as the initial current position two players alternate turns at each turna player must select grid element in the current row or column the value of the selected position is added to the player' scoreand that position becomes the current position and cannot be selected again players alternate until all grid elements in the current row and column are already selectedat which point the game ends and the player with the higher score wins othello played on six-by-six board is forced win for black prove this by writing program what is the final score if play on both sides is optimalreferences the original paper on huffman codes is [ variations on the algorithm are discussed in [ ][ ]and [ another popular compression scheme is ziv-lempel encoding [ ][ here the codes have fixed length but represent strings instead of characters [ and [ are good surveys of the common compression schemes the analysis of bin-packing heuristics first appeared in johnson' ph thesis and was published in [ improvements in the additive constants of the bounds for first fit and first fit decreasing were given in [ and [ ]respectively the improved lower bound for online bin packing given in exercise is from [ ]this result has been improved further in [ ][ ]and [ [ describes another approach to online bin packing theorem is from [ the closest points algorithm appeared in [ [ and describes the turnpike reconstruction problem and its applications the exponential worstcase input was given by [ books on computational geometry include [ ][ ][ ]and [ [ contains the lecture notes for computational geometry course taught at mitit includes an extensive bibliography the linear-time selection algorithm appeared in [ the best bound for selecting the median is currently ~ comparisons [ [ discusses the sampling approach that finds the median in expected comparisons the ( multiplication is from [ generalizations are discussed in [ and [ strassen' algorithm appears in the short paper [ the paper states the results and not much else pan [ gives several divideand-conquer algorithmsincluding the one in exercise coopersmith and winograd [ gave an on algorithm that was the best-known for over two decades this bound was silently lowered to on in by stothersand then to on by vassilevska-williams in [ the classic references on dynamic programming are the books [ and [ the matrix ordering problem was first studied in [ it was shown in [ that the problem can be solved in ( log ntime an ( algorithm was provided for the construction of optimal binary search trees by knuth [ the all-pairs shortest-path algorithm is from floyd [ theoretically better ( (log log nlog ) / algorithm is given by fredman [ ]but not surprisinglyit is not practical slightly improved bound (with / instead of / is given in [ ]lowered to ( log log nlog [ ]and most recently to ( log log nlog [ ]see also [ for related results for undirected graphsthe all-pairs problem can be solved in | ||vlog (| || |)where was previously seen in the union find analysis in [ under certain conditionsthe running time of dynamic programs can