nano-binary-search

A tiny, single-file binary search with no dependencies. After writing it countless times, I believe this version is done right and fits JavaScript — ripe for reuse.

TypeScript typings are included.

This is equivalent to C++ std::lower_bound / Python bisect.bisect_left.

Quick reference

import binarySearch from 'nano-binary-search';

// Lower bound (first element >= value):
binarySearch([1, 2, 4, 5], x => x < 3); // → 2

// Upper bound (first element > value):
binarySearch([1, 2, 4, 5], x => x <= 2); // → 2

// Insert keeping sorted order:
const idx = binarySearch(sortedArray, x => x < value);
sortedArray.splice(idx, 0, value);

// Remove all elements equal to value:
const lo = binarySearch(sortedArray, x => x < value);
const hi = binarySearch(sortedArray, x => x <= value, lo);
sortedArray.splice(lo, hi - lo);

// Edge cases — just work:
binarySearch([], x => x < 5); // → 0 (empty array)
binarySearch([1, 2, 3], x => x < 1); // → 0 (before all)
binarySearch([1, 2, 3], x => x < 4); // → 3 (after all)

Why?

Why do I think it is done right? Because it supports important invariants with splice().

No need to worry about inserting values

import binarySearch from 'nano-binary-search';

const sortedArray = [];

for (let i = 0; i < 100; ++i) {
  const value = Math.floor(Math.random() * 1000);

  // THIS IS THE IMPORTANT INVARIANT:
  // - works with `splice()` seamlessly to add values
  const index = binarySearch(sortedArray, x => x < value);
  sortedArray.splice(index, 0, value);
  // `sortedArray` is always sorted
}

What if the array is empty? That's fine. What if the value is outside the range of the array? That's fine too.

No need to worry about removing values

import binarySearch from 'nano-binary-search';

const sortedArray = [1, 3, 3, 4];

// THIS IS THE IMPORTANT INVARIANT:
// - works with `splice()` seamlessly to remove equal values
const lowerIndex = binarySearch(sortedArray, x => x < 3),
  upperIndex = binarySearch(sortedArray, x => x <= 3, lowerIndex);
sortedArray.splice(lowerIndex, upperIndex - lowerIndex);
// again, `sortedArray` is always sorted

What if there is no such value in the array? That's fine. It still works.

API that makes sense

There is no need to pass in a function and a comparison value every time. In modern JavaScript/TypeScript it is easier to capture the comparison value in a closure, as shown in the examples above.

Do you want to search a sub-array? Just pass in indices.

API

TypeScript-like API:

const index: number = binarySearch<T>(
  sortedArray: readonly T[],
  lessFn: (value: T, index: number, array: readonly T[]) => boolean,
  l: number = 0,
  r: number = sortedArray.length
): number;

• Inputs:
  • sortedArray — sorted array of values. The array must be sorted in a way compatible with lessFn.
  • lessFn — function that takes three arguments and returns true if the element (first argument) is less than the target value. The second argument is the index, the third is sortedArray. The signature mirrors the standard array callback convention.
  • l — left index. This index is inclusive. Defaults to 0.
  • r — right index. This index is exclusive. Defaults to sortedArray.length.

The function returns an index where the target value can be inserted with splice():

• With <: the index of the first element greater than or equal to the target (lower bound, C++ std::lower_bound / Python bisect_left).
• With <=: the index of the first element greater than the target (upper bound, C++ std::upper_bound / Python bisect_right).

That's all Folks!

Q & A

Is it fast?

Yes.

The only way to make it meaningfully faster is to inline the entire search in your code, eliminating the function-call overhead of lessFn().

What if I want to take into account the index of the searched value?

That's why lessFn(value, index, array) has extra arguments.

What if the array uses a custom comparator for sorting, while this binary search uses a less function?

Simple:

let compareFn; // some complex function defined elsewhere
sortedArray.sort(compareFn);

let value; // some search value defined elsewhere

const lessFn = x => compareFn(x, value) < 0,
  index = binarySearch(sortedArray, lessFn);

Why doesn't it use a comparator function for searching?

Binary search does not need equality comparison — a simple less function is sufficient and often easier to implement.

For example (two argument version for simplicity):

const stringLessFn = (a, b) => a < b;

// comparator #1 (two comparisons)
const stringCompareFn1 = (a, b) => (a < b ? -1 : a > b ? 1 : 0);

// comparator #2: smarter (a method call)
const stringCompareFn2 = (a, b) => a.localeCompare(b);

I still have questions!

Look at the code of index.js and tests/ for more details. Go to the GitHub repository and ask.

License

This project is licensed under the BSD-3-Clause license.

Release history

• 1.0.13 Updated dev deps
• 1.0.12 Exported LessFn type, added TS typing tests and CJS tests, improved docs and d.ts JSDoc
• 1.0.11 Technical release: more tests to increase coverage, more AI-friendly changes
• 1.0.10 Updated dev deps
• 1.0.9 Updated dev deps
• 1.0.8 Updated dev deps
• 1.0.7 Updated dev deps
• 1.0.6 Updated dev deps
• 1.0.5 Updated dev deps
• 1.0.4 Updated dev deps
• 1.0.3 Added a reference to the TS types
• 1.0.2 Improved docs
• 1.0.1 Added TS typings
• 1.0.0 Initial release