Consider the program below which uses six temporary variables a, b, c, d, e, and f.

a = 1 
b = 10
c = 20 
d = a + b
e = c + d 
f = c + e 
b = c + e 
e = b + f 
d = 5 + e
return d + f 

Assuming that all the above operations take their operands from registers, the minimum number of registers needed to execute this program without spilling is

Detailed Register Allocation Analysis

Objective: Determine the minimum number of registers needed to execute the program without spilling.

Live Range Analysis:

• a: Line 1 → 4
• b: Line 6 → 7
• c: Line 3 → 6
• d: Line 8 → 9
• e: Line 7 → 8
• f: Line 5 → 9

Max live variables: 3 (after lines 6 and 7)

✅ Final Answer: 3 registers are required to execute the program without spilling.