$.$What is the worst complexity of running AC$-3$ on a tree$-$structured CSP$?$Knowing that E is the number of edges, and D is the size of the largest domain:a$)()$O$($ED$)$b$)(/)$O$($E$/$D$)$c$)(2)$O$($ED $2)$d$)(2)$O$($E $2$ D$)$e$)()$O$($ED n $)$The name of the algorithm that results from the local beam search with $=1$k$=1$:a$)$ Depth$-$First Searchb$)$ Hill Climbing Searchc$)$ Uniform Cost Searchd$)$ Breadth$-$First Search...................... are mathematical problems defined as a set of objects whose state must satisfy a number of limitations:a$)$ Constraint Satisfaction Problemsb$)$ Uniform Search Problemsc$)$ Local Search Problemsd$)$ All of the aboveThe name of the algorithm that results from the local beam search with one initial state and no limit on the number of states retained:a$)$ Depth$-$First Searchb$)$ Hill Climbing Searchc$)$ Uniform Cost Searchd$)$ Breadth$-$First Search............... algorithm is used in robotics because percepts, states, and actions are continuous:a$)$ A$*$b$)$ Hill Climbing Searchc$)$ Uniform Cost Searchd$)$ Breadth$-$First Searche$)$ Depth$-$First SearchIf the constraint graph has no loops, the CSP can be solved in $...................$ time:a$)()$O$($nd$)$b$)(2)$O$($nd $2)$c$)(2)$O$($n $2$ d$)$d$)(22)$O$($n $2$ d $2)$e$)()$O$($nd n $)$