Parent Interval Check
Return nested for non-strict containment and proper only when nested and parentStart is strictly earlier.