Binary Search as Divide and Conquer in DSA C - Build from Scratch

Binary Search as Divide and Conquer

📖 Scenario: You have a sorted list of book page numbers where a special note is hidden. You want to find the page number quickly using a method that splits the search area in half each time.

🎯 Goal: Build a C program that uses binary search to find a target page number in a sorted array of page numbers.

📋 What You'll Learn

Create a sorted array of integers called pages with the exact values: 2, 5, 8, 12, 16, 23, 38, 56, 72, 91

Create an integer variable called target and set it to 23

Write a function called binary_search that takes the array, its size, and the target, and returns the index of the target or -1 if not found

Print the index returned by binary_search

💡 Why This Matters

🌍 Real World

Binary search is used in many real-world applications like searching in phone books, dictionaries, or databases where data is sorted.

💼 Career

Understanding binary search helps in optimizing search operations in software development, improving performance in data retrieval tasks.

1

Create the sorted array of page numbers

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

DSA C

# Create the array pages with the given values
// Your code here

Hint

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

2

Set the target page number

Create an integer variable called target and set it to 23 inside the main function.

DSA C

#include 

int pages[] = {2, 5, 8, 12, 16, 23, 38, 56, 72, 91};

int main() {
    // Create target variable and set to 23
    // Your code here
    return 0;
}

Hint

Inside main, write int target = 23;.

3

Write the binary search function

Write a function called binary_search that takes int arr[], int size, and int target as parameters. Use a divide and conquer approach with low, high, and mid variables to find the target. Return the index if found, or -1 if not found.

DSA C

#include 

int pages[] = {2, 5, 8, 12, 16, 23, 38, 56, 72, 91};

// Write binary_search function here
// Your code here

int main() {
    int target = 23;
    return 0;
}

Hint

Use a while loop with low and high to narrow down the search. Calculate mid and compare arr[mid] with target.

4

Call binary_search and print the result

Call binary_search with pages, its size 10, and target. Store the result in an integer variable called index. Then print index using printf.

DSA C

#include 

int pages[] = {2, 5, 8, 12, 16, 23, 38, 56, 72, 91};

int binary_search(int arr[], int size, int target) {
    int low = 0;
    int high = size - 1;
    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;
}

int main() {
    int target = 23;
    // Call binary_search and print the index
    // Your code here
    return 0;
}

Hint

Call binary_search(pages, 10, target), save to index, then print index with printf("%d\n", index);.

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