Why Binary Search Recursive Approach in DSA Typescript?

The Big Idea

What if you could find any name in a giant phone book in just a few steps?

The Scenario

Imagine you have a huge phone book and you want to find a friend's number. You start from the first page and check every name one by one until you find it.

The Problem

This way takes a lot of time because you might have to look through hundreds or thousands of pages. It is slow and tiring, and you can easily lose your place or make mistakes.

The Solution

Binary search uses a smart trick: it looks at the middle page, decides if your friend's name is before or after, and then only searches that half. It repeats this until it finds the name or knows it is not there. This saves a lot of time and effort.

Before vs After

✗ Before

function linearSearch(array: number[], target: number): number {
  for (let i = 0; i < array.length; i++) {
    if (array[i] === target) return i;
  }
  return -1;
}

✓ After

function binarySearch(array: number[], target: number, left: number, right: number): number {
  if (left > right) return -1;
  const mid = Math.floor((left + right) / 2);
  if (array[mid] === target) return mid;
  else if (array[mid] > target) return binarySearch(array, target, left, mid - 1);
  else return binarySearch(array, target, mid + 1, right);
}

What It Enables

It makes searching in sorted lists super fast, even if the list is huge.

Real Life Example

When you search for a word in a dictionary app, it quickly jumps to the middle of the list and narrows down where the word could be, instead of checking every word.

Key Takeaways

Manual search checks every item one by one, which is slow.

Binary search splits the list and searches only the needed half each time.

This approach is much faster for sorted lists.

Practice

1. What is the main idea behind the binary search recursive approach?

easy

A. Search each element one by one from start to end

B. Divide the array into halves and search recursively in the correct half

C. Sort the array after each recursive call

D. Use a queue to store elements for searching

Solution

1. Step 1: Understand binary search logic

   Binary search works by dividing the sorted array into two halves and deciding which half to search next based on the middle element.

2. Step 2: Apply recursion in binary search

   The recursive approach calls the same function on the half where the target might be, reducing the search space each time.

3. Final Answer:

   Divide the array into halves and search recursively in the correct half -> Option B

4. Quick Check:

   Binary search = divide and conquer [OK]

Hint: Remember: binary search splits array, then recurses [OK]

Common Mistakes:

• Thinking binary search checks every element
• Sorting array inside recursion
• Using linear search logic

2. Which of the following is the correct TypeScript function signature for a recursive binary search?

easy

A. function binarySearch(arr: number[], target: string): boolean

B. function binarySearch(arr: string[], target: number): number

C. function binarySearch(arr: number[], target: number, left: number, right: number): number

D. function binarySearch(arr: number[], target: number): void

Solution

1. Step 1: Check parameters needed for recursion

   Recursive binary search needs the array, target, and the current left and right indices to search between.

2. Step 2: Verify return type

   The function returns the index of the target if found, so the return type is number.

3. Final Answer:

   function binarySearch(arr: number[], target: number, left: number, right: number): number -> Option C

4. Quick Check:

   Parameters + return type match recursive binary search [OK]

Hint: Recursive binary search needs left and right indices [OK]

Common Mistakes:

• Missing left and right parameters
• Wrong return type (void or boolean)
• Mismatched array and target types

3. What will be the output of the following TypeScript code?

function binarySearch(arr: number[], target: number, left: number, right: number): number {
  if (left > right) return -1;
  const mid = Math.floor((left + right) / 2);
  if (arr[mid] === target) return mid;
  else if (arr[mid] > target) return binarySearch(arr, target, left, mid - 1);
  else return binarySearch(arr, target, mid + 1, right);
}

const nums = [2, 4, 6, 8, 10];
console.log(binarySearch(nums, 6, 0, nums.length - 1));

medium

A. 2

B. 1

C. -1

D. 3

Solution

1. Step 1: Identify middle index and compare

   Initial call: left=0, right=4, mid=2. arr[2] = 6 matches target 6.

2. Step 2: Return index when found

   Since arr[mid] equals target, function returns mid = 2 immediately.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Target found at index 2 [OK]

Hint: Check middle element first, then recurse [OK]

Common Mistakes:

• Miscomputing mid index
• Returning wrong index
• Confusing array values with indices

4. Find the error in this recursive binary search function:

function binarySearch(arr: number[], target: number, left: number, right: number): number {
  if (left >= right) return -1;
  const mid = Math.floor((left + right) / 2);
  if (arr[mid] === target) return mid;
  else if (arr[mid] > target) return binarySearch(arr, target, left, mid - 1);
  else return binarySearch(arr, target, mid + 1, right);
}

medium

A. The base case condition should be left > right, not left >= right

B. The mid calculation is incorrect

C. The function should return boolean instead of number

D. The recursive calls have wrong parameters

Solution

1. Step 1: Analyze base case condition

   The base case currently returns -1 if left >= right, but it should allow left == right to check that element.

2. Step 2: Correct base case to left > right

   Changing to left > right ensures the search includes the last element before stopping.

3. Final Answer:

   The base case condition should be left > right, not left >= right -> Option A

4. Quick Check:

   Base case must allow left == right [OK]

Hint: Base case stops when left passes right, not equals [OK]

Common Mistakes:

• Stopping search too early with wrong base case
• Miscomputing mid index
• Wrong return type

5. Given a sorted array arr = [1, 3, 5, 7, 9, 11, 13], write a recursive binary search call to find the index of 7. What will be the sequence of mid indices checked?

hard

A. [3, 5]

B. [3, 1]

C. [3, 1, 2]

D. [3]

Solution

1. Step 1: Calculate initial mid index

   left=0, right=6, mid = floor((0+6)/2) = 3. arr[3] = 7 matches target immediately.

2. Step 2: No further recursive calls needed

   Since target found at first mid, no other mid indices are checked.

3. Final Answer:

   [3] -> Option D

4. Quick Check:

   Target found at first mid index 3 [OK]

Hint: First mid often finds target if array is balanced [OK]

Common Mistakes:

• Assuming multiple recursive calls always happen
• Miscomputing mid index
• Confusing indices with values