ITPEC FE Subject B April 2024 Question 12

String Processing — checking whether a string is a palindrome using two-pointer traversal with minimum iterations.

The program uses two indices: i starts at 1 (left end), j starts at len (right end). Each iteration compares str[i] with str[j], then moves them inward (i ← i + 1, j ← j - 1).

The blank is the while loop condition — it must allow exactly ⌊len / 2⌋ iterations (the minimum needed to compare all symmetric pairs).

Since len ÷ 2 is integer division, the condition i < (len ÷ 2) + 1 gives exactly the right number of passes:
- For "ABBA" (len = 4): len ÷ 2 = 2, loop runs while i < 3 → iterations at i = 1, 2 ✓
- For "MADAM" (len = 5): len ÷ 2 = 2, loop runs while i < 3 → iterations at i = 1, 2 (middle character needs no check) ✓

Why not others:
- (a) `i < j - 1` — stops one step too early; skips the innermost pair (e.g., positions 2 and 3 in "ABBA")
- (c) `i < (len ÷ 2) - 1` — too few iterations; misses multiple character pairs
- (d) `i < len ÷ j` — j changes each iteration, making the condition unstable; for len = 4, the loop never executes (1 < 4 ÷ 4 = 1 is false)
- (e) `i < j ÷ 2` — also unstable; stops too early because j shrinks each iteration

Key rule: for palindrome checking with 1-based indexing, the loop needs exactly ⌊len / 2⌋ iterations — use a fixed boundary like (len ÷ 2) + 1, not a moving pointer.

AI-generated — may contain errors