Algorithms | Analysis of Algorithms | Question 19

Consider the following two functions. What are time complexities of the functions? 

C

int fun1(int n)
{
    if (n <= 1) return n;
    return 2*fun1(n-1);
}

C

int fun2(int n)
{
    if (n <= 1) return n;
    return fun2(n-1) + fun2(n-1);
}

(A)

O(2^n) for both fun1() and fun2()

(B)

O(n) for fun1() and O(2^n) for fun2()

(C)

O(2^n) for fun1() and O(n) for fun2()

(D)

O(n) for both fun1() and fun2()

Answer: (B)
Explanation:

Time complexity of fun1() can be written as T(n) = T(n-1) + C which is O(n)

Time complexity of fun2() can be written as T(n) = 2T(n-1) + C which is O(2^n)

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