Please written by computer source Given two strings x1…xn, y1…ym find the length of their longest common subsequence, that is, the largest k for which there exist indices i1<…

For the following sets A C WHILE-data, state whether they are WHILE-decidable and explain your answer. In cases where A is decidable this explanation should consist of a description of the decision procedure. Recall that p denotes the encoding of WHILE-program p in D. WHILE i. A= {p| [p]" (d) = c} where c, d = D are fixed. ii. A = {˜ [p, k]¯ | p with input nil terminates in / steps or less }.

n For n distinct elements a₁,..., an with positive weights w₁,..., wn s.t. -1 W₁ = 1, design a linear-time algorithm returning the element ak, which satisfies the following: Σ w₁ ≤ 1/2 and Σ wi ≤ 1/2. ai ak Assume that such an ak always exists. You should also justify the time complexity.

Write down a summation version of the run-time of each of the following two algorithms and then figure out and prove the asymptotic complexity (-set) of that run-time function. (a) FUNCTION Wa(n = N) x < 0 i 1 WHILE i < n² DO x + + i ← 5i RETURN(x) (b) FUNCTION W₁(n = N) x < 0 FOR 1 TO ² DO j← 3 WHILE j ≤ i DO x + + j← 2j RETURN(x)

Please answer the following question in depth with full detail. Consider the 8-puzzle that we discussed in class. Suppose we define a new heuristic function h3 which is the average of h1 and h2, and another heuristic function h4 which is the sum of h1 and h2. That is, for every state s ∈ S: h3(s) =h1(s) + h2(s) 2 h4(s) =h1(s) + h2(s) where h1 and h2 are defined as “the number of misplaced tiles”, and “the sum of the distances of the tiles from their goal positions”, respectively. Are h3 and h4 admissible? If admissible, compare their dominance with respect to h1 and h2, if not, provide a counterexample, i.e. a puzzle configuration where dominance does not hold.

Assume that void some_fct (int X); has time complexity Ⓒ(X) for (k 0; k <= N; k k+1) { some fct (k); // } Final answer: TCfor-k = O(_ =