4.29 1 a. Show that if all nodes in a splay tree are accessed in sequential order, the resulting tree consists of a chain of left children. 2 3 4 5 6 7 8 10 11 12 13

5. Suppose we have a binary tree of height h. Prove that the number of leaves of this binary tree is at most 2" (that is 2 to the power of h).

Topic: Binary Tree Graph

Write the program that allows the user to sort using the Bubble Sort, Selection Sort, Insertion Sort  and Shell Short  The program should be able to read in data from a binary file.  The first element of the binary file will be used to tell how many elements to read in.  Once all the data has been read in, the program should sort the data.  The user should be able to choose which algorithm to use to sort the data.  The program should print the time before and after the sort - be sure to not print the start time until after the algorithm has been chosen from your menue.  The last part of the program should print out the value and location of three random positions in your array   The name of each algorithm:Insertion Sort   A description of the elapsed time found for each input file: 10numbers; 12 seconds 100number: 30 seconds ...   A screenshot of the output of your program showing the start time and stop time of each algorithm running on the largest file (1000000numbers) as well as the…