Day- 4: Binary Search Is Not Just About Finding An Element

Most beginners think Binary Search ends the moment the target is found.

Interviewers know that's where the interesting part begins.

Today we'll learn one of the most important Binary Search patterns:

First Occurrence & Last Occurrence

The Beginner Trap

Suppose the array is:

[1, 2, 2, 2, 3]

Target = 2

You run Binary Search.

Mid lands on a 2.

Answer found?

Not necessarily.

Because there are multiple 2s.

Which one did you find?

The first?

The last?

Or just a random one?

This changes everything.

The Core Idea

Normal Binary Search asks:

"Does the element exist?"

Boundary Search asks:

"Where does the element start?"

and

"Where does the element end?"

This small change creates an entirely new pattern.

Visual Thinking

Imagine a row of students wearing the same school uniform.

You are asked:

"Find the first student wearing blue."

Finding any blue student is easy.

Finding the very first blue student is different.

Even after finding one,

you must keep checking further left.

The same idea applies here.

Finding First Occurrence

When Target = Mid

Don't stop immediately.

Store the answer.

Then continue searching on the left side.

Because another occurrence may exist earlier.

ans = mid

high = mid - 1

Keep moving left.

Finding Last Occurrence

When Target = Mid

Again,

don't stop.

Store the answer.

Then continue searching on the right side.

Because another occurrence may exist later.

ans = mid

low = mid + 1

Keep moving right.

Example

Input:

arr = [1, 2, 2, 2, 3]

target = 2

First Occurrence:

Index = 1

Last Occurrence:

Index = 3

Output:

First = 1

Last = 3

What Changed?

Only one thing.

When we found the target,

we did not stop.

We treated the answer as a possible boundary.

And continued searching.

That is the birth of Boundary Search.

Interview Lens

This pattern appears everywhere:

* Count Occurrences

* Lower Bound

* Upper Bound

* Search Insert Position

* Range Queries

* Database Indexing

Many interview problems are simply boundary searches in disguise.

Memory Rule

If duplicates exist,

finding the element is easy.

Finding the boundary is the real challenge.

The biggest Binary Search upgrade happens when you stop asking:

"Did I find the target?"

and start asking:

"Can I find a better answer?"

That single shift unlocks an entire category of interview problems.

#BinarySearch #DSA #Algorithms #Coding #Programming #InterviewPrep #GeeksforGeeks #DataStructures #ProblemSolving #CodingJourney

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