In a balanced binary search tree with n elements, what is the worst case time complexity of reporting all elements in range [a, b]? Assume that the number of reported elements is k.

Consider the following C program.

#include < stdio.h >
int main () {
    int a [4] [5] = {{1, 2, 3, 4, 5},
                           {6, 7, 8, 9, 10},
                           {11, 12, 13, 14, 15},
                           {16, 17, 18, 19, 20}};
    printf (“%d\n”, *(*(a+**a+2) +3));
    return (0);
}

The output of the program is _______.

Let G = (V, E) be a directed, weighted graph with weight function w: E $$ \to $$ R. For some function f: V $$ \to $$ R, for each edge (u, v) $$ \in $$ E, define w'(u, v) as w(u, v) + f(u) - f(v).

Which one of the options completes the following sentence so that it is TRUE?
“The shortest paths in G under w are shortest paths under w’ too, _______”.

Consider the array representation of a binary min-heap containing 1023 elements. The minimum number of comparisons required to find the maximum in the heap is _______.