PProblem $1.$ Consider the following RANDOM$-$SEARCH algorithm that searches for an integer value x in an array A$[]$ that consists of n elements. The algorithm picks a random index k into A$.$ If A$[$k$]=$ x then it terminates; otherwise, it continues the search by picking random indices into A$[]$ until it finds an index j such that A$[$j$]=$ x or until it checked every element of A$[].$ Note that it picks from the whole set of indices each time, so that it may examine a given element more than once. It uses a random number generator $($or a pseudo random number generator$)$ Random$($u$,$ v$)$ that returns a random integer in the range $[$u$,$ v$],$ where each integer is equally likely. RANDOM$-$SEARCH int visited$[$n$]$ Comment: visited$[$k$]$ indicates if element A$[$k$]$ has been searched int numberVisited $=0$ Comment: keeps track of the number of nodes visited so far for i $=1,2,...$ n visited$[$n$]=0$ Comment: initialize visited while numberVisited $<$ n Comment: keep searching if there are some elements that haven$$t been visited k $=$ Random$(1,$n$)$ if visited$[$k$]=0$ then visited$[$k$]=1$ numberVisited $=$ numberVisited $1$ if A$[$k$]=$ x then return k; $($a$)[5$ pt$]$ Suppose there is exactly one index k such that A$[$k$]=$ x$.$ What is the expected number of indices into A$[]$ that the algorithm must pick before it finds x and RANDOM$-$SEARCH terminates? $($b$)[5$ pt$]$ Suppose there are no indices k such that A$[$k$]=$ x$.$ What is the expected number of indices into A$[]$ that the algorithm picks before it checked all elements of A$[]$ and RANDOM$-$SEARCH terminates.roblem $1.$ Consider the following RANDOM$-$SEARCH algorithm that searches for an integer value x in an array A$[]$ that consists of n elements. The algorithm picks a random index k into A$.$ If A$[$k$]=$ x then it terminates; otherwise, it continues the search by picking random indices into A$[]$ until it finds an index j such that A$[$j$]=$ x or until it checked every element of A$[].$ Note that it picks from the whole set of indices each time, so that it may examine a given element more than once. It uses a random number generator $($or a pseudo random number generator$)$ Random$($u$,$ v$)$ that returns a random integer in the range $[$u$,$ v$],$ where