The algorithm given in this chapter to partition a simple polygon into monotone pieces constructs a doubly-connected edge list for the parti- tioned polygon. During the algorithm, new edges are added to the DCEL (namely, diagonals to get rid of split and merge vertices). In general, adding an edge to a DCEL cannot be done in constant time. Discuss why adding an edge may take more than constant time, and argue that in the polygon-partitioning algorithm we can add a diagonal in O(1) time nevertheless.

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.