Binary heap parent index calculator
Enter a node's index and pick the numbering: in a zero-based heap, index 5 has its parent at 2, because the floor of 4 over 2 is 2. The root has no parent and is refused rather than given a made-up slot. Free in your browser.
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Run — free
Worked example
- Index
- 5
- Indexing
- Zero
- Parent
- 2
- Root
- 0
A binary heap stored in an array is the structure behind priority queues, heapsort, and many shortest-path implementations. Every textbook lists a parent formula, but the two indexing conventions disagree by one, and an off-by-one there silently corrupts sift-up. This binary heap parent index calculator accepts the array index of a node and the numbering convention — zero-based, with the root at index zero, or one-based, with the root at index one — and returns the parent using the matching closed form. Zero-based heaps use parent equals floor of index minus one over two. One-based heaps use parent equals floor of index over two. The root has no parent and is rejected instead of inventing a negative or dummy slot.
Zero-based and one-based parent formulas
A binary heap laid out in an array never stores parent or child pointers. The walk from a node to its parent is a closed-form index formula, and that formula depends on whether the array is numbered from zero or from one.
In the zero-based convention used by C, Java, JavaScript, Python, and most production heaps, the root occupies index zero, the children of node i sit at two i plus one and two i plus two, and the parent of a non-root node is the floor of i minus one divided by two.
In the one-based convention used by many textbooks, CLRS-style pseudocode, and some contest templates, the root occupies index one, the children sit at two i and two i plus one, and the parent is simply the floor of i divided by two. Both identities are exact for integer indices; they are not approximations and they are not interchangeable. This calculator applies the matching identity after you select the convention, and it refuses the root because the root has no parent.
Confusing the two conventions is the classic off-by-one: treating a language array as one-based, or a textbook diagram as zero-based, yields a parent that is one slot away from the truth and silently breaks sift-up and decrease-key.
What you enter, what comes back and when it refuses
When indexing is zero the index must be at least zero; when indexing is one the index must be at least one. The root of the selected convention — zero in a zero-based heap, one in a one-based heap — is rejected with a message that names that root, because inventing a parent at minus one or wrapping to the last slot would be a lie. Example: index five with the default zero-based convention yields parent two, because floor of four over two is two.
Example: index four with one-based indexing yields parent two, whereas the same four in a zero-based heap would have parent one — that pair is the whole reason the convention is a field. Failed validation is not billed.
Where a heap parent-index calculator earns its keep
Interview prep, algorithms courses, and production priority queues all need the same parent walk, and they disagree about numbering. Students checking a sift-up trace want to confirm that the parent of five is two in a language array and that the parent of four is two on a one-based worksheet, without flipping the formula by hand at each step. Autograders for data-structures homework need a deterministic oracle that rejects the root as having no parent instead of returning a silent minus one that a buggy submission might treat as success.
Engineers porting a textbook heap into a zero-based language, or the reverse, can pin both conventions in tests and catch the off-by-one before it ships. Visualizers and contest scaffolds that draw the tree from an array can ask for the parent of every non-root slot and lay out edges without embedding two copies of the formula. Keep requests small, pin the parent integer in tests, and you get reproducible walks for homework, LMS plugins, and edge workers without standing up a local heap library of your own.
What you can do with it
Homework and interview traces
Check the parent of any array slot while tracing sift-up or heapsort, switching between textbook one-based numbering and language zero-based arrays.
Autograders and contest oracles
Mark heap-index questions with a deterministic parent formula that rejects the root as having no parent instead of inventing a dummy index.
Porting heaps across conventions
Pin parent walks when translating CLRS-style one-based pseudocode into a zero-based language array, or the reverse, before the off-by-one ships.
FAQ
How do I find the parent of a node in a binary heap array?
Send index (the node’s array slot) and optional indexing. For zero-based heaps the parent is floor((index − 1) / 2). For one-based heaps the parent is floor(index / 2).
What is the difference between zero-based and one-based heap indexing?
Zero-based heaps put the root at index 0 and use parent = floor((i − 1) / 2). One-based heaps put the root at index 1 and use parent = floor(i / 2). The same numeric index can name different parents under the two conventions.
What happens if I ask for the parent of the root?
The root (index 0 when indexing is zero, index 1 when indexing is one) has no parent, and the calculator will not invent one.
What is the parent of index 5 in a zero-based binary heap?
Two. floor((5 − 1) / 2) = 2. The same index in a one-based heap is also 2, but index 4 is the pair that diverges: parent 1 when zero-based, parent 2 when one-based.
Why does an off-by-one in the parent formula matter so much?
Because the result is a real slot one place away from the true parent, so nothing crashes. Sift-up and decrease-key simply compare and swap the wrong elements, and the heap order breaks without any warning.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/dev/heap-parent-index \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"index":5}'const res = await fetch("https://api.kit.forhosting.com/dev/heap-parent-index", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"index": 5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/dev/heap-parent-index",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"index": 5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/dev/heap-parent-index", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"index":5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"index":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/dev/heap-parent-index", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"index": 5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "dev.heap_parent_index",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Zero-based and one-based parent formulas
The response echoes the index and convention you sent, names the parent, names the root index for that convention, restates the formula as a string you can print next to the answer, and sets is_root to false on every successful walk so clients can treat success as “a real parent exists.”
Input contract, response shape, and error behaviour
POST a JSON body with index required: a finite integer naming the array slot of the node whose parent you want. indexing is optional and defaults to zero, meaning a zero-based array with the root at index zero; send one when your heap is numbered from one. Aliases i and node are accepted for index, and convention is accepted for indexing, so snippets copied from lecture notes still parse. Non-finite values, booleans, empty strings, and a missing index fail with invalid_input. Indices above the safe integer limit are rejected so JSON numbers stay exact under floor division. On success the body includes the echoed index and indexing, parent as the computed integer, is_root false, root as the convention’s root slot, and formula as either parent equals floor of open parenthesis index minus one close parenthesis over two, or parent equals floor of index over two.
Technical questions
What does the binary heap parent index calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.