Suppose we have a circular linked list of numbers, implemented as a pair of arrays, one storing the actual numbers and the other storing successor pointers. Specifically, let X[L be an array of n distinct real numbers, and let N[1.n be an array of indices with the following property: If Xli] is the largest element of X, then X[N[i) is the smallest element of X; otherwise, X[N[i]] is the smallest element of Xthat is larger than Xi]. For example: Xi83 54 16 31 45 99 78 62 27 N[i6 8 9 5 2 3 1 7 4 Describe and analyze a randomized algorithm that determines whether a given number x appears in the array X in O(Vn) expected time. Your algorithm may not modify the arrays X and N Hint: Think of how random sampling can help here. Suppose we have a circular linked list of numbers, implemented as a pair of arrays, one storing the actual numbers and the other storing successor pointers. Specifically, let X[L be an array of n distinct real numbers, and let N[1.n be an array of indices with the following property: If Xli] is the largest element of X, then X[N[i) is the smallest element of X; otherwise, X[N[i]] is the smallest element of Xthat is larger than Xi]. For example: Xi83 54 16 31 45 99 78 62 27 N[i6 8 9 5 2 3 1 7 4 Describe and analyze a randomized algorithm that determines whether a given number x appears in the array X in O(Vn) expected time. Your algorithm may not modify the arrays X and N Hint: Think of how random sampling can help here