MPATE-GE 2618: C Programming for Music Technology. Unit 4.3

Transcription

1 MPATE-GE 68: C Programming for Music Technology Unit 4.

2 Heap sort Heap sort is a variant of selection sort. However, it improves on selection sort greatly by using a new data structure called a heap to speed up finding the smallest remaining value. e heap allows finding the next smallest element to be O(log n) instead of O(n) as is the case for selection sort. us the worst-case running time for heap sort is O(n log n).

3 Heaps A balanced binary tree e depth of a node in a binary tree is the distance from that node to the root. Let d be the maximum depth of a node in a tree In a balanced binary tree, every leaf has depth either d or d- Each parent has a value greater than or equal to its children Balanced Unbalanced A Heap 7 6

4 Heapsort algorithm How can we use a heap to sort?. Arrange data in a heap.. Remove the root (largest element).. Move a leaf of the tree and make it the root. 4. Reheap the tree.. Go back to.

5 Heapsort Remove root (largest element) Make a leaf node the root Reheap 6 Remove root Make a leaf node the root Reheap

6 Remove root Heapsort Make a leaf node the root Reheap Remove root Make a leaf node the root Reheap Remove root Make a leaf node the root DONE

7 Using arrays to represent binary trees Trees represented by arrays Put the root of the tree at array[0] Left child of index i is (i * ) + Right child of index i is (i * ) + e parent of index i is (i-) / Now we can combine steps and in our algorithm:. Remove root (largest element). Move a leaf of the tree and make it the root We can exchange the root with the leaf and then treat and then treat the array as being one element smaller. A[0] A[] A[] A[0] A[] A[] A[] A[4] A[] A[6] A[] A[4] A[] A[6]

8 Swap root and last leaf Heapsort Reheap first n- elements Swap root and last leaf 9 0 Swap root and last leaf 9 0 Swap root and last leaf 9 0 Swap root and last leaf 9 0 Reheap 9 0 Reheap 9 0 Reheap 9 0 Reheap 9 0 Swap root and last leaf 9 0

9 Heap sort: analysis Analysis: Running time is O(n log n) Building the initial heap (heapify) from the array takes O(n) time. For n elements, the depth of the heap is at most d = log n. Each reheaping (sifting) takes at most d comparisons and d + moves, which is O(log n) time. Pros: doesn t use extra memory or recursion Cons: slower than merge sort and quick sort

10 Websites with sorting demos

11 AIFF format Audio Interchange File Format (AIFF) is a file format for storing digital audio (waveform) data. It supports a variety of bit resolutions, sample rates, and channels of audio. It s popular on Apple platforms and is widely used in professional programs that process digital audio. e format uses the Interchange File Format (IFF) method for storing data in chunks. IFF is a generic file format originally introduced by the Electronic Arts company in 98 (in cooperation with Commodore-Amiga) in order to ease transfer of data between software products produced by different companies.

12 IFF chunk Each chunk begins with what the IFF spec calls a Type ID is is followed by a -bit unsigned integer (all integers in IFF files structure are big-endian) specifying the size of the following data (the chunk content) in bytes. Because the spec includes explicit lengths for each chunk, it is possible for a parser to skip over chunks which it either can't or doesn't care to process.

13 AIFF chunk types An Audio IFF file is a collection of a number of different types of chunks. e main encapsulating chunk for all AIFF files is a FORM chunk. Within the FORM there is a required Common Chunk which contains important parameters describing the waveform, such as its length and sample rate. e Sound Data chunk, which contains the actual waveform data, is also required if the waveform data has a length greater than 0 (i.e., there actually is waveform data in the FORM). All other chunks are optional. Among the other optional chunks are ones which define markers, list instrument parameters, store application-specific information, etc. Example: see audio.c in PS4

14 Binary file I/O Reading binary data: use fread and fwrite. Open files using fopen as before, but add a b to mode string. FILE *inptr = fopen(infile, "rb"); FILE *outptr = fopen(outfile, "wb"); int num; fread(&num, sizeof(int),, inptr); fwrite(&num, sizeof(int),, outptr); fread and fwrite take 4 parameters: e location you re reading into or from e size of the object type in bytes e number of those objects to be read/written Pointer to a file See files distributed with Problem Set 4 for examples