Give an argument for why the Prim's algorithm will always return a Minimum Spanning Tree?

Suppose you started with an empty binary search tree. We've seen previously that inserting the keys 1, 2, 3, 4, 5, 6, 7 (in that order) would lead to a binary search tree whose shape we called degenerate. Propose a second ordering of the same keys that would also lead to a degenerate-shaped binary search tree. If possible, propose a third ordering of the same keys that would also lead to a degenerate-shaped binary search tree. If there are no more orderings other than the one we provided and the second one you proposed, briefly explain why there are no more.

1. Suppose that we are given a binary search tree T with distinct keys. We would like to find out the kth smallest and largest keys in T. The value of k is of course smaller than the size of T. Please provide efficient approaches to find these two keys and analyze your methods.

Which one is the key thing in backtracking? Insertion Recursion Submission   In what manner is a state-space tree for a backtracking algorithm constructed? Depth-first search Breadth-first search Twice around the tree Nearest neighbour first   What does the following function do? int fun(int x, int y) {     if (y == 0)   return 0;     return (x + fun(x, y-1)); } x + y x + x*y x*y xy     Consider the following recursive function fun(x, y). What is the value of fun(4, 3) int fun(int x, int y) {   if (x == 0)     return y;   return fun(x - 1,  x + y); } 10 9 13 12   Predict output of following program   16 4 Runtime Error 8   Assume you have the following backtracking based sorting algorithm:bool Backtracking_Sort(sorted_list, unsorted_list, index, length) {    if (index == length) {        return true;    }    Potential_values = [];     If (index != 0) {Potential_values = get_larger_unused_values(sorted_list, unsorted_list, index);} else {    Potential_values = copy(unsorted_list);}…