Binary Search Recursive Approach in DSA Go - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the middle index in the recursive binary search.

DSA Go

mid := low + ([1] - low) / 2

Drag options to blanks, or click blank then click option'

Ahigh

Blen(arr)

Cmid

Dlow

Attempts:

3 left

💡 Hint

Common Mistakes

Using low instead of high causes incorrect middle calculation.

Using length of array instead of high index.

The middle index is calculated as low plus half the distance between high and low.

2fill in blank

medium

Complete the code to check if the middle element is equal to the target value.

DSA Go

if arr[mid] == [1] {

Drag options to blanks, or click blank then click option'

Amid

Blow

Chigh

Dtarget

Attempts:

3 left

💡 Hint

Common Mistakes

Comparing with index instead of target value.

Using low or high instead of target.

We compare the middle element with the target value to find a match.

3fill in blank

hard

Fix the error in the recursive call when the target is less than the middle element.

DSA Go

return binarySearch(arr, low, [1], target)

Drag options to blanks, or click blank then click option'

Ahigh

Bmid + 1

Cmid - 1

Dlow

Attempts:

3 left

💡 Hint

Common Mistakes

Using mid + 1 searches the right half incorrectly.

Using low or high without adjustment causes infinite recursion.

When target is less than middle element, search left half by setting high to mid - 1.

4fill in blank

hard

Fill both blanks to correctly call the recursive function when the target is greater than the middle element.

DSA Go

return binarySearch(arr, [1], [2], target)

Drag options to blanks, or click blank then click option'

Amid + 1

Bmid - 1

Chigh

Dlow

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping low and high values.

Using mid - 1 instead of mid + 1 for low.

When target is greater, search right half by setting low to mid + 1 and keeping high same.

5fill in blank

hard

Fill all three blanks to complete the base case that stops recursion when the target is not found.

DSA Go

if [1] > [2] {
    return [3]
}

Drag options to blanks, or click blank then click option'

Alow

Bhigh

C-1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Returning 0 instead of -1.

Checking if high > low instead of low > high.

If low is greater than high, target is not in array, so return -1.

Practice

1. What is the main idea behind the binary search recursive approach on a sorted array?

easy

A. Sort the array first and then search linearly

B. Divide the array into halves and search recursively in the half where the target may exist

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

D. Use a queue to store elements and search iteratively

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 comparison with 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 half where the target may exist -> Option B

4. Quick Check:

   Binary search = divide and conquer [OK]

Hint: Remember: binary search splits array and searches half recursively [OK]

Common Mistakes:

• Trying to search linearly instead of dividing
• Not using recursion properly
• Ignoring that array must be sorted

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

easy

A. func binarySearch(arr []int, target int, mid int) int

B. func binarySearch(arr []int, target int) int

C. func binarySearch(arr []int, target int, low int, high int) int

D. func binarySearch(arr []int) int

Solution

1. Step 1: Identify parameters needed for recursion

   Recursive binary search needs the array, target, and the current low and high indices to know the search range.

2. Step 2: Check function signatures

   func binarySearch(arr []int, target int, low int, high int) int includes low and high indices, which are essential for recursion. Others miss these or have incorrect parameters.

3. Final Answer:

   func binarySearch(arr []int, target int, low int, high int) int -> Option C

4. Quick Check:

   Parameters include low and high indices [OK]

Hint: Recursive binary search needs low and high index parameters [OK]

Common Mistakes:

• Omitting low and high indices in parameters
• Adding unnecessary parameters like mid
• Using wrong return types

3. What will be the output of the following Go code snippet?

func binarySearch(arr []int, target, low, high int) int {
    if low > high {
        return -1
    }
    mid := (low + high) / 2
    if arr[mid] == target {
        return mid
    } else if arr[mid] > target {
        return binarySearch(arr, target, low, mid-1)
    } else {
        return binarySearch(arr, target, mid+1, high)
    }
}

func main() {
    arr := []int{2, 4, 6, 8, 10}
    result := binarySearch(arr, 6, 0, len(arr)-1)
    fmt.Println(result)
}

medium

A. 0

B. 3

C. -1

D. 2

Solution

1. Step 1: Trace the recursive calls for target 6

   Initial call: low=0, high=4, mid=2, arr[2]=6 equals target, so return 2 immediately.

2. Step 2: Confirm output

   Since target found at index 2, output is 2.

3. Final Answer:

   2 -> Option D

4. Quick Check:

   Target 6 found at index 2 [OK]

Hint: Check mid index value first to find target quickly [OK]

Common Mistakes:

• Confusing index with value
• Not updating low and high correctly
• Returning wrong index or -1 incorrectly

4. Identify the error in the following recursive binary search function and select the fix:

func binarySearch(arr []int, target, low, high int) int {
    if low >= high {
        return -1
    }
    mid := (low + high) / 2
    if arr[mid] == target {
        return mid
    } else if arr[mid] > target {
        return binarySearch(arr, target, low, mid-1)
    } else {
        return binarySearch(arr, target, mid+1, high)
    }
}

medium

A. Change condition to if low > high instead of low >= high

B. Change mid calculation to mid := (low + high + 1) / 2

C. Return 0 instead of -1 when not found

D. Remove else if and use only if statements

Solution

1. Step 1: Analyze base case condition

   The base case should stop recursion when low is greater than high, meaning no elements left to search. Using low >= high skips searching when low equals high, missing that element.

2. Step 2: Correct the condition

   Changing to low > high allows searching the last element when low equals high.

3. Final Answer:

   Change condition to if low > high instead of low >= high -> Option A

4. Quick Check:

   Base case must allow low == high search [OK]

Hint: Base case should be low > high, not low >= high [OK]

Common Mistakes:

• Stopping recursion too early with wrong base case
• Incorrect mid calculation causing infinite recursion
• Returning wrong default value when not found

5. Given a sorted array with possible duplicate elements, how can you modify the recursive binary search to find the first occurrence of a target value?

hard

A. When target found, check if previous element is same; if yes, search left half recursively

B. Return the first found index immediately without further checks

C. Search only the right half recursively after finding target

D. Use linear search after binary search to find first occurrence

Solution

1. Step 1: Understand duplicates in binary search

   Standard binary search returns any occurrence of target. To find first occurrence, we must check if earlier elements are also equal.

2. Step 2: Modify recursion to check left side

   When target found at mid, check if mid is first index or previous element is different. If previous element is same, recursively search left half to find earlier occurrence.

3. Final Answer:

   When target found, check if previous element is same; if yes, search left half recursively -> Option A

4. Quick Check:

   Check left side for first occurrence [OK]

Hint: On finding target, move left if previous equals target [OK]

Common Mistakes:

• Returning first found index without checking duplicates
• Searching right half instead of left for first occurrence
• Using linear search unnecessarily