Consider the following ANSI-C function. The maximum possible value that can be…
2026
Consider the following ANSI-C function.
The maximum possible value that can be returned from this function is ____________. (answer in integer)
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Correct answer: 1
To find the maximum return value, we analyze how the 'length' variable changes in each recursive call.
1. If length % 3 == 0: length decreases by 1 (start increases by 1).
2. If length % 3 == 1: length decreases by 1 (end decreases by 1), and 1 is added to the result.
3. If length % 3 == 2: length decreases by 2 (start increases by 2).
Notice the cycle of remainders modulo 3:
- From 1 mod 3, we go to 0 mod 3 (add 1).
- From 0 mod 3, we go to 2 mod 3 (subtract 1).
- From 2 mod 3, we go to 0 mod 3 (subtract 2).
Once the length is not congruent to 1 mod 3, it enters a cycle between 0 and 2, never returning to 1. Thus, the value '1' is added at most once.
The maximum possible value is 1.