/** * finds the index of v in a if present * * * * */ public static int findinsortedarray(int[] a, int v) {...

Transcription

1 1

2 2 /** * finds the index of v in a if present * * * * */ public static int findinsortedarray(int[] a, int v) {... }

3 3 /** * finds the index of v in a if present * a[i] < a[i+1] * a[j] == v $implies $ret == j a[j]!= v for all j * $implies $ret == -1 */ public static int findinsortedarray(int[] a, int v) {... }

4 4 /** * finds the index of v in a if present * a[i] <= a[i+1] * $ret == j $implies a[j] == v $ret == -1 $implies a[j]!= v for all j $ret >= -1 && $ret < a.length */ public static int findinsortedarray(int[] a, int v) {... }

5 5 caller, client callee, supplier

6 6 invariants state

7 7 package tau.software1.lecture4; public class CounterExample { public int c; } public CounterExample() { c = 0; } public void increment() { c++; } /** none $ret == #calls to increment() */ public int counter() { return c; }

8 8

9 9 c invariant increment counter

10 10 package tau.software1.lecture4; public class CounterExample { public int c; } public CounterExample() { c = 0; } public void increment() { c++; } /** none $ret == #calls to increment() */ public int counter() { return c; }

11 11 increment increment c==0 k k+1 increment c==k k+1

12 12 increment increment c==0 k k+1 increment c==k k+1

13 13 increment increment c==0 k k+1 increment c==k c k+1

14 14 package tau.software1.lecture4; public class Counter { private int c; } public CounterExample() { c = 0; } public void increment() { c++; } /** none $ret == #calls to increment() */ public int counter() { return c; }

15 15 public class Counter { c == #calls to increment */ private int c; } none */ public Counter() { c = 0; } none */ public void increment() { c++; } none $ret == #calls to increment() */ public int counter() { return c; }

16 16 public

17 17 state visibility encasulation information hiding counter() public

18 18

19 19 package tau.software1.lecture4; public class DontUsePackageVisibility { int c; } public CounterExample() { c = 0; } public void increment() { c++; } /** none $ret == #calls to increment() */ public int counter() { return c; }

20 20 public private

21 21

22 22 last in first out LIFO isempty pop pop push StackOfInts s1 = new StackOfInts(); System.out.println("isEmpty() == " + s1.isempty()); s1.push(1); System.out.println("s1.top() == " + s1.top()); s1.push(2); System.out.println("s1.top() == " + s1.top()); s1.pop(); System.out.println("s1.top() == " + s1.top()); System.out.println("isEmpty() == " + s1.isempty());

23 23

24 24 tuple (7, 33, 45, 9, -3) abstraction function

25 (i 1, i 2,..., i n ) or () for the empty stack */ public class StackOfInts { AF(this) == () */ public StackOfInts(){... } $ret == i 1 */ public int top() {... } $ret == (AF(this) == ()) */ public boolean isempty() {... } AF(this) == (i 2, i 3,..., i n ) */ public void pop() {... } AF(this) == (x, i 1,..., i n ) */ public void push(int x) {... } } $ret == n */ public int count() {... } 25

26 (i 1, i 2,..., i n ) or () for the empty stack */ public class StackOfInts { AF(this) == () */ public StackOfInts(){... } $ret == i 1 */ public int top() {... } $ret == (AF(this) == ()) */ public boolean isempty() {... } AF(this) == (i 2, i 3,..., i n ) */ public void pop() {... } AF(this) == (x, i 1,..., i n ) */ public void push(int x) {... } } $ret == n */ public int count() {... } 26

27 (i 1, i 2,..., i n ) or () for the empty stack */ public class StackOfInts { AF(this) == () */ public StackOfInts(){... } $ret == i 1 */ public int top() {... } $ret == (AF(this) == ()) */ public boolean isempty() {... } AF(this) == (i 2, i 3,..., i n ) */ public void pop() {... } AF(this) == (x, i 1,..., i n ) */ public void push(int x) {... } } $ret == n */ public int count() {... } 27

28 (i 1, i 2,..., i n ) or () for the empty stack */ public class StackOfInts { AF(this) == () */ public StackOfInts(){... } $ret == i 1 */ public int top() {... } $ret == (AF(this) == ()) */ public boolean isempty() {... } AF(this) == (i 2, i 3,..., i n ) */ public void pop() {... } AF(this) == (x, i 1,..., i n ) */ public void push(int x) {... } } $ret == n */ public int count() {... } 28

29 29

30 30 public class StackOfInts { public static int DEFAULT_STACK_CAPACITY = 10; private int[] rep; private int t; public StackOfInts() { t = -1; rep = new int[default_stack_capacity]; } public int top() { return rep[t]; } public boolean isempty() { return t == -1; } public void pop() { t--; } public int count() { return t + 1; }...

31 31... public void push(int x) { if (t == rep.length 1) enlargerep(); t++; rep[t] = x; } /** allocate storage space in rep */ private void enlargerep(){ int[] biggerarr = new int[rep.length * 2]; System.arraycopy(rep, 0, biggerarr, 0, rep.length); rep = biggerarr; } }

32 count

33 33 TreeSet HashSet

34 34

35 t==1???

36 t==1 (2,1)

37 AF(this) (x 1,, x n ) such that i in 1,,n we have x i = rep[t i + 1] and n = t

38 t==1 (2,1) t==1

39 39 rep invariant t== t==-9

40 40 t < rep.length t >= -1 isempty() top() == rep[t] isempty() == (t==-1) */ public class StackOfInts { implementation post condition $ret == rep[t] */ public int top() {... }

41 41 rep count

42 42 as m as cs as AF(cs.m()) == AF(cs).m() AF(cs.m()) == AF(cs).m() == as.m() == as

43 43 cs AF() as m() m() cs AF() as

44 44

45 45 AF(this) = (this.getx(), this.gety())

46 46 Map<String, Integer>

47 47 public class StackOfInts { public static int DEFAULT_STACK_CAPACITY = 10; private int[] rep; private int t; public StackOfInts() { t = -1; rep = new int[default_stack_capacity]; }

48 48 public class StackOfInts { public static int DEFAULT_STACK_CAPACITY = 10; private int[] rep; private int t; public StackOfInts() { t = -1; rep = new int[default_stack_capacity]; } public StackOfInts(int expectedoccupancy) { t = -1; rep = new int[expectedoccupancy]; }

49 49 public class StackOfInts { public static int DEFAULT_STACK_CAPACITY = 10; private int[] rep; private int t; public StackOfInts() { this( DEFAULT_STACK_CAPACITY ); } public StackOfInts(int expectedoccupancy) { t = -1; rep = new int[expectedoccupancy]; }

50 50 public class StackOfInts { public static int DEFAULT_STACK_CAPACITY = 10; private int[] rep; private int t; public StackOfInts() { this( DEFAULT_STACK_CAPACITY ); } public StackOfInts(int expectedoccupancy) { t = -1; rep = new int[expectedoccupancy]; }

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