When Should Binary Search Click in Your Mind?

Think Binary Search when you see:

• Sorted array / rotated sorted array
• Minimum / Maximum answer
• Capacity / speed / days / size
• "Can we do it?" → Yes / No type logic

If the answer looks like:

false false false true true true

👉 Binary Search is the correct approach.

Pattern 1: Classic Binary Search (Search an Element)

When to use:

• Array is sorted
• Find exact target

Template:

let l = 0, r = nums.length - 1;

while (l <= r) {
  const mid = l + Math.floor((r - l) / 2);
  if (nums[mid] === target) return mid;
  if (nums[mid] < target) l = mid + 1;
  else r = mid - 1;
}
return -1;

Problems:

• Binary Search

Pattern 2: First / Last Occurrence (Duplicates)

When to use:

• Sorted array
• Duplicates exist
• Need first or last position

Key idea:

If found:

• First → move left
• Last → move right

Problems:

• Find First and Last Position of Element
• First Bad Version

Pattern 3: Lower Bound / Upper Bound

When to use:

• Find insertion position
• First value ≥ target or > target

Lower Bound: First index where value >= target

Upper Bound: First index where value > target

Problems:

• Search Insert Position
• Find Smallest Letter Greater Than Target

Pattern 4: Binary Search on Answer (MOST IMPORTANT)

When to use:

• Question asks for minimum / maximum answer
• You can check an answer using Yes / No

Pattern: Find minimum X such that isPossible(X) is true

Template:

let l = min, r = max, ans = -1;

while (l <= r) {
  const mid = Math.floor((l + r) / 2);
  if (isPossible(mid)) {
    ans = mid;
    r = mid - 1;
  } else {
    l = mid + 1;
  }
}
return ans;

Problems:

• Koko Eating Bananas
• Capacity To Ship Packages Within D Days
• Minimum Days to Make Bouquets

Pattern 5: Rotated Sorted Array

When to use:

• Sorted array rotated at some pivot

Key idea:

• One half is always sorted
• Decide which half to discard

Problems:

• Search in Rotated Sorted Array
• Find Minimum in Rotated Sorted Array

Pattern 6: Binary Search on Matrix

When to use:

• Matrix rows sorted
• Treat matrix like a 1D array

Problems:

• Search a 2D Matrix

Common Mistakes to Avoid

❌ Using binary search on unsorted data

❌ mid = (l + r) / 2 (overflow risk)

✅ Always use:

mid = l + Math.floor((r - l) / 2);

❌ Infinite loops

✅ Ensure l or r always moves

Must-Solve Binary Search Questions (In Order)

Easy

• Binary Search
• Search Insert Position
• First Bad Version

Medium

• Find First and Last Position
• Search in Rotated Sorted Array
• Koko Eating Bananas
• Capacity To Ship Packages

Hard

• Median of Two Sorted Arrays
• Split Array Largest Sum

Final Tip (Interview Gold)

If you can answer:

"Can I validate a candidate answer using Yes / No?"

👉 Binary Search is the correct solution.

If this helped you, consider upvoting 👍
Happy Coding 🚀