Binary Search Recursive Approach in DSA Typescript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Recursive Binary Search on Sorted Array

What is the output of the following TypeScript code that uses recursive binary search to find the index of the target value 7?

DSA Typescript

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 array = [1, 3, 5, 7, 9, 11];
const result = binarySearch(array, 7, 0, array.length - 1);
console.log(result);

A -1

B 3

C 2

D 4

💡 Hint

Think about the position of 7 in the sorted array and how binary search divides the array.

The array is [1, 3, 5, 7, 9, 11]. The target 7 is at index 3 (0-based). The recursive binary search finds it and returns 3.

❓ Predict Output

intermediate

Result when target is not in the array

What does the recursive binary search function return when searching for the target value 8 in the array [2, 4, 6, 10, 12]?

DSA Typescript

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 array = [2, 4, 6, 10, 12];
const result = binarySearch(array, 8, 0, array.length - 1);
console.log(result);

A -1

B 2

C 3

D 0

💡 Hint

If the target is not found, the function returns -1.

The target 8 is not in the array. The recursive calls eventually cross over (left > right), so the function returns -1.

🧠 Conceptual

advanced

Understanding Recursive Call Depth in Binary Search

If you perform a recursive binary search on a sorted array of 64 elements, what is the maximum number of recursive calls that can happen before the search ends?

A 6

B 64

C 7

D 8

💡 Hint

Binary search divides the array size by 2 each call. Think about powers of 2.

Binary search halves the search space each call. For 64 elements (2^6), the worst-case recursion depth is log₂(64) + 1 = 7 calls total (6 recursive calls + initial).

🔧 Debug

advanced

Identify the error in this recursive binary search implementation

What error will this TypeScript recursive binary search code produce when searching for target 7 in array [1, 3, 5, 7]?

DSA Typescript

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 array = [1, 3, 5, 7];
const result = binarySearch(array, 7, 0, array.length - 1);
console.log(result);

A Returns -1 even though target exists

B Throws a runtime error due to infinite recursion

C Returns the wrong index (off by one)

D Returns the correct index 2

💡 Hint

Check the base case condition carefully.

The base case uses 'left >= right' which causes the function to return -1 prematurely when left equals right, missing the last element check. So it returns -1 even if the target is present.

🚀 Application

expert

Find the first occurrence of a target in a sorted array with duplicates using recursive binary search

Given a sorted array with duplicates, which recursive binary search modification correctly returns the index of the first occurrence of the target value 4 in [1, 2, 4, 4, 4, 5, 6]?

DSA Typescript

function firstOccurrence(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) {
    if (mid === 0 || arr[mid - 1] < target) return mid;
    else return firstOccurrence(arr, target, left, mid - 1);
  } else if (arr[mid] < target) {
    return firstOccurrence(arr, target, mid + 1, right);
  } else {
    return firstOccurrence(arr, target, left, mid - 1);
  }
}

const array = [1, 2, 4, 4, 4, 5, 6];
const result = firstOccurrence(array, 4, 0, array.length - 1);
console.log(result);

A -1

B 3

C 4

D 2

💡 Hint

Check if the found target is the first or if you need to search left side.

The function finds the first index where 4 appears by checking if the previous element is less than 4 or if it's the first element. The first occurrence of 4 is at index 2.

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