The decrease by variable factor approach involves reducing the problem size by a variable factor in each step. Which algorithm uses this approach?

The correct answer is Option 1) Merge sort.

Key Points

• Merge Sort uses the Decrease by Variable Factor approach by dividing the problem into smaller parts in each recursive step.
• In merge sort, the array is recursively divided into subarrays — typically halves — and then merged after sorting.
• Though typically split in halves, the actual size of subarrays in recursive calls may vary depending on implementation and size, hence the term variable factor.
• It follows the Divide and Conquer strategy:
  1. Divide the array into two (or more) parts
  2. Recursively sort each part
  3. Merge the sorted parts
• Time complexity: O(n log n) in all cases (best, average, and worst)

Additional Information

• Option 2 – Bubble Sort: Uses a simple comparison approach, not based on decreasing the problem size by a factor.
• Option 3 – Selection Sort: Selects the smallest (or largest) element and places it correctly; no recursive size reduction involved.
• Option 4 – Insertion Sort: Builds the final sorted array one item at a time; again, no divide-and-conquer or variable factor reduction used.
• Conclusion: Only Merge Sort among these follows the decrease by variable factor (via recursive subproblems) approach.