CMI2012-A-10

Question

Consider the following functions $f$ and $g$.
 

f(){ x = x-50; y = y+50; }

g( ) { a = a+x; a = a+y; }

Suppose we start with initial values of $100$ for $x, 200$ for $y$, and $0$ for $a$, and then execute $f$ and $g$ in parallel - that is, at each step we either execute one statement from $f$ or one statement from $g$. Which of the following is not a possible final value of $a$?

• A. $300$
• B. $250$
• C. $350$
• D. $200$

Answer 1

Answer is (D) $200$

If we execute first $f()$ and then $g()$ then we get $300$

If we execute $1^{st}$ line of $g()$ , then $f()$ all the lines and then last line of $g()$ ,will get $350$

If we execute $1^{st}$ line of $f()$, then $1^{st}$ line of $g()$, then 2nd line of $g()$ and then $2^{nd}$ line of $f()$, we get $250$

Comments

if we execute g first a=a+x -> 100 a=a+y -> 100+200 = 300 then final value will be 300 not 200

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there are $\frac{4!}{2! * 2!}$ ways we can execute these, right???

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f(){ A) x = x-50; B) y = y+50; }

g( ) { 1) a = a+x; 2) a = a+y; }

Number of possible interleavings of f and g = Number of arrangements of A,B,1,2 such that A$\rightarrow$B and 1$\rightarrow$2 = $\frac{4!}{2!*2!}$

Order	a's value
A$\rightarrow$B$\rightarrow$1$\rightarrow$2	300
A$\rightarrow$1$\rightarrow$B$\rightarrow$2	300
A$\rightarrow$1$\rightarrow$2$\rightarrow$B	250
1$\rightarrow$2$\rightarrow$A$\rightarrow$B	300
1$\rightarrow$A$\rightarrow$2$\rightarrow$B	300
1$\rightarrow$A$\rightarrow$B$\rightarrow$2	350

Answer 2

as we are adding y to a's value and minimum value of 'a' at point a=a+x; can be 50....so the final value of 'a'  (at a=a+y;) has to be greater than 200 (max. value of 'a' can be 350)