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notes87

# notes87 - Sorting using Priority Queues Selection sort-it...

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Sorting using Priority Queues Selection sort -it uses an unsorted-list priority queue Phase 1: insert items from sequence s into priority queue p . Phase 2: Remove items from p one by one and insert them into s . S = {5, 9, 3, 6} P = { } Phase 1: insert items from s into p S = { } P = {5, 9, 3, 6} O(n) Phase 2: remove items from p one by one and insert into s. Find the minimum value first and remove from p then place into s. S = {3} P = {5, 9, 6} O (n) 1 S = {3, 5} P = {9, 6} O (n) 2 S = {3, 5, 6} P = {9} O (n) 3 S = {3, 5, 6, 9}P = { } O (n) 4 = O (n 2 ) And ta da! S is sorted. Insertion Sort -it uses a priority queue with a sorted sequence -it uses the same steps as selection sort; the only difference is that it uses a sorted sequence. S = {5, 9, 3, 6} P = { } Phase 1: remove items from s and insert into p in order S = {9, 3, 6} P = {5} S = {3, 6} P = {5, 9} S = {6} P = {3, 5, 9} S = { } P = {3, 5, 6, 9} This step is O (n 2 ) Phase 2: remove items from P and put back into S S = {3, 5, 6, 9} P = { } This step is O (n)

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Both selection and insertion sort will take O (n 2 ) -Selection sort will always take a number of operations proportional to O (n 2 )
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notes87 - Sorting using Priority Queues Selection sort-it...

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