Binary Search Recursive Approach in DSA Go - Build from Scratch

Binary Search Recursive Approach

📖 Scenario: You have a sorted list of book IDs in a library system. You want to find if a specific book ID exists using a fast method.

🎯 Goal: Build a recursive binary search function in Go to find a book ID in a sorted list.

📋 What You'll Learn

Create a sorted slice of integers called bookIDs with exact values

Create two integer variables left and right for the search range

Write a recursive function binarySearch that takes bookIDs, left, right, and target as parameters

The function returns the index of target if found, or -1 if not found

Call the function with the correct parameters and print the result

💡 Why This Matters

🌍 Real World

Binary search is used in many software systems to quickly find data in sorted lists, like searching for a book ID in a library database.

💼 Career

Understanding binary search helps in roles involving data processing, software development, and algorithm optimization.

1

Create the sorted list of book IDs

Create a slice of integers called bookIDs with these exact values: 2, 5, 8, 12, 16, 23, 38, 56, 72, 91

DSA Go

bookIDs := []int{2, 5, 8, 12, 16, 23, 38, 56, 72, 91}
// Your code here

Hint

Use a slice literal with the exact numbers in order.

2

Set the initial search range variables

Create two integer variables called left and right. Set left to 0 and right to the last index of bookIDs (which is 9).

DSA Go

package main

import "fmt"

func main() {
    bookIDs := []int{2, 5, 8, 12, 16, 23, 38, 56, 72, 91}
    left := 0
    right := 9
    // Your code here
}

Hint

Remember the last index is length minus one.

3

Write the recursive binary search function

Write a recursive function called binarySearch that takes parameters bookIDs []int, left int, right int, and target int. It should return an int. Implement the binary search logic: if left is greater than right, return -1. Otherwise, find the middle index, compare bookIDs[middle] with target, and recursively search the left or right half accordingly.

DSA Go

package main

import "fmt"

func main() {
    bookIDs := []int{2, 5, 8, 12, 16, 23, 38, 56, 72, 91}
    left := 0
    right := 9
}

func binarySearch(bookIDs []int, left int, right int, target int) int {
    // Your code here
}

Hint

Use the middle index formula and recursive calls for left and right halves.

4

Call the function and print the result

Call binarySearch with bookIDs, left, right, and target set to 23. Store the result in a variable called index. Then print index.

DSA Go

package main

import "fmt"

func main() {
    bookIDs := []int{2, 5, 8, 12, 16, 23, 38, 56, 72, 91}
    left := 0
    right := 9
    index := binarySearch(bookIDs, left, right, 23)
    // Your code here
}

func binarySearch(bookIDs []int, left int, right int, target int) int {
    if left > right {
        return -1
    }
    middle := left + (right-left)/2
    if bookIDs[middle] == target {
        return middle
    } else if bookIDs[middle] > target {
        return binarySearch(bookIDs, left, middle-1, target)
    } else {
        return binarySearch(bookIDs, middle+1, right, target)
    }
}

Hint

The index of 23 in the list is 5. Use fmt.Println to print the index.

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