Big O & ArrayList Fall 2018 Margaret Reid-Miller

Transcription

1 Big O & ArrayList Fall 2018 Margaret Reid-Miller

2 Today Exam 1: Thursday, Oct 4, 2018 Exam 2 date: Currently Thur. Oct 25 th Move to Tues Oct 30 or Thur Nov 1? (Withdraw deadline Tues Nov 6.) Homework 3 due tomorrow night Homework 1: To be returned tomorrow in lab Big O ArrayLists Fall (Reid-Miller) 2

3 Big O: Formal Definition Let T(n) the number of operations performed in an algorithm as a function of n. T(n) O(f(n)) if and only if there exists two constants, n 0 > 0 and c > 0 and a function f(n) such that for all n > n 0, cf(n) T(n). Fall (Reid-Miller) 3

4 Big O: Example Let T(n) = 5n 2 + 3n + 9. Show that T(n) = O(n 2 ). Find constants c and n 0, such that for all n > n 0, cn 2 > 5n 2 +3n +9. Find intersection point such that cn 2 = 5n 2 +3n +9 Let n = n 0 and solve for c: c = 5 + 3/n + 9/n 2 If n 0 = 3 then c = 7. Thus, 7n 2 > 5n 2 + 3n + 9 for all n > 3, and 5n 2 + 3n +9 O(n 2 ). Fall (Reid-Miller) 4

5 More on Big O Big O gives us an upper-bound approximation on the complexity of a computation. That is, think of Big O as <= n is O(n), but it s also O(n 2 ) and O(n 3 ). We try to keep the bound as tight as possible, though. Fall (Reid-Miller) 5

6 Order of Complexity Suppose an algorithm is A followed by B. Then the overall complexity of the algorithm is max (O(A), O(B)). Examples: O(log n) + O(n) = O(n) O(n log n) + O(n) = O(n log n) O(n log n) + O(n 2 ) = O(n 2 ) O(2 n ) + O(n 2 ) = O(2 n ) Fall (Reid-Miller) 6

7 Order of Complexity Suppose an algorithm is A enclosing B. (e.g., nested loops) Then the overall complexity of the algorithm is Examples: O(A) * O(B), where O(A) excludes the complexity of B. O(log n) * O(n) = O(n log n) O(n log n) * O(n) = O(n 2 log n) O(n) * O(1) = O(n) Fall (Reid-Miller) 7

8 Quiz ArrayLists Fall (Reid-Miller) 8

9 The ArrayList Class For Java folks, an ArrayList is like an array, but: It s a class, so we construct it and call methods on it. It s resizable. It grows as we add elements and shrinks as we remove them. For Python folks, an ArrayList is like a Python list, but: We do not use subscript notation. ArrayLists (like arrays) are homogeneous. ArrayList <String> names = new ArrayList<String>(); Fall (Reid-Miller) 9

10 Autoboxing ArrayLists can only store references to objects, not primitives. All primitive types have a corresponding object type (wrapper class). Example: int Integer Integer i = 21; Integer j = new Integer(62); Integer k = new Integer( 12 ) Fall (Reid-Miller) 10

11 Autoboxing (cont d) Integer a = i++; Integer b = i+j; int p = a + b; System.out.println( a.tostring() + b.tostring); System.out.println(a + b); ArrayList<Integer> intlist = new ArrayList<Integer>(); Fall (Reid-Miller) 11

12 ArrayList methods java.util.arraylist<e> int size() boolean add(e obj) Appends obj to end of this list; returns true void add(int index, E obj) Inserts obj at position index (0 <= index <= size) E get(int index) Returns the element at position index E set(int index, E obj) Replaces element at position index with obj; Returns the element formerly at position index Fall (Reid-Miller) 12

13 ArrayList methods boolean contains(object obj) Returns true if this list contains obj E remove(int index) Removes element at position index; Returns the element formerly at position index. boolean remove(object obj) Removes the first occurrence of obj, if present; Returns true if this list contained obj, false otherwise. int indexof(object obj) Returns the index of the first occurrence of obj in this list, or returns -1 if this list does not contain obj Fall (Reid-Miller) 13

14 ArrayList complexity java.util.arraylist<e> int size() boolean add(e obj) void add(int index, E obj) E get(int index) E set(int index, E obj) boolean contains(object obj) E remove(int index) boolean remove(object obj) int indexof(object obj) Worst Best O(1) O(1) O(n) O(1) O(1) O(1) O(n) O(1) O(n) O(1) O(n) O(1) O(n) O(1) Fall (Reid-Miller) 14

15 ArrayList demo import java.util.arraylist; ArrayList<String> names = new ArrayList<String>(); names.add( Margaret ); names.add( Dave ); names.get(1); names.set(0, Mark ); names.add(1, Tom ); names.remove(1); Margaret Margaret Dave Dave Mark Dave Mark Tom Dave Mark Dave Fall (Reid-Miller) 15

16 Example: count // Returns the number of names in the given list // with the given number of letters public static int count( ArrayList<String> names, int numletters) { int count = 0; for (int i = 0; i < names.size() ; i++) { if ( names.get(i).length() == numletters) { count++; return count; Fall (Reid-Miller) 16

17 Example: getnamesoflength // Returns a list of names in the given list // with the given number of letters public static ArrayList<String> getnamesoflength( ArrayList<String> names, int numletters) { ArrayList<String> result; result = new ArrayList<String>() ; for (int i = 0; i < names.size() ; i++) { if (names.get(i).length() == numletters) { result.add(names.get(i)) ; return result; Fall (Reid-Miller) 17

18 Example: removenamesoflength // Removes all names in the given list // with the given number of letters public static void removenamesoflength( ArrayList<String> names,int numletters) { for (int i = 0; i < names.size(); i++) { if (names.get(i).length() == numletters) { names.remove(i); Oops! When doesn t this code work correctly? It won t remove 2 consecutive names. Fall (Reid-Miller) 18

19 Example: removenamesoflength // Removes all names in the given list // with the given number of letters public static void removenamesoflength( ArrayList<String> names,int numletters) { for (int i = 0; i < names.size(); i++) { if (names.get(i).length() == numletters) { names.remove(i); i--; Solution 1: Decrement i after each removal. Ugly Fall (Reid-Miller) 19

20 Example: removenamesoflength // Removes all names in the given list // with the given number of letters public static void removenamesoflength( ArrayList<String> names,int numletters) { int i = 0; while (i < names.size()) { if (names.get(i).length() == numletters) names.remove(i); else i++; Solution 2: Increment only when don t remove. Fall (Reid-Miller) 20

21 Example: removenamesoflength // Removes all names in the given list // with the given number of letters public static void removenamesoflength( ArrayList<String> names,int numletters) { for (int i = names.size()-1; i >= 0; i--) { if (names.get(i).length() == numletters) { names.remove(i); Solution 3: Loop backward. Move only the elements you are keeping. Sweet. Fall (Reid-Miller) 21