Binary Search Recursive Approach in DSA C - Build from Scratch

Binary Search Recursive Approach

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

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

📋 What You'll Learn

Create an array called books with these exact values: 2, 5, 8, 12, 16, 23, 38, 56, 72, 91

Create two integer variables low and high to represent the start and end indexes of the array

Write a recursive function binary_search that takes the array, low, high, and the target book ID as parameters

Print the result index returned by binary_search

💡 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 in a library database.

💼 Career

Understanding binary search and recursion is fundamental for software developers working with efficient data retrieval and algorithm design.

1

Create the sorted array of book IDs

Create an integer array called books with these exact values: 2, 5, 8, 12, 16, 23, 38, 56, 72, 91

DSA C

# Create the array books with the given values
# Your code here

Hint

Use int books[] = { ... }; to create the array with the exact numbers.

2

Set the low and high index variables

Create two integer variables called low and high. Set low to 0 and high to 9 (the last index of the array).

DSA C

int books[] = {2, 5, 8, 12, 16, 23, 38, 56, 72, 91};
// Create low and high variables
# Your code here

Hint

Remember the first index is 0 and the last index is 9 for 10 elements.

3

Write the recursive binary search function

Write a recursive function called binary_search that takes parameters: int arr[], int low, int high, and int target. It should return the index of target if found, or -1 if not found. Use the binary search logic with recursion.

DSA C

int books[] = {2, 5, 8, 12, 16, 23, 38, 56, 72, 91};
int low = 0;
int high = 9;

// Write the recursive binary_search function below
# Your code here

Hint

Use the middle index to compare and call the function recursively on the left or right half.

4

Call the function and print the result

Call binary_search with books, low, high, and target 23. Print the returned index using printf.

DSA C

int books[] = {2, 5, 8, 12, 16, 23, 38, 56, 72, 91};
int low = 0;
int high = 9;

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

// Call binary_search for target 23 and print the result
# Your code here

Hint

The index of 23 in the array is 5. Use printf("%d\n", result); to print it.

Practice

1. What is the main idea behind the binary search recursive approach when searching for an element in a sorted array?

easy

A. Check every element one by one from start to end

B. Divide the array into halves and search recursively in the half where the element can be

C. Sort the array first and then search linearly

D. Use a queue to store elements and search iteratively

Solution

1. Step 1: Understand binary search principle

   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 element might be, reducing the search space each time.

3. Final Answer:

   Divide the array into halves and search recursively in the half where the element can be -> Option B

4. Quick Check:

   Binary search = divide and conquer [OK]

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

Common Mistakes:

• Thinking binary search checks every element
• Not using recursion to reduce search space
• Searching unsorted arrays with binary search

2. Which of the following is the correct base case condition in a recursive binary search function in C?

easy

A. if (low == high) return -1;

B. if (low < high) return -1;

C. if (low > high) return -1;

D. if (low >= high) return -1;

Solution

1. Step 1: Understand base case in recursion

   The base case stops recursion when the search space is invalid, meaning low index is greater than high index.

2. Step 2: Identify correct condition

   When low > high, it means the element is not found, so return -1 to indicate failure.

3. Final Answer:

   if (low > high) return -1; -> Option C

4. Quick Check:

   Base case = low > high [OK]

Hint: Base case ends when low index passes high index [OK]

Common Mistakes:

• Using low == high as base case incorrectly
• Returning wrong value in base case
• Not handling base case leading to infinite recursion

3. What will be the output of the following C code snippet using recursive binary search?

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

int main() {
  int arr[] = {2, 4, 6, 8, 10};
  int n = 5;
  int result = binarySearch(arr, 0, n - 1, 6);
  printf("%d", result);
  return 0;
}

medium

A. 2

B. 1

C. -1

D. 3

Solution

1. Step 1: Trace the recursive calls

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

2. Step 2: Understand output

   The function returns index 2 where element 6 is found, so printf prints 2.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Element 6 found at index 2 [OK]

Hint: Check mid index and compare to target first [OK]

Common Mistakes:

• Confusing index with value
• Off-by-one errors in mid calculation
• Not returning correct index on match

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

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

medium

A. Return mid + 1 instead of mid when found

B. Change mid calculation to mid = low - (high - low) / 2;

C. Remove else if condition and use only if

D. Change base case to if (low > high) return -1;

Solution

1. Step 1: Analyze base case condition

   The base case uses if (low >= high) which incorrectly stops search when low equals high, missing the last element.

2. Step 2: Correct base case

   It should be if (low > high) to allow checking when low equals high, ensuring all elements are searched.

3. Final Answer:

   Change base case to if (low > high) return -1; -> Option D

4. Quick Check:

   Base case must allow low == high [OK]

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

Common Mistakes:

• Stopping recursion too early
• Incorrect mid calculation causing infinite recursion
• Returning wrong index on match

5. Given a sorted array arr = {1, 3, 5, 7, 9, 11, 13}, you want to find the index of element 8 using recursive binary search. What will be the sequence of mid indices checked before concluding the element is not found?

hard

A. [3, 5, 4]

B. [3, 1, 0]

C. [3, 1, 2]

D. [3, 4, 5]

Solution

1. Step 1: Calculate first mid index

   Initial low=0, high=6, mid = (0+6)/2 = 3, arr[3]=7 less than 8, search right half next.

2. Step 2: Calculate second mid index

   New low=4, high=6, mid = (4+6)/2 = 5, arr[5]=11 greater than 8, search left half next.

3. Step 3: Calculate third mid index

   New low=4, high=4, mid = (4+4)/2 = 4, arr[4]=9 greater than 8, search left half next low=4, high=3 ends recursion.

4. Final Answer:

   [3, 5, 4] -> Option A

5. Quick Check:

   Mid indices checked = 3, 5, 4 [OK]

Hint: Track low, high, mid updates carefully each recursion [OK]

Common Mistakes:

• Not updating low and high correctly
• Miscomputing mid index
• Stopping search too early