Assume that we haveksorted files, of sizesn1,n2, ..., nKand we want tomerge them to one sorted file. (Size is number of elements in the file.) Design a divide and conquer algorithm for this purpose, and derive its time complexity. You should describe the algorithm, first, and then write a recurrence relation, and then derive the time complexity of the algorithm. ( Assume that you have a linear time merge algorithm for merging two sorted files. )

Assume we capture students' webpage browsing records. We separate the records into two files: male and female, each with more than 10 billion records. The format of each record is: [student ID], [gender], [date], [time], [url], and they are not sorted. The main memory we can use is 16GB. We try to find the common urls visited by male and female students. Please use MapReduce to solve this problem. Some important points you must clarify: 1. How to separate data? 2. What is the Map task? What's the format of <key, value> pairs? 3. What is the Reduce task? How do we get the final results? You may earn extra credits if you can optimize your soultion.

1. Stable sorting algorithms maintain the relative order of records with equal keys (i.e. values). That is, a sorting algorithm is stable if whenever there are two records R and S with the same key (i.e. value) and with R appearing before S in the original list, R will appear before S in the sorted list. Consider Insertion Sort, Merge Sort, Quick Sort. Which of these is not a stable sorting algorithm? Justify your answer.

Given this array containing characters: Data X B A L J Z K C D M Index 0 1 2 3 4 5 6 789 What pivot is selected for partitioning when using the median-of-three algorithm? A/