Fenwick tree index calculator
Type an index and see how a Fenwick tree moves from it: index 13 is 1101 in binary, its lowest set bit is 1, the update step goes to 14 and the query step to 12. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Index
- 13
- Size
- 16
- Lowest set bit
- 1
- Update next
- 14
- Query parent
- 12
- Binary
- 0b1101
A Fenwick tree, also called a binary indexed tree, answers prefix sums and point updates in logarithmic time by storing partial ranges whose lengths are powers of two. Every navigation step depends on one bit trick: the lowest set bit of the current 1-based index, written lsb equals i bitwise-and negative i in two's complement. Adding that lsb walks the update chain; subtracting it walks the prefix-query chain. Students, competitive programmers, and library authors need those parent and next indices without re-deriving the identities under exam pressure. This Fenwick tree index calculator accepts a positive index i and optionally a tree size n, returns the lsb, the one-step update next and query parent, binary forms for teaching, and when n is set the full update path and query path used by classic BIT code.
How Fenwick indices use the lowest set bit
In a 1-based binary indexed tree the cell at index i is responsible for a contiguous segment of the underlying array whose length equals the lowest set bit of i. That length is computed as lsb equals i bitwise-and the two's-complement negation of i, often written i and minus i in languages that use modular arithmetic on fixed-width integers. Geometrically, flipping all bits below the least significant one-bit isolates that power of two; the bitwise and with the original index yields exactly that power.
The classic update loop starts at the modified index and repeatedly replaces i with i plus lsb while i stays within the tree size n, so each step jumps to the next index that must absorb the delta. Together those two walks implement range sums via inclusion of two prefixes.
Understanding a single step—update next equals i plus lsb, query parent equals i minus lsb—is enough to debug off-by-one bugs, to draw the responsibility tree on a whiteboard, and to verify that an implementation matches the textbook identities before you integrate it into a contest template or a production analytics pipeline.
Where Fenwick index steps help most
Competitive programming coaches and online judges use a Fenwick tree index calculator so learners can check parent and next steps while they write update and query loops by hand. Interview prep tools need a deterministic oracle that agrees with every standard BIT tutorial on the same integer inputs, including awkward indices that are one less than a power of two. Failed validation does not consume balance.
Keep indices within the thirty-two-bit positive range, pin the path arrays in tests when size is set, and you get reproducible navigation for homework, documentation screenshots, and edge workers without standing up a full data-structure sandbox of your own.
What you can do with it
Interview and template validation
Compare candidate BIT implementations to a deterministic oracle of update and prefix-query index sequences for fixed sizes.
FAQ
Are indices 0-based or 1-based?
1-based, as in the standard Fenwick / binary indexed tree formulation. Index must be an integer from 1 through 2147483647.
Why use i & -i for the lowest set bit?
In two's complement, -i flips bits below the least significant 1-bit of i; the bitwise AND isolates that power of two, which is exactly the responsibility length of cell i.
What are the update and query paths for index 13 in a tree of size 16?
With size 16 the update path is 13, 14, 16, the cells that absorb a change at 13. The query path is 13, 12, 8, the cells you add up to get the prefix sum up to 13.
What is a Fenwick tree used for?
It answers prefix sums and single-value updates in logarithmic time. Each cell stores a partial range whose length is a power of two, so both an update and a sum only touch a few cells.
Which indices can I enter?
Any whole number from 1 to 2147483647, the largest positive 32-bit value. If you also give a tree size, it must be at least as large as the index and stay within the same limit.
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/fenwick-index \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"index":13}'const res = await fetch("https://api.kit.forhosting.com/dev/fenwick-index", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"index": 13
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/dev/fenwick-index",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"index": 13
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/dev/fenwick-index", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"index":13}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"index":13}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/dev/fenwick-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": 13
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "dev.fenwick_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
The pure deterministic logic matches free browser use and paid API calls byte for byte.
How Fenwick indices use the lowest set bit
The classic prefix-query loop starts at the right endpoint of the prefix and repeatedly replaces i with i minus lsb while i remains positive, summing the responsible cells that tile the range from one through the original index.
Input contract, response fields, and validation
Example: index thirteen has binary zero-b one one zero one, lowest set bit one, update next fourteen, query parent twelve; with size sixteen the update path is thirteen then fourteen then sixteen, and the query path is thirteen then twelve then eight. POST a JSON body with required field index: a positive integer in the closed range from one through two to the thirty-first minus one, the positive signed thirty-two-bit maximum where JavaScript bitwise operators remain faithful. Aliases i, idx, and position are accepted. Optional field size (aliases n, n_max, tree_size) is the maximum index of the tree; when present it must be an integer at least as large as index and at most the same upper bound. Missing, non-integer, zero, or out-of-range values fail with invalid_input naming the field and are not billed. On success the body always includes index, lowest_set_bit, update_next, query_parent, binary and lsb_binary strings with a zero-b prefix, and a short formula string restating the identities. When size is provided the body also includes size, update_path as the ordered list of indices visited by the update loop, query_path as the ordered list visited by the prefix loop, and update_next_in_range as a boolean telling whether the one-step update neighbor still lies inside the tree. Pair the response with your own array visualization if you need a diagram; this endpoint only computes index arithmetic and does not store tree values or perform sum queries over user arrays.
Integration use cases
Contest and homework BIT drills
Give students index i and optional size n; verify lowest_set_bit, update_next, query_parent, and full paths against handwritten Fenwick loops.
Docs and library golden paths
Generate update_path and query_path fixtures for binary indexed tree documentation, unit tests, and portability checks across languages.
Technical questions
How do I compute Fenwick tree parent and next indices?
Send a positive 1-based index i. The API returns lsb = i & -i, update_next = i + lsb, and query_parent = i - lsb, plus binary forms of i and the lsb.
What does the optional size parameter do?
When size n is set (n >= index), the response adds update_path (i += lsb while i <= n) and query_path (i -= lsb while i > 0), matching classic BIT loops.
What does the Fenwick tree 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.