Abhishek Gupta

Posted on Apr 22

🧠 Binary Search: 0 Monster Guide (JavaScript, Simple Words)

If binary search ever felt confusing, it’s not because it’s hard—it’s because it’s taught in pieces.

This guide will take you from:
👉 absolute beginner
👉 to solving advanced interview problems

No fluff. Just clear thinking + simple JS code.

🚀 0. What You MUST Know First

👉 Binary search ONLY works on sorted arrays

If the array is not sorted → ❌ don’t use binary search

🔍 1. Core Idea (Super Simple)

Instead of checking every number:

👉 Go to the middle
👉 Decide:

go LEFT
go RIGHT

Repeat.

🧩 2. Basic Binary Search

👉 Find if a number exists

function binarySearch(arr, target) {
  let low = 0, high = arr.length - 1;

  while (low <= high) {
    let mid = Math.floor((low + high) / 2);

    if (arr[mid] === target) return mid;

    if (arr[mid] < target) {
      low = mid + 1; // go right
    } else {
      high = mid - 1; // go left
    }
  }

  return -1;
}

🧠 3. The ONLY Thing You Need to Master

👉 Direction decision:

arr[mid] < target → go RIGHT
arr[mid] > target → go LEFT

Everything else = variation of this

📍 4. First Occurrence (Leftmost)

👉 When duplicates exist

Example:

[1, 2, 2, 2, 3]
        ↑ want THIS one

function firstOccurrence(arr, target) {
  let low = 0, high = arr.length - 1;
  let ans = -1;

  while (low <= high) {
    let mid = Math.floor((low + high) / 2);

    if (arr[mid] === target) {
      ans = mid;
      high = mid - 1; // go left again
    } else if (arr[mid] < target) {
      low = mid + 1;
    } else {
      high = mid - 1;
    }
  }

  return ans;
}

👉 Rule: found → still go LEFT

📍 5. Last Occurrence (Rightmost)

function lastOccurrence(arr, target) {
  let low = 0, high = arr.length - 1;
  let ans = -1;

  while (low <= high) {
    let mid = Math.floor((low + high) / 2);

    if (arr[mid] === target) {
      ans = mid;
      low = mid + 1; // go right again
    } else if (arr[mid] < target) {
      low = mid + 1;
    } else {
      high = mid - 1;
    }
  }

  return ans;
}

👉 Rule: found → still go RIGHT

📊 6. Lower Bound (first ≥ target)

👉 First number ≥ target

function lowerBound(arr, target) {
  let low = 0, high = arr.length;

  while (low < high) {
    let mid = Math.floor((low + high) / 2);

    if (arr[mid] < target) {
      low = mid + 1;
    } else {
      high = mid;
    }
  }

  return low;
}

📊 7. Upper Bound (first > target)

👉 First number > target

function upperBound(arr, target) {
  let low = 0, high = arr.length;

  while (low < high) {
    let mid = Math.floor((low + high) / 2);

    if (arr[mid] <= target) {
      low = mid + 1;
    } else {
      high = mid;
    }
  }

  return low;
}

🔁 8. One Template to Rule Them All

👉 Instead of memorizing everything:

while (low <= high) {
  let mid = Math.floor((low + high) / 2);

  if (condition) {
    high = mid - 1; // go left
  } else {
    low = mid + 1;  // go right
  }
}

👉 Just change the condition

🔥 9. Binary Search on Answer (GAME CHANGER)

👉 Not searching array
👉 Searching answer range

💡 Example Thinking

Question:
👉 Minimum speed to finish work?

Search space:

low = 1
high = max possible

🧠 Pattern:

function searchAnswer(low, high) {
  let ans = -1;

  while (low <= high) {
    let mid = Math.floor((low + high) / 2);

    if (isPossible(mid)) {
      ans = mid;
      high = mid - 1; // try better
    } else {
      low = mid + 1;
    }
  }

  return ans;
}

💥 10. REAL SECRET (Most Important Insight)

Binary search is NOT about arrays.

👉 It is about finding a boundary