Algorithm算法代写代考

IEOR 142: Introduction to Machine Learning and Data Analytics, Spring 2021 Name: SID: Instructions: Practice Midterm Exam 3 March 2021 1. Answer the questions in the spaces provided on the question sheets. If you run out of room for an answer, continue on the back of the page. 2. You are allowed one (double sided)

Summary for midterm test 2 • Hash tables, direct-addressing hash table, average length of list in hash table, hash functions, universal family of hash functions, open addressing hash table. • Dynamic programming algorithms, structure of optimal solution, recursive definition for value of optimal solution (Bellman equation), pseudo code of algorithm, running time, apply dynamic programming

5. Weighted FSAs 1 Reminder/summary: (Boolean) FSAs Generation of strings is fundamentally defined like this: (1) x1x2…xn ∈L(M) ⇐⇒ 􏰌 􏰌 ··· 􏰌 􏰆I(q0)∧∆(q0,x1,q1)∧···∧∆(qn−1,xn,qn)∧F(qn)􏰇 q0∈Q q1∈Q qn∈Q Forward and backward are useful “helper functions” whose values can be computed recursively: (2) (3) We (4) (5) (6) fwdM (ε)(q) = I(q) fwdM(x1…xn)(q)= 􏰌 􏰆fwdM(x1…xn−1)(qn−1)∧∆(qn−1,xn,q)􏰇 qn−1 ∈Q

3. Introducing finite-state automata First some standard stage-setting definitions: (1) For any set Σ, we define Σ∗ as the smallest set such that: • ε∈Σ∗,and • ifx∈Σandu∈Σ∗ then(x:u)∈Σ∗. We often call Σ an alphabet, call the members of Σ symbols, and call the members of Σ∗ strings. (2) Foranytwostringsu∈Σ∗ andv∈Σ∗,wedefineu+vasfollows: • ε+v=v • (x:w)+v=x:(w+v) Although