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DSA Pattern

Binary Indexed Tree Pattern

Recognise the Binary Indexed Tree pattern once — then solve any problem that uses it. Below are every Binary Indexed Tree problem we index, grouped by the module that teaches them.

Problems

Walkthroughs ready

0E · 1M · 0H

Difficulty mix

Java · Python

Languages

Where this pattern shows up

Binary Indexed Tree problems by module

Trees & BST1 problem

Fenwick Tree (Binary Indexed Tree)

GoogleAmazontwo-sigma

mediumExplained

Pattern guide

Mastering the Binary Indexed Tree pattern

Overview

The Binary Indexed Tree pattern is one of the reusable techniques that experienced candidates spot instantly. Rather than memorising individual problems, strong interviewees recognise that a new question "is just Binary Indexed Tree" and reach for the matching template. That recognition is exactly what this collection is designed to build.

We index 1 problems that use the Binary Indexed Tree pattern (0 easy, 1 medium, 0 hard), each worked brute-force → optimal in Java and Python with line-by-line explanations. Solving them back-to-back is the fastest way to internalise when and how to apply Binary Indexed Tree.

Pattern-first practice compounds: once Binary Indexed Tree is automatic, you'll see it inside problems that never mention it by name.

Study playbook

1
Solve them in a single sitting
Work several Binary Indexed Tree problems in a row. The shared skeleton becomes obvious when you see the same structure solve different-looking questions.
2
Name the trigger
Write down the signal that should make you reach for Binary Indexed Tree (e.g. 'contiguous sub-range', 'sorted + pair', 'k largest'). In the interview, that trigger is your cue.
3
Keep one template
Maintain a single mental template for Binary Indexed Tree that you can write from memory and adapt, instead of re-deriving it under pressure.
4
Compare with neighbours
Know how Binary Indexed Tree differs from adjacent patterns so you pick the right tool when a problem could go more than one way.

Common pitfalls

Forcing Binary Indexed Tree onto a problem that doesn't fit because it's the pattern you just practised.
Recalling a specific solution instead of re-deriving from the pattern when given a variation.
Skipping the brute force and the complexity discussion that frame your optimal answer.
Missing the edge cases the pattern is notorious for (empty input, boundaries, duplicates).

Frequently asked

What is the Binary Indexed Tree pattern?

It's a reusable problem-solving technique that recurs across many interview questions. Learning it once lets you solve a whole family of problems instead of memorising each one.

When should I use Binary Indexed Tree?

When a problem shows the pattern's trigger signal. The problems below all share that signal, so working through them trains you to recognise it quickly.

How many Binary Indexed Tree problems should I do?

Enough that the template feels automatic — usually solving the indexed set here in sequence is sufficient to recognise Binary Indexed Tree on sight.

Related patterns

Binary Search22 Binary Search On Answer4 Binary Lifting1 Binary Tree1

Keep exploring

Browse DSA another way

Curriculum

18 modules · theory + practice

Explore

Curated sheets

Blind 75, NeetCode 150, Grind 75

DSA Pattern

Binary Indexed Tree Pattern

Recognise the Binary Indexed Tree pattern once — then solve any problem that uses it. Below are every Binary Indexed Tree problem we index, grouped by the module that teaches them.

Problems

Walkthroughs ready

0E · 1M · 0H

Difficulty mix

Java · Python

Languages

Where this pattern shows up

Binary Indexed Tree problems by module

Trees & BST1 problem

Fenwick Tree (Binary Indexed Tree)

GoogleAmazontwo-sigma

mediumExplained

Pattern guide

Mastering the Binary Indexed Tree pattern

Overview

Pattern-first practice compounds: once Binary Indexed Tree is automatic, you'll see it inside problems that never mention it by name.

Study playbook

1
Solve them in a single sitting
Work several Binary Indexed Tree problems in a row. The shared skeleton becomes obvious when you see the same structure solve different-looking questions.
2
Name the trigger
Write down the signal that should make you reach for Binary Indexed Tree (e.g. 'contiguous sub-range', 'sorted + pair', 'k largest'). In the interview, that trigger is your cue.
3
Keep one template
Maintain a single mental template for Binary Indexed Tree that you can write from memory and adapt, instead of re-deriving it under pressure.
4
Compare with neighbours
Know how Binary Indexed Tree differs from adjacent patterns so you pick the right tool when a problem could go more than one way.

Common pitfalls

Forcing Binary Indexed Tree onto a problem that doesn't fit because it's the pattern you just practised.
Recalling a specific solution instead of re-deriving from the pattern when given a variation.
Skipping the brute force and the complexity discussion that frame your optimal answer.
Missing the edge cases the pattern is notorious for (empty input, boundaries, duplicates).

Frequently asked

What is the Binary Indexed Tree pattern?

It's a reusable problem-solving technique that recurs across many interview questions. Learning it once lets you solve a whole family of problems instead of memorising each one.

When should I use Binary Indexed Tree?

When a problem shows the pattern's trigger signal. The problems below all share that signal, so working through them trains you to recognise it quickly.

How many Binary Indexed Tree problems should I do?

Enough that the template feels automatic — usually solving the indexed set here in sequence is sufficient to recognise Binary Indexed Tree on sight.