Binary Search as Divide and Conquer in DSA C - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to find the middle index in binary search.

DSA C

int mid = low + (high [1] low) / 2;

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

A-

B+

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication instead of addition.

Dividing before subtracting.

The middle index is calculated by adding low to half the difference between high and low.

2fill in blank

medium

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

DSA C

if (arr[mid] [1] target) return mid;

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

A==

B<

C>

D!=

Attempts:

3 left

💡 Hint

Common Mistakes

Using assignment operator '=' instead of comparison '=='.

Using inequality operators instead of equality.

We check if the middle element equals the target to return its index.

3fill in blank

hard

Fix the error in updating the low index when target is greater than middle element.

DSA C

if (arr[mid] < target) low = [1];

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

Amid

Bmid + 1

Cmid - 1

Dlow + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Setting low to mid instead of mid + 1.

Decreasing low index.

If the target is greater than the middle element, we move low to mid + 1 to search the right half.

4fill in blank

hard

Fill both blanks to update high index when target is less than middle element.

DSA C

if (arr[mid] > target) high = [1]; else low = [2];

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

Amid - 1

Bmid + 1

Cmid

Dhigh - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using mid instead of mid - 1 or mid + 1.

Swapping low and high updates.

If target is less, high moves to mid - 1; else low moves to mid + 1.

5fill in blank

hard

Fill all three blanks to complete the binary search function.

DSA C

int binarySearch(int arr[], int low, int high, int target) {
    while (low <= high) {
        int mid = low + (high [1] low) / 2;
        if (arr[mid] == target) return [2];
        else if (arr[mid] < target) low = mid [3] 1;
        else high = mid - 1;
    }
    return -1;
}

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

A+

Bmid

C-

Dlow

Attempts:

3 left

💡 Hint

Common Mistakes

Incorrect mid calculation causing infinite loops.

Returning wrong index or updating low/high incorrectly.

The middle index is calculated by adding low to half the difference (high - low). If the middle element matches target, return mid. If target is greater, move low to mid + 1.

Practice

1. What is the main idea behind Binary Search as a divide and conquer algorithm?

easy

A. It searches every element one by one until the target is found.

B. It divides the search range in half each time to find the target efficiently.

C. It sorts the array before searching for the target.

D. It uses recursion to add all elements in the array.

Solution

1. Step 1: Understand divide and conquer in binary search

   Binary search splits the array into two halves and decides which half to search next.

2. Step 2: Identify the efficiency of halving the search space

   By halving the search space each time, it quickly narrows down the target location.

3. Final Answer:

   It divides the search range in half each time to find the target efficiently. -> Option B

4. Quick Check:

   Divide and conquer = halving search space [OK]

Hint: Binary search halves the search space each step [OK]

Common Mistakes:

• Thinking binary search checks every element
• Confusing binary search with sorting
• Believing binary search sums elements

2. Which of the following is the correct syntax to calculate the middle index in binary search in C?

easy

A. int mid = (low + high) / 2;

B. int mid = (low * high) / 2;

C. int mid = low + (high - low) / 2;

D. int mid = (low - high) / 2;

Solution

1. Step 1: Understand safe middle index calculation

   Using low + (high - low) / 2 prevents integer overflow when low and high are large.

2. Step 2: Compare with other options

   int mid = (low + high) / 2; can overflow if low + high exceeds integer limit; options B and C are incorrect formulas.

3. Final Answer:

   int mid = low + (high - low) / 2; -> Option C

4. Quick Check:

   Safe mid calculation = low + (high - low)/2 [OK]

Hint: Use low + (high - low)/2 to avoid overflow [OK]

Common Mistakes:

• Using (low + high)/2 causing overflow
• Subtracting incorrectly in mid calculation
• Multiplying low and high instead of adding

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

int arr[] = {2, 4, 6, 8, 10};
int low = 0, high = 4, target = 6;
while (low <= high) {
  int mid = low + (high - low) / 2;
  if (arr[mid] == target) {
    printf("%d", mid);
    break;
  } else if (arr[mid] < target) {
    low = mid + 1;
  } else {
    high = mid - 1;
  }
}

medium

A. 2

B. 3

C. 1

D. 4

Solution

1. Step 1: Trace the binary search steps

   Initial low=0, high=4, mid=2. arr[2]=6 matches target 6.

2. Step 2: Print the mid index

   Since arr[mid] == target, the code prints 2 and breaks the loop.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Target found at index 2 [OK]

Hint: Check mid index value matches target first [OK]

Common Mistakes:

• Not updating low and high correctly
• Confusing index with value
• Off-by-one errors in mid calculation

4. Identify the error in this binary search code snippet and choose the correct fix:

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

medium

A. Change while condition to low <= high

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

C. Remove else if and use only if statements

D. Return 0 instead of -1 when not found

Solution

1. Step 1: Analyze the loop condition

   The loop uses while (low < high), which misses checking when low equals high.

2. Step 2: Correct the loop condition

   Changing to while (low <= high) ensures the last element is checked.

3. Final Answer:

   Change while condition to low <= high -> Option A

4. Quick Check:

   Loop must include low == high to check all elements [OK]

Hint: Use while(low <= high) to include all elements [OK]

Common Mistakes:

• Using < instead of <= in loop condition
• Incorrect mid calculation causing overflow
• Returning wrong value when target not found

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

hard

A. Use linear search instead of binary search.

B. Return the first found index immediately without further search.

C. Search only the right half after finding the target.

D. After finding target, continue searching left half to find earlier occurrence.

Solution

1. Step 1: Understand duplicates in binary search

   Standard binary search returns any occurrence, not necessarily the first.

2. Step 2: Modify search to find first occurrence

   After finding target at mid, continue searching left half to check for earlier occurrences.

3. Final Answer:

   After finding target, continue searching left half to find earlier occurrence. -> Option D

4. Quick Check:

   Find first occurrence by searching left after match [OK]

Hint: Search left half after match to find first occurrence [OK]

Common Mistakes:

• Stopping at first found index ignoring duplicates
• Searching right half instead of left after match
• Switching to linear search unnecessarily