Which recurrence best describes the work in the divide-and-conquer algorithm for closest points AFTER realizing that there are at most a constant number of points on or near the dividing line that could be closer than the minim distance detected so far? a. T(n) = T(n/2) + θ(n)
b. T(n) = T(n/2) + θ(n^2)
c. T(n) = 2T(n/2) + θ(n)
d. T(n) = 2T(n/2) + θ(n^2)
e. T(n) = T(n-1) + θ(n)
f. T(n) = T(n-1) + θ(n^2)
g. T(n) = 2T(n-1) + θ(n)
h. T(n) = 2T(n-1) + θ(n^2)

Per the previous question, what is that upper bound on the constant number of points that can be on the mid-point line or just on the other side of it, such that they are closer to a given point than the minimum distance detected so far on either side of the mid-line?

Design a class tictactoe that: holds the following information about the game: two-dimensional array (3 by 3), and winner. add additional variables as needed. includes the functions to perform the various operations on objects. for example, function to print the board, getting the move, checking if move is valid, determining if there is a winner after each move. add additional operations as needed. includes constructor(s). write the functions of the class, and write a program that uses the class. the program should declare an object of type tictactoe. the program will create the board and store it in the array. the program will allow two players to play the tic-tac-toe game. after every valid move update the array, check if there is a winner. if there is no winner and no tie, then print the board again to continue.