# 35 - 04/20/09 20:17:40 1 35 CS 61B: Lecture 36 Monday,...

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Unformatted text preview: 04/20/09 20:17:40 1 35 CS 61B: Lecture 36 Monday, April 20, 2009 Counting Sort------------- If the items we sort are naked keys, with no associated values, bucket sort can be simplified to become _counting_sort_. In counting sort, we don’t need queues at all; we need merely keep a count of how many copies of each key we have encountered. Suppose we sort 6 7 3 0 3 1 5 0 3 7: 0 1 2 3 4 5 6 7----------------------------------------------------------------- counts | 2 | 1 | 0 | 3 | 0 | 1 | 1 | 2 |----------------------------------------------------------------- When we are finished counting, it is straightforward to reconstruct the sorted keys from the counts: 0 0 1 3 3 3 5 6 7 7. Counting Sort with Complete Items--------------------------------- Now let’s go back to the case where we have complete items (key plus associated value). We can use a more elaborate version of counting sort. The trick is to use the counts to find the right index to move each item to. Let x be an input array of objects with keys (and perhaps other information). 0 1 2 3 4 5 6 7 8 9 ----------------------------------------------------------------------- x | . | . | . | . | . | . | . | . | . | . |----|------|------|------|------|------|------|------|------|------|--- v v v v v v v v v v ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- | 6 | | 7 | | 3 | | 0 | | 3 | | 1 | | 5 | | 0 | | 3 | | 7 |----- ----- ----- ----- ----- ----- ----- ----- ----- ----- Begin by counting the keys in x. for (i = 0; i < x.length; i++) { counts[x[i].key]++; } Next, do a _scan_ of the "counts" array so that counts[i] contains the number of keys _less_than_ i. 0 1 2 3 4 5 6 7----------------------------------------------------------------- counts | 0 | 2 | 3 | 3 | 6 | 6 | 7 | 8 |----------------------------------------------------------------- total = 0; for (j = 0; j < counts.length; j++) { c = counts[j]; counts[j] = total; total = total + c; } Let y be the output array, where we will put the sorted objects. counts[i] tells us the first index of y where we should put items with key i. Walk through the array x and copy each item to its final position in y. When you copy an item with key k, you must increment counts[k] to make sure that the next item with key k goes into the next slot. for (i = 0; i < x.length; i++) { y[counts[x[i].key]] = x[i]; counts[x[i].key]++; }--------------------- --------------------------------- y |.|.|.|.|.|.|.|.|.|.| counts | 0 | 2 | 3 | 3 | 6 | 6 | 8 | 8 |---------------|----- --------------------------------- v 6---------------------...
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## This note was uploaded on 02/21/2010 for the course CS 61B taught by Professor Canny during the Spring '01 term at Berkeley.

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35 - 04/20/09 20:17:40 1 35 CS 61B: Lecture 36 Monday,...

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