Let $1<2<3<4<5<6$ be $6$ numbers accessible with the following probabilities: $1=220,2=120,3=220,4=520,5=120$ and $6=320.$ Let $0$ be the probability of searching for an item $<1,6$ the probability of searching for an item $>6,$ and $$ the probability of searching for an item between $$ and $+1$ for $=1,2,3,4,5.$ Take $0=6=0,1=220$ and $=120$ for i$=2,3,4,5.$ You are to construct an optimal binary search tree. a$.$ Write down a table for the $\text{'}$s$,$ and a table for the $\text{'}$s and their corresponding $\text{'}$s as defined in the algorithm for optimal binary search trees. b$.$ Construct the optimal binary search tree.