Given a sequence X[1, . . . , n], find a longest increasing subsequence. Precisely define the subproblem. Provide the recurrence equation. Describe the algorithm in pseudocode to compute the optimal value. Describe the algorithm in pseudocode to print out an optimal solution.

Consider the Trisection method, which is analogous to the Bisection method except that at each step, the interval is subdivided into 3 equal subintervals, instead of 2; then takes a subinterval where the function values at the endpoints are of opposite signs. Is the Trisection method guaranteed to converge if for the initial interval [a, b], we havef(a)f(b) < 0? Why or why not? Considering computational cost (e.g. function evaluations,  oating point operations), would you prefer Bisection or Trisection method? Explain.

Please write it on paper

Algorithm OPTIMAL-PARAMETRIZATION.Given F(x, y, z) ∈ Q[x, y, z], an irreducible homogeneous polynomial defining a rational plane curve C, the algorithm computes an optimal rational parametrization of C