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 ________.

To construct the Directed Acyclic Graph (DAG) for the given basic block, we identify unique subexpressions:

1. a = b + c:

   • Leaf nodes: b (Node 1) and c (Node 2)

   • Operator node: + with children b and c (Node 3, labeled a)

2. e = a + 1:

   • Leaf node: 1 (Node 4)

   • Operator node: + with children Node 3 (a) and Node 4 (1) (Node 5, labeled e)

3. d = b + c:

   • Common subexpression: b + c is already computed at Node 3. Thus, Node 3 is also labeled with d.

4. f = d + 1:

   • Since d refers to Node 3 and 1 refers to Node 4, d + 1 is identical to a + 1, which is already represented by Node 5. Thus, Node 5 is also labeled with f.

5. g = e + f:

   • Since e and f are both associated with Node 5, this is + applied with both left and right children being Node 5 (Node 6, labeled g).

Listing all nodes in the DAG:

• Leaf nodes (3):b, c, 1

• Internal/operator nodes (3):

  • + (labeled a, d)

  • + (labeled e, f)

  • + (labeled g)

Total number of nodes in the DAG = $3 + 3 =$ 6.