HOMEWORK ASSIGNMENT #3 CS589

HOMEWORK ASSIGNMENT #3
CS589

After November 28 the homework assignment will not be accepted.
This is an individual assignment. Identical or similar solutions will be penalized.
Submission: All homework assignments must be submitted on the Blackboard as a pdf file. The
hardcopy submissions will not be accepted.
PROBLEM #1 (35 points): Testing polymorphism
For the following function F() and the inheritance relationships between five classes side, A, B, C,
and D, design a set of test cases using polymorphic testing, i.e., for each polymorphic call all
bindings should be “executed/tested” at least once. For each test case show which binding of the
polymorphic call(s) is “executed”. Notice that statements, where polymorphic calls are made, are
highlighted in bold.
1: int F(int a, int b, int c, int d){
 side *pa, *pb, *pc, *t;
2: pa=new A;
3: pc=new C;
4: pa->set(a);
5: pc->set(c);
6: if (pa->get() < pc->get()) {
7: t = pa;
8: pa = pc;
9: pc = t;
 }
10,11: if (d<0) pb=new D;
12: else pb=new B;
13: pb->set(b);
14: if (pa->get() > pc->get()) {
15: t = pa;
16: pa = pb;
17: pb = t;
 }
18: if (pa->get() > pb->get()) {
19: t = pc;
20: pc = pb;
21: pb = t;
 }
22: if (pa->get() + pc->get() <= pb->get())
23: return 0;
24: else return 1;
}
class side {
public:
virtual void set(int y) {x=y;};
virtual void set_x(int y) {x=y;};
virtual int get(){return x;};
private:
int x;
};
class A: public side {
public:
void set(int y) {if (y<10) set_x(10); else set_x(y);};
};
class B: public side {
public:
void set(int y) {if (y<25) set_x(25);else set_x(y);};
};
class C: public side {
public:
void set(int y) {if (y<0) set_x(0); else set_x(y);};
};
class D: public B {
public:
int get() {if (side::get()<0) return 0;
 else return side::get();}
};
A sample test case: Test #1: a=4, b=7, c=6, d=1
PROBLEM #2 (35 points): Symbolic evaluation
For the following function F(int a, int b, int c) use symbolic evaluation to show that the multiplecondition (True, False) in line 15 is not executable, i.e.,
((a == c) || (b == c))
True False
In your solution provide the symbolic execution tree.
1: int F(int a, int b, int c)
{ int type, t;
2: type = 0;
3: if (a > b) {
4: t = a;
5: a = b;
6: b = t;
}
7: if (a > c) {
8: t = a;
9: a = c;
10: c = t;
}
11: if (b > c) {
12: t = b;
13: b = c;
14: c = t;
}
15: if ((a == c) || (b == c)) {
16: type = 1;
}
17: return type;
}
PROBLEM #3 (30 points): Program proving
The following function F() computes the summation of absolute values of elements of the array a[]
consisting of n elements. Prove that function F() is correct for the given pre-condition and postcondition:
Pre-condition: 1 ≤ n ≤ 100
Post-condition:
1 int F (int a[], int n) {
 int i, sum;
2 i = n;
3 sum=0;
4 while (i > 0) {
5,6 if (a[i]>0) sum = sum + a[i];
7,8 else sum = sum - a[i];
9 i = i - 1;
 };
10 return sum;
 }