is divided into smaller chunks that can fit into memory. In this phase, we read the input data sequentially and write the chunks to temporary files. 5. Intermediate Sorting Phase: Each of the temporary files created in the initial splitting phase is sorted in memory. For each file, you read its content into memory, sort it, and write the sorted data back to a new temporary file. 6. 7. Merging Phase: The sorted temporary files are merged together in a way that minimizes the number of passes. In this phase, data is read from the temporary files and written into a final output file. To calculate the cost of performing this modified external merge sort, you can break down the costs into these phases: Sequential Reads: You mentioned that 8 sequential reads are "free" and that the cost of 8 sequential reads is 1. You'll want to count how many sets of 8 sequential reads are needed in each phase (initial splitting, intermediate sorting, and merging). For any leftover reads, you can apply the cost of single reads. Sequential Writes: Sequential writes are never free. You mentioned that the cost of N writes is always 2N. So, count the total number of writes in each phase and calculate the cost accordingly. Here's a simplified example to illustrate how to calculate the cost: Suppose you have an external merge sort with: Input size: 80 pages Memory can hold: 10 pages Number of temporary files created in the initial splitting phase: 8 Number of temporary files created in the merging phase: 2 1. Initial Splitting Phase: Sequential Reads: 10 reads per file x 8 files 80 reads = Sequential Writes: 10 writes per file x 8 files 80 writes 2. Intermediate Sorting Phase (Assuming each sorted file fits in memory): B. Sequential Reads: 1 read per file x 8 files 8 reads Sequential Writes: 2 writes per file x 8 files 16 writes 4. Merging Phase: