Following questions have been asked in GATE CS 2008 exam.

**1. What is printed by the following C program?**

`int` `f(` `int` `x, ` `int` `*py, ` `int` `**ppz)` `{ ` ` ` `int` `y, z; ` ` ` `**ppz += 1; ` ` ` `z = **ppz; ` ` ` `*py += 2; ` ` ` `y = *py;` ` ` `x += 3;` ` ` `return` `x + y + z;` `}` ` ` `void` `main()` `{` ` ` `int` `c, *b, **a;` ` ` `c = 4; ` ` ` `b = &c;` ` ` `a = &b; ` ` ` `printf` `( ` `"%d"` `, f(c,b,a));` ` ` `getchar` `();` `}` |

(A) 18

(B) 19

(C) 21

(D) 22

Answer (B)

`/* Explanation for the answer */` ` ` ` ` `/*below line changes value of c to 5. Note that x remains unaffected ` ` ` `by this change as x is a copy of c and address of x is different from c*/` ` ` `**ppz += 1 ` ` ` ` ` `/* z is changed to 5*/` ` ` `z = **ppz;` ` ` ` ` `/* changes c to 7, x is not changed */` ` ` `*py += 2;` ` ` ` ` `/* y is changed to 7*/` ` ` `y = *py; ` ` ` ` ` `/* x is incremented by 3 */` ` ` `x += 3; ` ` ` ` ` `/* return 7 + 7 + 5*/` ` ` `return` `x + y + z; ` |

**2. Choose the correct option to fill ?1 and ?2 so that the program below prints an input string in reverse order. Assume that the input string is terminated by a newline character.**

`void` `reverse(` `void` `)` ` ` `{` ` ` `int` `c;` ` ` `if` `(?1) reverse() ;` ` ` `?2` `}` `main()` `{` ` ` `printf` `(` `"Enter Text "` `) ;` ` ` `printf` `(` `"\n"` `) ;` ` ` `reverse();` ` ` `printf` `(` `"\n"` `) ;` `}` |

(A) ?1 is (getchar() != ’\n’)

?2 is getchar(c);

(B) ?1 is (c = getchar() ) != ’\n’)

?2 is getchar(c);

(C) ?1 is (c != ’\n’)

?2 is putchar(c);

(D) ?1 is ((c = getchar()) != ’\n’)

?2 is putchar(c);

Answer(D)

getchar() is used to get the input character from the user and putchar() to print the entered character, but before printing reverse is called again and again until ‘\n’ is entered. When ‘\n’ is entered the functions from the function stack run putchar() statements one by one. Therefore, last entered character is printed first.

You can try running below program

`void` `reverse(` `void` `); ` `/* function prototype */` ` ` `void` `reverse(` `void` `)` ` ` `{` ` ` `int` `c;` ` ` `if` `(((c = ` `getchar` `()) != ` `'\n'` `)) ` ` ` `reverse(); ` ` ` `putchar` `(c);` `}` `main()` `{` ` ` `printf` `(` `"Enter Text "` `) ;` ` ` `printf` `(` `"\n"` `) ;` ` ` `reverse();` ` ` `printf` `(` `"\n"` `) ;` ` ` `getchar` `();` `}` |

**For questions 3 & 4, consider the following C functions:**

`int` `f1(` `int` `n)` `{` ` ` `if` `(n == 0 || n == 1)` ` ` `return` `n;` ` ` `else` ` ` `return` `(2*f1(n-1) + 3*f1(n-2));` `}` ` ` `int` `f2(` `int` `n)` `{` ` ` `int` `i;` ` ` `int` `X[N], Y[N], Z[N] ;` ` ` `X[0] = Y[0] = Z[0] = 0;` ` ` `X[1] = 1; Y[1] = 2; Z[1] = 3;` ` ` `for` `(i = 2; i <= n; i++)` ` ` `{` ` ` `X[i] = Y[i-1] + Z[i-2];` ` ` `Y[i] = 2*X[i];` ` ` `Z[i] = 3*X[i];` ` ` `}` ` ` `return` `X[n] ;` `}` |

3. The running time of f1(n) and f2(n) are

(A) Θ(n) and Θ(n)

(B) Θ(2^n) and Θ(n)

(C) Θ(n) and Θ(2^n)

(D) Θ(2^n) and Θ(2^n)

Answer (B)**For f1()**, let T(n) be the function for time complexity.

T(n) = T(n-1) + T(n-2)

Above recursion is a standard one for Fibonacci Numbers. After solving the recursion, we get

T(n) = 1/sqrt(5)[(1 + sqrt(5))/2]^n - 1/sqrt(5)[(1 - sqrt(5))/2]^n

Above recursion can also be written as Θ(1.618.^n)

(Please see this).

**In f2()**, there is a single loop, so time complexity is Θ(n)

Among all the 4 given choices, (B) looks closest.

**4. f1(8) and f2(8) return the values**

(A) 1661 and 1640

(B) 59 and 59

(C) 1640 and 1640

(D) 1640 and 1661

Both functions perform same operation, so output is same, means either (B) or (C) is correct.

f1(2) = 2*f1(1) + 3*f1(0) = 2

f1(3) = 2*f1(2) + 3*f1(1) = 2*2 + 3*1 = 7

f1(4) = 2*f1(3) + 3*f1(2) = 2*7 + 3*2 = 20

f1(5) = 2*f1(4) + 3*f1(3) = 2*20 + 3*7 = 40 + 21 = 61

We can skip after this as the only remaining choice is (C)

f1(6) = 2*f1(5) + 3*f1(4) = 2*61 + 3*20 = 122 + 60 = 182

f1(7) = 2*f1(6) + 3*f1(5) = 2*182 + 3*61 = 364 + 183 = 547

f1(8) = 2*f1(7) + 3*f1(6) = 2*547 + 3*182 = 1094 + 546 = 1640

Please write comments if you find any of the answers/explanations incorrect, or you want to share more information about the topics discussed above.

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