Using the Dynamic Programming method $($See Appendix C$),$ calculate m$14$ to complete the table

below which determines the least number of multiplications which can be used to compute M$.$

$[3$ marks$]$

m$11=0$ m$22=0$ m$33=0$ m$44=0$

m$12=12500$ m$23=37500$ m$34=60000$

m$13=27500$ m$24=67500$

m$14=$

$($ii$)$ Using the sigma notation write an expression to determine the computational complexity of the

algorithm given in appendix C$.[2$ marks$]$

$($iii$)$ Without performing a full algebraic analysis, suggest a complexity class for the algorithm,

based on your expression in part $($ii$)$ above. Justify your answer.