Write an algorithm the find any item in the crowded objects

b$)$ Optimize using clusters

c$)$ What are the complexities

Three separate group of objects are clustered and the clustered are further ordered $($Some kind of tree with tree roots$).$ If we have $N$ cards what is this datastructure complexity of

a$)$ Adding new cards

b$)$ Ordering

c$)$ Changing some cards between clusters and ordering

If a vehicle network with average speed of $v$ and the network is double linked maybe more cross links$($roads in a town$).$ If we are at a fixed point what is the complexity of getting a vehicle$($taxi$)$ on the route beside us$.$ Assume $N$ vehicles are present and a fraction $B$ of them is empty.

Write an algorithm of throwing $N$ balls in an room that balls can reflect from sidewalls and can come to you. Every t time you throw a ball. You should follow balls with a scanning algorithm in order to make the final catch move. Design such a game is there modes according to the catch and throw intervals.