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Your program is to first take as input 2 values: n indicates the number of values to be sorted, and k indicates the number of values to store in each heap. You may assume that n is a multiple of k. The program should then read a set of n integer values each of which is in the range 1..n.

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The program should represent the k values in each heap as an array. Create a min-heap from the first k values in the input list, a second min-heap from the next k values, etc. Note that because n is a multiple of k, the last heap also contains exactly k values. You should use the most efficient method to create each of these heaps. Join the heaps together in a linked list, so that the 1st heap points to the 2nd, etc.

Now apply a radix sort on the heaps, as follows:

⦁ Each individual data item in the heap should be considered a “digit” for the purposes of the radix sort. Therefore a heap of k values can be considered to have k digits. There are n possible values for each of these digits.

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⦁ At the end of the radix sort, the first heap in the linked list will be the “lowest” heap, the second will be the next “lowest”, etc.

Now repeatedly apply the following steps until the list of heaps is empty:

⦁ Remove the smallest item from the first heap, and print it. Replace this item with the smallest item from the second heap and apply trickle-down as necessary.

⦁ Repeat this process, inserting the smallest item from the third heap into the second heap, …, the smallest item from the last heap into the next-to-last heap.

⦁ When the last heap becomes empty, remove it from the linked list of heaps.

Part A (70 marks): Submit the results of running your program on the input in the following files, available from the course home page: assn3input1.txt, assn3input2.txt

For each of the above, print the initial list of values, and then print the item removed and the remaining data structure (i.e. “list of heaps”) as each item is removed, in a manner similar to the example shown on the following page.

Part B (20 marks): For this part, you must first construct a random sequence of integer values, with all values in the range 1..10000. This same random sequence must be used to compare the performance of your program for all of the following runs:

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(n = 10000, k = 10000), (n = 10000, k = 1000), (n = 10000, k = 100), (n = 10000, k = 10), (n = 10000, k = 1).

You should provide the following information for each run: execution time, total swaps required by trickle-down during initial construction of the heaps, and total swaps required as a result of a remove operation. Note: you can check the current time in milliseconds using System.currentTimeMillis().

Alternatively, you can investigate System.nanoTime(). Submit the results of this comparison, and write a short paragraph commenting on the results and what you think they mean.

For this part, the sorting output should be given electronically only, and should consist of only n, k, the initial list of items and the sorted list of items.

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