FPSC- Programmer (BS-17) - PMD High Yield - 2026 — Test 4

Correct Answer: C. (x & (x - 1)) == 0
Explanation: A power of 2 has exactly one bit set. Note that x % 2 == 0 only tests whether x is even; 6 is even but is not a power of 2. ALSO KNOW (related points): • Which expression extracts bit k (0 = least significant) of x? → (x >> k) & 1 • What does this code test?: for (i = 0; i < n / 2; i++); if (s[i] != s[n - 1 - i]) return 0;; return 1; → Whether s is a palindrome

Correct Answer: A. When every element is positive (it returns 0, which is not in the array)
Explanation: Initialize min to the first element, or to INT_MAX. ALSO KNOW (related points): • With f(0) = f(1) = 1 and f(n) = f(n-1) + f(n-2), what is f(5)? → 8 • A prime-test loop checks for divisors from 2 up to sqrt(n) and returns 'prime' when none is found. Without a separate n < 2 check, which input is wrongly reported as prime? → 1

Correct Answer: A. About 3n/2
Explanation: Compare elements in pairs, then compare the smaller of each pair with the current minimum and the larger with the current maximum. That is 3 comparisons per 2 elements. ALSO KNOW (related points): • In the naive recursive fib(n) with base cases n <= 1, how many total calls (including the first one) does fib(4) make? → 9 • What happens with the 'swap' a = b; b = a;? → Both variables end up holding b's original value • What is the minimum number of comparisons needed to find the maximum of n elements? → n - 1

Correct Answer: C. 1
Explanation: Bitwise & is not short-circuiting, so both operands are evaluated. Using && would leave j at 0. ALSO KNOW (related points): • What is the main logical weakness of the swap a = a + b; b = a - b; a = a - b;? → a + b can overflow (and with floating point, precision can be lost) • How does isEven(3) evaluate, given these mutually recursive functions?: isEven(n): if n == 0 return True; else return isOdd(n-1); isOdd(n): if n == 0 return False; else return isEven(n-1) → False

Correct Answer: A. max = a always executes, because the ; ends the if with an empty statement
Explanation: A stray semicolon after if(...) is a classic logic bug, just like the one after for(...). ALSO KNOW (related points): • In Python, when is if x == 'a' or 'e': true? → Always, because the non-empty string 'e' is truthy • In C or C++, what type can the controlling expression of a switch statement have? → An integral or enumeration type (char, int, enum, and so on)

Correct Answer: A. 3
Explanation: In each outer iteration, j = 0 prints 'Hi' and j = 1 breaks the inner loop only. That gives 3 outer iterations × 1 print each. ALSO KNOW (related points): • What is the final value of b?: a = 1; b = 1; repeat 4 times:; t = a + b; a = b; b = t → 8 • How many stars does this print?: for i in range(1, 4):; for j in range(1, i + 1):; print('*', end='') → 6 • What does this Python code print?: i = 0; while i < 3:; i += 1; else:; print(i) → 3 • What is the output?: int i;; for (i = 0; i < 5; i++) { if (i == 3) break; }; printf("%d", i); → 3

Correct Answer: D. O(n)
Explanation: The total work is 1 + 2 + 4 + ... + (a value less than n), which is less than 2n. Multiplying the loop counts (log n × n) overestimates it. ALSO KNOW (related points): • What is the worst-case time complexity of binary search on a sorted array? → O(log n) • What does it mean for an algorithm to run in O(1) time? → Its running time is bounded by a constant that does not depend on the input size

Correct Answer: A. O(n²)
Explanation: The inner loop runs 0 + 1 + ... + (n - 1) = n(n - 1)/2 times in total, which is still quadratic. ALSO KNOW (related points): • What is the time complexity of this code?: for (i = 0; i < n; i++); for (j = 1; j < n; j *= 2); x++; → O(n log n) • What is the auxiliary space complexity of standard (array-based) merge sort? → O(n)

Correct Answer: A. An asymptotic lower bound
Explanation: A common misconception equates Ω with the best case. It is a lower bound, which can be applied to any case. ALSO KNOW (related points): • Which statement about Big-O notation is correct? → It gives an upper bound and can be used to describe the best, average, or worst case • Is the statement 'n² is in O(n³)' true? → True, because Big-O is only an upper bound

Correct Answer: D. n!
Explanation: The order of growth is n log n < n³ < 2^n < n!. ALSO KNOW (related points): • What does O(2n + 5) simplify to? → O(n)