An algorithm has to store several keys generated by an adversary in a hash table. The adversary is malicious who tries to maximize the number of collisions. Let $$k$$ be the number of keys, $$m$$ be the number of slots in the hash table, and $$k > m$$. Which one of the following is the best hashing strategy to counteract the adversary?

Let A be a priority queue for maintaining a set of elements. Suppose A is implemented using a max-heap data structure. The operation EXTRACT-MAX(A) extracts and deletes the maximum element from A. The operation INSERT(A, key) inserts a new element key in A. The properties of a max-heap are preserved at the end of each of these operations.

When A contains n elements, which one of the following statements about the worst case running time of these two operations is TRUE?

Consider the C function foo and the binary tree shown.

typedef struct node {
    int val;
    struct node *left, *right;
} node;
int foo(node *p) {
    int retval;
    if (p == NULL)
        return 0;
    else {
        retval = p->val + foo(p->left) + foo(p->right);
        printf("%d ", retval);
        return retval;
    }
}

When foo is called with a pointer to the root node of the given binary tree, what will it print?

Consider a sequence a of elements $$a_0=1,a_1=5,a_2=7,a_3=8,a_4=9$$, and $$a_5=2$$. The following operations are performed on a stack S and a queue Q, both of which are initially empty.

I: push the elements of a from a$$_0$$ to a$$_5$$ in that order into S.

II: enqueue the elements of a from a$$_0$$ to a$$_5$$ in that order into Q.

III: pop an element from S.

IV: dequeue an element from Q.

V: pop an element from S.

VI: dequeue an element from Q.

VII: dequeue an element from Q and push the same

VIII: Repeat operation VII three times.

IX: pop an element from S.

X: pop an element from S.

The top element of S after executing the above operations is ____________.