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Bucket Sort Puzzlers 08 A: Sorting IV CS1102S: Data Structures and Algorithms Martin Henz March 12, 2010 Generated on Friday 12 th March, 2010, 11:26 CS1102S: Data Structures and Algorithms 08 A: Sorting IV 1 Bucket Sort Puzzlers 1

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Bucket Sort Puzzlers

08 A: Sorting IV

CS1102S: Data Structures and Algorithms

Martin Henz

March 12, 2010

Generated on Friday 12th March, 2010, 11:26 CS1102S: Data Structures and Algorithms 08 A: Sorting IV 1

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Bucket Sort Puzzlers

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Bucket Sort

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Puzzlers

CS1102S: Data Structures and Algorithms 08 A: Sorting IV 2

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Bucket Sort Puzzlers Recall: A Counter-Example Bucket Sort

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Bucket Sort Recall: A Counter-Example Bucket Sort

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Puzzlers

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Bucket Sort Puzzlers Recall: A Counter-Example Bucket Sort

Counter-example: Sorting Small Distinct Integers

Input Array a of N distinct integers from 1 to M Sorting algorithm int [ ] helper = new int [M] ; for ( int i =0; i < N; i ++) helper [ a [ i ] ] = a [ i ] ; int index = 0; for ( int j =0; j < M; j ++) i f ( helper [ j ] ! = 0 ) a [ index ++] = helper [ j ] ;

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Bucket Sort Puzzlers Recall: A Counter-Example Bucket Sort

Counter-example: Sorting Small Distinct Integers

int [ ] helper = new int [M] ; for ( int i =0; i < N; i ++) helper [ a [ i ] ] = a [ i ] ; int index = 0; for ( int j =0; j < M; j ++) i f ( helper [ j ] ! = 0 ) a [ index ++] = helper [ j ] ; Analysis Runtime O(M + N)

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Bucket Sort Puzzlers Recall: A Counter-Example Bucket Sort

A Couple of Ideas

We do not have to store the element in the array; boolean values will do How can we drop the condition “distinct integers”? Instead of boolean values in the array helper, we count the number of occurrences of a given integer

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Bucket Sort Puzzlers Recall: A Counter-Example Bucket Sort

Bucket Sort

int [ ] helper = new int [M] ; for ( int i =0; i < N; i ++) helper [ a [ i ] ] + + ; int index = 0; for ( int j =0; j < M; j ++) while ( helper [ j ]−− != 0) a [ index ++] = j ;

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Bucket Sort Puzzlers Recall: A Counter-Example Bucket Sort

Bucket Sort

int [ ] helper = new int [M] ; for ( int i =0; i < N; i ++) helper [ a [ i ] ] + + ; int index = 0; for ( int j =0; j < M; j ++) while ( helper [ j ]−− != 0) a [ index ++] = j ; Analysis Runtime O(M + N)

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Bucket Sort Puzzlers Previous Puzzler: The Last Laugh This Week’s Puzzler: Printing Money

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Bucket Sort

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Puzzlers Previous Puzzler: The Last Laugh This Week’s Puzzler: Printing Money

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Bucket Sort Puzzlers Previous Puzzler: The Last Laugh This Week’s Puzzler: Printing Money

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Bucket Sort

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Puzzlers Previous Puzzler: The Last Laugh This Week’s Puzzler: Printing Money

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Bucket Sort Puzzlers Previous Puzzler: The Last Laugh This Week’s Puzzler: Printing Money

Previous Puzzler: The Last Laugh

What does the following program print? public class LastLaugh { public static void main ( String [ ] args ) { System . out . p r i n t l n ( ”H” + ” a ” ) ; System . out . p r i n t l n ( ’H ’ + ’a ’ ) ; } }

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Bucket Sort Puzzlers Previous Puzzler: The Last Laugh This Week’s Puzzler: Printing Money

Previous Puzzler: The Last Laugh

What does the following program print? public class LastLaugh { public static void main ( String [ ] args ) { System . out . p r i n t l n ( ”H” + ” a ” ) ; System . out . p r i n t l n ( ’H ’ + ’a ’ ) ; } } This program prints: Ha 169

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Bucket Sort Puzzlers Previous Puzzler: The Last Laugh This Week’s Puzzler: Printing Money

Why?

Characters in Java are 16-bit numbers. Therefore, ’H’ + ’a’ performs addition of the corresponding character codes as integers: 72 + 97 = 169. What if I want to use characters as strings? Write: ”” + ’H’ + ’a’ What does this code print: System.out.println(”2 + 2 = ” + 2+2);

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Bucket Sort Puzzlers Previous Puzzler: The Last Laugh This Week’s Puzzler: Printing Money

Summary

Special treatment of + The + operator performs string concatenation if and only if at least one of its operands is of type String.

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Bucket Sort Puzzlers Previous Puzzler: The Last Laugh This Week’s Puzzler: Printing Money

New Puzzler: Printing Money

class Money {} class Dollar extends Money {} class MoneyPrinter { public void p r i n t (Money x ) { System . out . p r i n t l n ( ”Money ! ” ) ; } } class D o l l a r P r i n t e r extends MoneyPrinter { public void p r i n t ( Dollar x ) { System . out . p r i n t l n ( ” Dollar ! ” ) ; } }

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Bucket Sort Puzzlers Previous Puzzler: The Last Laugh This Week’s Puzzler: Printing Money

New Puzzler: Printing Money

Dollar d = new Dollar ( ) ; MoneyPrinter p = new D o l l a r P r i n t e r ( ) ; p . p r i n t ( d ) ;

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