Binary search can be implemented using which programming approaches?

Question

BlackTom AI · Accepted Answer

Binary search divides a sorted collection by repeatedly halving the search interval until the target is found or the interval is empty. Relevant concepts: - Preconditions: the data must be sorted and ideally support random access (arrays). - Two common implementation patterns: iterative (loop) and recursive (function calls). - Time complexity: O(log n). Space: iterative O(1); recursive O(log n) due to call stack. Step-by-step reasoning (example): Given sorted array [1,3,5,7,9,11,13,15,17,19], search for 13. 1. Initialize low = 0, high = 9. 2. Compute mid = (low + high) // 2 = (0+9)//2 = 4 → a[4] = 9. Since 9 < 13, set low = mid + 1 = 5. 3. Compute mid = (5+9)//2 = 7 → a[7] = 15. Since 15 > 13, set high = mid - 1 = 6. 4. Compute mid = (5+6)//2 = 5 → a[5] = 11. Since 11 < 13, set low = 6. 5. Compute mid = (6+6)//2 = 6 → a[6] = 13 → found. Iterative approach: implement the above with a while (low <= high) loop updating low/high. Recursive approach: implement a function that checks mid and calls itself on the left or right subinterval until base case (low > high) or found. Both produce the same mid-updating logic; recursion just expresses it via function calls. Why the correct answer is correct: Binary search’s halving logic maps naturally to both a loop (explicit iteration) and recursion (implicit iteration via function calls). Both forms are standard and widely taught/used. Why other options are incorrect: - "Iterative only": false — recursion is a valid/standard implementation. - "Recursive only": false — iterative implementation is common and avoids recursion overhead. - "Only with linked lists": false — binary search requires efficient midpoint access; arrays are the typical structure. Linked lists need O(n) mid-finding, making binary search impractical. Conclusion: Binary search can be implemented using both iterative and recursive approaches — correct answer: Both iterative and recursive.

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