AP CSP Day 53: Variables & Assignment | Cycle 2
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Complex variable tracing involves code where multiple variables reference each other in sequence, such as a series of three assignments where the final value of each variable depends on the order of execution. Students who evaluate all right-hand sides before performing any assignments will get incorrect results for sequential code. AP CSP Cycle 2 variable review questions present multi-variable swap and transform sequences and ask students to determine which variable holds which value at a specified line. Executing one assignment at a time in strict top-to-bottom order is the only reliable tracing method.
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Complex Variable Traces: Multi-Step Dependencies
Chain Dependencies
In a sequence where variable A is assigned first, then B is assigned using A, then C is assigned using B and A, each variable's value depends on the exact state at the moment of its assignment. Changing the order of assignments can produce completely different final values.
Reference vs. Value
In AP CSP pseudocode, each assignment copies the current value of the right-hand side expression. Later changes to variables used in a previous assignment do not retroactively change the already-assigned variable.
Practice Question
What is displayed after the following code runs?
a ← 1
b ← 2
c ← 3
a ← b + c
b ← a + c
c ← a + b
DISPLAY(c)Trace each assignment using current values: a = b+c = 2+3 = 5. Then b = a+c = 5+3 = 8 (using updated a). Then c = a+b = 5+8 = 13 (using updated a and b). DISPLAY shows 13.
A) 6 uses original values (1+2+3). Students who don't update variables get this wrong answer. C) 8 is the value of b, not c. D) 16 results from arithmetic errors in the trace.
Students use the original values (a=1, b=2, c=3) throughout all three computations instead of using the updated value of each variable as soon as it changes.
In multi-step assignment problems, update your variable table immediately after each assignment. The next line must use the new values, not the originals.
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