Bucket Sort Puzzlers. 08 A: Sorting IV. CS1102S: Data Structures and Algorithms. Martin Henz. March 12, 2010

Transcription

1 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

2 1 2 CS1102S: Data Structures and Algorithms 08 A: Sorting IV 2

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

4 Recall: A Counter-Example Counter-example: Sorting Small Distinct Integers Input Array a of N distinct integers from 1 to M Sorting algorithm i n t [ ] helper = new i n t [M] ; for ( i n t i =0; i<n; i ++) helper [ a [ i ] ] = a [ i ] ; i n t index = 0; for ( i n t j =0; j<m; j ++) i f ( helper [ j ]! = 0 ) a [ index ++] = helper [ j ] ; CS1102S: Data Structures and Algorithms 08 A: Sorting IV 4

5 Recall: A Counter-Example Counter-example: Sorting Small Distinct Integers i n t [ ] helper = new i n t [M] ; for ( i n t i =0; i<n; i ++) helper [ a [ i ] ] = a [ i ] ; i n t index = 0; for ( i n t 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

6 A Couple of Ideas Recall: A Counter-Example 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

7 Recall: A Counter-Example i n t [ ] helper = new i n t [M] ; for ( i n t i =0; i<n; i ++) helper [ a [ i ] ] + + ; i n t index = 0; for ( i n t j =0; j<m; j ++) while ( helper [ j ]!= 0) a [ index ++] = j ; CS1102S: Data Structures and Algorithms 08 A: Sorting IV 7

8 Recall: A Counter-Example i n t [ ] helper = new i n t [M] ; for ( i n t i =0; i<n; i ++) helper [ a [ i ] ] + + ; i n t index = 0; for ( i n t 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

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11 What does the following program print? public class LastLaugh { public s t a t i c void main ( S t r i n g [ ] 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

12 What does the following program print? public class LastLaugh { public s t a t i c void main ( S t r i n g [ ] 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

13 Why? Characters in Java are 16-bit numbers. Therefore, H + a performs addition of the corresponding character codes as integers: = 169. What if I want to use characters as strings? Write: + H + a What does this code print: System.out.println( = + 2+2); CS1102S: Data Structures and Algorithms 08 A: Sorting IV 13

14 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

15 New Puzzler: Printing Money class Money {} class D o l l a r 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 ( D o l l a r x ) { System. out. p r i n t l n ( D o l l a r! ) ; } } CS1102S: Data Structures and Algorithms 08 A: Sorting IV 15

16 New Puzzler: Printing Money D o l l a r d = new D o l l a r ( ) ; 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