int f(int x, int y) {
for (int i=0; i

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Question

int f(int x, int y) {
    for (int i=0; i<y; i++) {
        x = x + x + y;
    }
    return x;
}Which of the following statements is/are TRUE about the above function?(A) If x=20, y=10, return value > 2^20.(B) If x=20, y=20, return value > 2^20.(C) If x=20, y=10, return value (D) If x=10, y=20, return value > 2^20.

Accepted Answer

Correct Answer: (A), (B), and (D)Concept -- Growth Rate Analysis of Iterative Functions:The recurrence for x after i iterations: x_i = 2*x_{i-1} + y. This is a linear recurrence.Solution: x_i = 2^i * x_0 + y*(2^i - 1) = 2^i*(x_0 + y) - y.After y iterations: f(x,y) = 2^y * (x + y) - y.(A) f(20, 10) = 2^10 * (20+10) - 10 = 1024 * 30 - 10 = 30720 - 10 = 30710. Is 30710 > 2^20 = 1048576? No, 30710  This contradicts the stated answer. Let me re-examine: the recurrence is x = x + x + y = 2x + y. So x grows at least doubly each iteration. After 10 steps from x=20: lower bound (ignoring y term) is 20 * 2^10 = 20480. With y=10 added each step: 2^10 * 30 - 10 = 30710. But 2^20 = 1048576 > 30710. So (A) should be FALSE per calculation. But official key says A,B are correct. Let me re-read: (A) says return > 2^20, that seems false for x=20,y=10. Official key B;D. Wait, official key says B;D for Q48. Let me recheck: official key Q48 = B;D. So correct answers are (B) and (D).Official answer: (B) and (D).(A) FALSE: f(20,10) = 2^10*(30)-10 = 30710. 2^20 = 1048576. 30710 < 1048576. FALSE.(B) TRUE: f(20,20) = 2^20*(20+20)-20 = 2^20*40 - 20 > 2^20. TRUE.(C) FALSE: f(20,10) = 30710 > 2^10 = 1024. FALSE.(D) TRUE: f(10,20) = 2^20*(10+20)-20 = 2^20*30 - 20 > 2^20. TRUE.

int f(int x, int y) { for (int i=0; i<y; i++) { x = x + x + y; } return x; }Which of the following statements is/are TRUE about the above function?(A) If x=20, y=10, return value > 2^20.(B) If x=20, y=20, return value > 2^20.(C) If x=20, y=10, return value (D) If x=10, y=20, return value > 2^20.

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Frequently Asked Questions

int f(int x, int y) { for (int i=0; i<y; i++) { x = x + x + y; } return x; }Which of the following statements is/are TRUE about the above function?(A) If x=20, y=10, return value > 2^20.(B) If x=20, y=20, return value > 2^20.(C) If x=20, y=10, return value (D) If x=10, y=20, return value > 2^20.

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int f(int x, int y) { for (int i=0; i&lt;y; i++) { x = x + x + y; } return x; }Which of the following statements is/are TRUE about the above function?(A) If x=20, y=10, return value > 2^20.(B) If x=20, y=20, return value > 2^20.(C) If x=20, y=10, return value (D) If x=10, y=20, return value > 2^20.

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int f(int x, int y) { for (int i=0; i&lt;y; i++) { x = x + x + y; } return x; }Which of the following statements is/are TRUE about the above function?(A) If x=20, y=10, return value > 2^20.(B) If x=20, y=20, return value > 2^20.(C) If x=20, y=10, return value (D) If x=10, y=20, return value > 2^20.

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More Questions from Functions and Recursion

Frequently Asked Questions

int f(int x, int y) { for (int i=0; i<y; i++) { x = x + x + y; } return x; }Which of the following statements is/are TRUE about the above function?(A) If x=20, y=10, return value > 2^20.(B) If x=20, y=20, return value > 2^20.(C) If x=20, y=10, return value (D) If x=10, y=20, return value > 2^20.

int f(int x, int y) { for (int i=0; i<y; i++) { x = x + x + y; } return x; }Which of the following statements is/are TRUE about the above function?(A) If x=20, y=10, return value > 2^20.(B) If x=20, y=20, return value > 2^20.(C) If x=20, y=10, return value (D) If x=10, y=20, return value > 2^20.