Given a binary tree t = (v, e) with each vertex v ∈ v associated with a nonnegative weight w(v), design a dynamic programming based algorithm to partition the tree t into k or fewer subtrees by removing k − 1 or fewer edges from t such that the maximum weight of each subtree is minimized among all possible partitions, where the weight of a tree is the sum of weights of all vertices in the tree.

Consider the following function main: int main() { int alpha[20]; int beta[20]; int matrix[10][4]; . . } a. write the definition of the function inputarray that prompts the user to input 20 numbers and stores the numbers into alpha. b. write the definition of the function doublearray that initializes the elements of beta to two times the corresponding elements in alpha. make sure that you prevent the function from modifying the elements of alpha. c. write the definition of the function copyalphabeta that stores alpha into the first five rows of matrix and beta into the last five rows of matrix. make sure that you prevent the function from modifying the elements of alpha and beta. d. write the definition of the function printarray that prints any onedimensional array of type int. print 15 elements per line. e. write a c11 program that tests the function main and the functions discussed in parts a through d. (add additional functions, such as printing a two-dimensional array, as needed.)

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Suppose there is a relation r(a, b, c) with a b+-tree index with search keys (a, b).1. what is the worst-case cost of finding records satisfying 10 < a < 50 using this index, in terms of the number of records n1, retrieved and the height h of the tree? 2. what is the worst-case cost of finding records satisfying 10 < a < 50 and 5 < b < 10 using this index, in terms of the number of records n2 that satisfy this selection, as well as n1 and h defined above? 3. under what conditions on n1 and n2, would the index be an efficient way of finding records satisfying the condition from part (2)?