Number of paths ques

[4ET0pfjN]

Hi, for my assignment, for the given function:

public int getValue(int x, int y, int z) {

 if (x != 0)
  y = 5;
 else
  z = z-x;

 if (z > 1)
  z = z/x;
 else
  z = y;

 return z;
}

the question is:
Provide a general function/formula for the number of paths through
the program in terms of x, y, and z.

I want to say 4 paths, but that is not what the ques is asking. I'd appreciate any help for this.

[JLBorges]

In general, the algorithm is:

a. Identify the basic blocks in the code being analysed http://en.wikipedia.org/wiki/Basic_block

b. Generate the control flow graph http://en.wikipedia.org/wiki/Control_flow_graph

[4ET0pfjN]

Creating a control flow graph was actually the first part of this question and I did that already,
any other ideas?

[JLBorges]

int getValue( int x, int y, int z ) 
{
    
 if( x != 0 )
    y = 5;

 /* dead code from here */   
 else // x == 0 
    z = z-x ; // by constant folding, z = z-0 ; => dead code
 /* till here */
 
 /* getValue results in undefined behaviour if z > 1, and x ==0 */
 if( z > 1 )
  z = z/x ; // will lead to undefined behaviour if x==0 

 else // z < 2
  z = y;

 return z;

}

The invariant on entry is therefore:

if( x==0 ) z must be less than or equal to 1

if( x!= 0 ) a. z may be less than or equal to 1
            b. z may be greater than 1

Take it from there.