GATE CS 2014 Set 3 — Question 44
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Compiler Design → Code Optimization → Basic Blocks & Flow Graphs
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Question
Consider the basic block given below.The minimum number of nodes and edges present in the DAG representation of the above basic block respectively are
a = b + c
c = a + d
d = b + c
e = d - b
a = e + b
Correct answer
(A) 6 and 6
Solution
To find the minimum number of nodes and edges in the Directed Acyclic Graph (DAG) for the basic block, we process each statement while reusing existing nodes for common subexpressions and identifying redundant operations.
1.: Create leaf nodes for the initial values of and (let's call them and ). Create an internal node for the operator '+' with children and . Node is labeled with .
- Nodes: (3 nodes)
- Edges: (2 edges)
- Nodes: (5 nodes)
- Edges: (4 edges)
- Nodes: (6 nodes)
- Edges: (6 edges)
5.: The current value of is . Thus, is . We already have a node representing . Since addition is commutative, now points to the existing node . No new nodes or edges are added.
Final counts:- Nodes: 6
- Edges: 6
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