Sorting 1 GB of data with only 100 MB of available main memory

To sort 1 GB of data with only 100 MB of available main memory, we need to choose a sorting technique that can efficiently handle external sorting, where data is too large to fit entirely in main memory. Among the given options, merge sort is the most appropriate choice. Here's why:

Merge Sort
Merge sort is a divide and conquer algorithm that is well-suited for external sorting. It works by splitting the input into smaller chunks, sorting them individually, and then merging them back together.

Advantages of Merge Sort for External Sorting:
1. Efficient use of memory: Merge sort is designed to minimize the amount of memory required for sorting. It can handle large datasets by dividing them into smaller chunks that can fit into memory.
2. Stable sorting: Merge sort is a stable sorting algorithm, meaning that it preserves the relative order of elements with equal values. This is important when sorting data that is already partially sorted or contains duplicate values.
3. Good worst-case time complexity: Merge sort has a worst-case time complexity of O(n log n), which is efficient for large datasets. This makes it suitable for sorting 1 GB of data.
4. Easy to implement: Merge sort has a simple and intuitive algorithmic structure, making it easier to implement and debug.

How Merge Sort Works for External Sorting:
1. Divide: The input data is divided into smaller chunks that can fit into memory (e.g., 100 MB in this case).
2. Sort: Each chunk is sorted individually using an in-memory sorting algorithm like quick sort or insertion sort.
3. Merge: The sorted chunks are merged back together using a merge operation that compares and combines the elements in a sorted manner. This can be done efficiently even if the chunks are too large to fit in memory at once, by reading and writing data from/to external storage (e.g., hard disk).

Conclusion
Considering the constraints of limited available memory and the need for efficient external sorting, merge sort is the most appropriate technique among the given options. It provides efficient memory utilization, stability, good worst-case time complexity, and ease of implementation.