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Winter 2007 Midterm Solutions
Problem 1: True/False
(a)
(3 points) If a node n
1
dominates a node n
2
, then n
1
is always visited before n
2
in a
depthfirst search.
TRUE. By the definition of domination, all paths that lead to n
2
go through n
1
first. So, a
depthfirst search must reach n
1
first.
 OR 
FALSE. A postorder depthfirst search visits all children of a node before visiting the
node itself. By the definition of domination, n
2
must be visited first, since it is a child.
(b)
(3 points) If a node n
1
dominates a node n
2
, n
1
is always visited before n
2
in a reverse
post ordering.
TRUE. Justification is essentially identical to the "False" answer for 1(a)  if a post
ordering must list n
2
first, then a reverse postordering must list n
1
first.
(c)
(3 points) Given a monotone data flow framework, had all the interior points of the
data flow solver been initialized with the "bottom" of the semilattice, the answer at every
point in every program would have been "bottom."
FALSE. Even though any element met with bottom is itself bottom, this makes no
assumption about the results of the transfer function. Suppose the transfer function
returns a single constant value (not bottom). This is definitely monotone (no matter the
values of x and y, f(x)
≤
f(y)), and the values once the solution stabilizes will definitely not
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 Winter '09

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