08 A: Sorting IV CS1102S: Data Structures and Algorithms Martin - PowerPoint PPT Presentation

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 Bucket Sort 2 Puzzlers CS1102S: Data Structures and Algorithms 08 A: Sorting IV 2

Bucket Sort Recall: A Counter-Example Puzzlers Bucket Sort 1 Bucket Sort Recall: A Counter-Example Bucket Sort 2 Puzzlers CS1102S: Data Structures and Algorithms 08 A: Sorting IV 3

Bucket Sort Recall: A Counter-Example Puzzlers 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 ] ; CS1102S: Data Structures and Algorithms 08 A: Sorting IV 4

Bucket Sort Recall: A Counter-Example Puzzlers 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 ) CS1102S: Data Structures and Algorithms 08 A: Sorting IV 5

Bucket Sort Recall: A Counter-Example Puzzlers 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 CS1102S: Data Structures and Algorithms 08 A: Sorting IV 6

Bucket Sort Recall: A Counter-Example Puzzlers 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 ; CS1102S: Data Structures and Algorithms 08 A: Sorting IV 7

Bucket Sort Recall: A Counter-Example Puzzlers 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 ) CS1102S: Data Structures and Algorithms 08 A: Sorting IV 8

Bucket Sort Previous Puzzler: The Last Laugh Puzzlers This Week’s Puzzler: Printing Money 1 Bucket Sort 2 Puzzlers Previous Puzzler: The Last Laugh This Week’s Puzzler: Printing Money CS1102S: Data Structures and Algorithms 08 A: Sorting IV 9

Bucket Sort Previous Puzzler: The Last Laugh Puzzlers This Week’s Puzzler: Printing Money 1 Bucket Sort 2 Puzzlers Previous Puzzler: The Last Laugh This Week’s Puzzler: Printing Money CS1102S: Data Structures and Algorithms 08 A: Sorting IV 10

Bucket Sort Previous Puzzler: The Last Laugh Puzzlers 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 ’ ) ; } } CS1102S: Data Structures and Algorithms 08 A: Sorting IV 11

Bucket Sort Previous Puzzler: The Last Laugh Puzzlers 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 CS1102S: Data Structures and Algorithms 08 A: Sorting IV 12

Bucket Sort Previous Puzzler: The Last Laugh Puzzlers 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); CS1102S: Data Structures and Algorithms 08 A: Sorting IV 13

Bucket Sort Previous Puzzler: The Last Laugh Puzzlers 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. CS1102S: Data Structures and Algorithms 08 A: Sorting IV 14

Bucket Sort Previous Puzzler: The Last Laugh Puzzlers 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 extends MoneyPrinter { D o l l a r P r i n t e r public void p r i n t ( Dollar x ) { System . out . p r i n t l n ( ” Dollar ! ” ) ; } } CS1102S: Data Structures and Algorithms 08 A: Sorting IV 15

Bucket Sort Previous Puzzler: The Last Laugh Puzzlers 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 ) ; CS1102S: Data Structures and Algorithms 08 A: Sorting IV 16