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Consider the following function: int unknown(int n){ int i, j, k = 0; for (i = n/2; i <= n; i++) for (j = 2; j <= n; j = j * 2) k = k + n/2; return (k); } The return value of the function is

1. Θ(n²)
2. Θ(n² log n)
3. Θ(n³)
4. Θ(n³ log n)

Correct answer: Θ(n² log n)

Solution

Outer loop runs about n/2 times, inner loop (j doubling to n) runs log2(n) times, and each iteration adds n/2. Total return value ~ (n/2)(log n)(n/2) = Theta(n^2 log n).

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