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Data Structures and Algorithms Sorting Bin Sorts PLSD210

Lecture 9 - Key Points ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Sorting ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Sorting - Better than O(n log n) ? ,[object Object],[object Object],[object Object],[object Object]

Sorting - Bin Sort ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Sorting - Bin Sort: Analysis ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Key condition

Sorting - Bin Sort: Caveat ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Sorting - Bin Sort with duplicates ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Relax?

Sorting - Generalised Bin Sort ,[object Object],[object Object],[object Object],[object Object],36 9 0 25 1 49 64 16 81 4 0 1 2 3 4 5 6 7 8 9 0 1 81 64 4 25 36 16 9 49

Sorting - Generalised Bin Sort ,[object Object],[object Object],[object Object],0 1 2 3 4 5 6 7 8 9 0 1 81 64 4 25 36 16 9 49 0 1 2 3 4 5 6 7 8 9 0

Sorting - Generalised Bin Sort ,[object Object],[object Object],[object Object],0 1 2 3 4 5 6 7 8 9 0 1 81 64 4 25 36 16 9 49 0 1 2 3 4 5 6 7 8 9 0 1 Be careful to add after anything in the bin already!

Sorting - Generalised Bin Sort ,[object Object],[object Object],[object Object],0 1 2 3 4 5 6 7 8 9 0 1 81 64 4 25 36 16 9 49 0 1 2 3 4 5 6 7 8 9 0 1 81

Sorting - Generalised Bin Sort ,[object Object],[object Object],[object Object],0 1 2 3 4 5 6 7 8 9 0 1 81 64 4 25 36 16 9 49 0 1 2 3 4 5 6 7 8 9 0 1 81 64

Sorting - Generalised Bin Sort ,[object Object],[object Object],[object Object],0 1 2 3 4 5 6 7 8 9 0 1 81 64 4 25 36 16 9 49 0 1 2 3 4 5 6 7 8 9 0 1 4 81 64

Sorting - Generalised Bin Sort ,[object Object],[object Object],[object Object],1 2 3 4 5 6 7 8 9 81 64 25 36 16 49 0 1 2 3 4 5 6 7 8 9 0 1 81 64 4 25 36 16 9 49 0 0 1 4 9 Note that the 0 bin had to be quite large!

Sorting - Generalised Bin Sort ,[object Object],[object Object],[object Object],1 2 3 4 5 6 7 8 9 81 64 25 36 16 49 0 1 2 3 4 5 6 7 8 9 0 1 81 64 4 25 36 16 9 49 0 0 1 4 9 How much space is needed in each phase? n items m bins

Sorting - Generalised Bin Sort ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Sorting - Radix Sort - Analysis ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],struct date { int day; /* 1 .. 31 */ int month; /* 1 .. 12 */ int year; /* 0 .. 99 */ } Phase 1 - s 1 = 31 bins Phase 2 - s 2 = 12 bins Phase 3 - s 3 = 100 bins

Radix Sort - Analysis ,[object Object],radixsort( A, n ) { for(i=0;i<k;i++) { for(j=0;j<s[i];j++) bin[j] = EMPTY; for(j=0;j<n;j++) { move A[i] to the end of bin[A[i]->fi] } for(j=0;j<s[i];j++) concat bin[j] onto the end of A; } } O( s i ) O( n ) O( s i ) For each of k radices

Radix Sort - Analysis ,[object Object],radixsort( A, n ) { for(i=0;i<k;i++) { for(j=0;j<s[i];j++) bin[j] = EMPTY; for(j=0;j<n;j++) { move A[i] to the end of bin[A[i]->fi] } for(j=0;j<s[i];j++) concat bin[j] onto the end of A; } } O( s i ) O( n ) O( s i ) Clear the s i bins for the i th radix

Radix Sort - Analysis ,[object Object],radixsort( A, n ) { for(i=0;i<k;i++) { for(j=0;j<s[i];j++) bin[j] = EMPTY; for(j=0;j<n;j++) { move A[i] to the end of bin[A[i]->fi] } for(j=0;j<s[i];j++) concat bin[j] onto the end of A; } } O( s i ) O( n ) O( s i ) Move element A[i] to the end of the bin addressed by the i th field of A[i]

Radix Sort - Analysis ,[object Object],radixsort( A, n ) { for(i=0;i<k;i++) { for(j=0;j<s[i];j++) bin[j] = EMPTY; for(j=0;j<n;j++) { move A[i] to the end of bin[A[i]->fi] } for(j=0;j<s[i];j++) concat bin[j] onto the end of A; } } O( s i ) O( n ) O( s i ) Concatenate s i bins into one list again

Radix Sort - Analysis ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object], O( s i + n ) = O(kn +  s i ) = O(n +  s i ) i= 1 i= 1 i= 1 k k k

Radix Sort - Analysis ,[object Object],[object Object],[object Object]

Radix Sort - Analysis ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],i= 1 i= 1 log n log n

Radix Sort - Analysis ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Radix Sort - Realities ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Lecture 9 - Key Points ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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