GATE CS 2021 Set 1 Q.60 (CS Q.50): Intermediate Code Generation, Data Flow Analysis and Code Optimization

Consider the following C code segment:

a = b + c;
e = a + 1;
d = b + c;
f = d + 1;
g = e + f;

In a compiler, this code segment is represented internally as a directed acyclic graph (DAG). The number of nodes in the DAG is __________

Your answer

Official answer and solution

Solution

Construct the Directed Acyclic Graph (DAG) for the basic block by reusing identical subexpression nodes.

Let us trace the DAG construction statement by statement:

Initial leaves: Variables b and c are live upon entry. Create leaf node $N_1(\text{b})$ and leaf node $N_2(\text{c})$ .
Statement a = b + c: Create interior operator node $N_3(+)$ with left child $N_1$ and right child $N_2$ . Attach label a to $N_3$ .
Create constant leaf node $N_4(1)$ .
Statement e = a + 1: Create interior operator node $N_5(+)$ with left child $N_3$ and right child $N_4$ . Attach label e to $N_5$ .

Statement d = b + c: The subexpression b + c already corresponds to existing node $N_3$ . Attach label d to $N_3$ without creating a new node.
Statement f = d + 1: Since d refers to $N_3$ , d + 1 is $N_3 + N_4$ , which already corresponds to node $N_5$ . Attach label f to $N_5$ without creating a new node.
Statement g = e + f: Both e and f refer to node $N_5$ . Create interior operator node $N_6(+)$ with left child $N_5$ and right child $N_5$ . Attach label g to $N_6$ .

Count total nodes in the DAG:

Leaf nodes: $N_1(\text{b}), N_2(\text{c}), N_4(1)$ (3 leaf nodes)
Operator nodes: $N_3(+), N_5(+), N_6(+)$ (3 interior nodes)
Total number of nodes $= 3 + 3 = 6$ .

Final answer

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