2. Assume a declarative interface where n and max are constant integers, and A is an array of integers of size max. Consider the following correctness statement: ASSERT ( 1 < n <= max int i; i = n-1; A [n-1] = 1; while( i >= 1) { A[i-1] = A[i]ni + 1; i = i-1%; } ASSERT ForAll(k = 0%; k < n) A[k] == (n-k)* (n-k+1)/2) 1 (a) Give a complete proof tableau for the above correctness statement by adding all the intermediate assertions. State all the mathematical facts that are used in the proof. Hints: As our discussion in class will also emphasize the following two assertions are obvious tautologies: Forall (k=i; k Forall (k=i; k P(i) && Forall (k=i+1; k

Implement in C Programming 6.11.2: Modify an array parameter. Write a function SwapArrayEnds() that swaps the first and last elements of the function's array parameter. Ex: sortArray = {10, 20, 30, 40} becomes {40, 20, 30, 10}. #include <stdio.h> /* Your solution goes here  */ int main(void) {   const int SORT_ARR_SIZE = 4;   int sortArray[SORT_ARR_SIZE];   int i;   int userNum;    for (i = 0; i < SORT_ARR_SIZE; ++i) {      scanf("%d", &sortArray[i]);   }    SwapArrayEnds(sortArray, SORT_ARR_SIZE);    for (i = 0; i < SORT_ARR_SIZE; ++i) {      printf("%d ", sortArray[i]);   }   printf("\n");    return 0;}

Exercise 2: Consider the following class: public class Sequence { private ArrayList values; public Sequence() { values = new ArrayList(); } public void add(int n) { values.add(n); } public String toString() { return values.toString(); } } Add a method public Sequence merge(Sequence other) that merges two sequences, alternating ele- ments from both sequences. If one sequence is shorter than the other, then alternate as long as you can and then append the remaining elements from the longer sequence. For example, if a is 1 4 9 16 and b is 9 7 4 9 11 then a.merge(b) returns the sequence 1 9 4 7 9 4 16 9 11 without modifying a or b.

A) Write a generic Java queue class (a plain queue, not a priority queue). Then, call it GenericQueue, because the JDK already has an interface called Queue. This class must be able to create a queue of objects of any reference type. Consider the GenericStack class shown below for some hints.  Like the Stack class below, the GenericQueue should use an underlying ArrayList<E>.    Write these methods and any others you find useful: enqueue() adds an E to the queue peek() returns a reference to the object that has been in the queue the longest, without removing it from the queue dequeue() returns the E that has been in the queue the longest, and removes it from the queue contains(T t) returns true if the queue contains at least one object that is equal to t *in the sense that calling .equals() on the object with t the parameter returns true.* Otherwise contains returns false.  size() and isEmpty() are obvious.