The following binary search tree (BST) operations can be implemented efficiently on splay trees. For simplicity, assume that all elements are distinct. Join (T1, T2): Assume every element in BST T1 is less than or equal to every element in BST T2, and returns the BST formed by combining the trees T1 and T2. Split (T, a): Split BST T, containing element a, into two BSTs: T1, containing all elements in T with key less or equal to a; and T2, containing all elements in T with key greater than a. Show how to correctly implement those operations on splay trees so that the amortized running time of your operations is O(log n). Justify your procedures and their corresponding running times. Would you be able to also implement the Join and Split operations on a Red-Black tree in O(log n) worst-case running time? Briefly justify your answer.

3. (6 pts) internally in the computer, with few exceptions, all numerical computation is done using binary numbers. output, however, often uses ascii, which is formed by appending 011 to the left of a bcd code. thus, an algorithm that directly converts a binary integer to a bcd integer is very useful. here is one such algorithm 1) draw lines to the left of the binary number to bound the expected bcd decades. (each decade is a group of 4 bits.) move the binary number one bit to the left. add 0011 to each bcd decade containing a binary value> 0100 repeat steps 2-3 until the last bit in the binary number has been moved into the least significant decade position. (note that when the last bit has been shifted into bcd decade, step 3 is not repeated.) read the bcd result. 2) 3) 4) 5) a) execute the algorithm for the binary number 1101101 b) execute the algorithm for the binary number 01110101110 4. (4 pts) represent the decimal number 3568 in bcd; excess-3 code; ascil; and hex.

10. when you create a pivottable, you need to specify where to find the data for the pivottable. is it true

Write a program that reads a set of floating-point values. ask the user to enter the values, then print • the average of the values. • the smallest of the values. • the largest of the values. • the range, that is the difference between the smallest and largest. of course, you may only prompt for the values once.