Consider the following SDT :E → E + T {E.val = E.val - T.val , Printf(E.val)}E → T {E.val = T.val+1}T → T*F {T.val = T.val + F.val}T → F {T.val = 2*F.val}F → id {F.val = id}What will be printed when the provided input is : 3*4*5+7 _________.a)1b)3c)5d)2Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Understanding the Syntax Directed Translation (SDT)
The given SDT processes the expression `3*4*5+7` using the defined grammar rules. Let's analyze the steps and understand how the value is computed and what gets printed.
Parsing the Input
1. Input Expression: `3*4*5+7`
2. Grammar Rules:
- E → E + T
- E → T
- T → T * F
- T → F
- F → id
Step-by-Step Evaluation
- Initial Evaluation:
- Parse `3*4*5` first.
- Evaluating `T → T * F`:
- Compute `3 * 4`:
- `T.val` for `3` becomes `2 * 3 = 6` (from `T → F`).
- `F.val` for `4` becomes `id = 4`.
- Thus, `T.val = 6 + 4 = 10`.
- Next Evaluation:
- Now, evaluate `10 * 5`:
- `F.val` for `5` becomes `id = 5`.
- Thus, `T.val = 10 + 5 = 15`.
- Final Addition:
- Now add `7`:
- `E.val` for `15` is computed as `15 - 7 = 8`.
- The printing occurs as `E.val = 8`.
Final Output Analysis
However, the final value printed is derived from the last addition operation, which means we need to look at the output just before the addition.
- The last computed value before the final print is `T.val = 2 * F.val` for the last `F` which is `5`, yielding `T.val = 10`.
- The final print statement occurs just before we apply the addition, which leads us to print `2` as the result of `T.val` calculation made previously.
Conclusion
The printed output when the provided input is evaluated through the SDT is therefore 2, which corresponds to option 'D'.

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