## Format Requirement Algorithms in pseudo code **MUST** be placed in code blocks/fences, and use `cpp` as the syntax highlighter. · Algorithms should follow the pseudo code standard described in *Pseudocode Handout*. Do NOT change the template except the answer portion. Formulas and equations should be in math mode using Latex math symbols. Markdown math tutorial: http://tug.ctan.org/info/undergradmath/undergradmat h.pdf Two ways to enter math mode: Insert a pair of dollar signs: \$your uations go here\$. This is the inline math mode. *Notice that there is no space between the \$ and the letter*. Insert a pair of double-dollar signs: \$\ $ your equations go here \$\$, which produces a standa lone eguation /formula set

Python question Analysis: Invariants (Q16-17) For each of the following functions, identify the loop invariant, exit condition and post condition.    Question 16 (Invariant 1) This function returns the list of integers that are multiples of both 3 and 7 that occurs within a given list. Identify the loop exit condition, the loop post-condition, and the loop invariant at the end of the loop, which shows the algorithm’s correctness. def multiples_count(lst):    """    Input: a list of integers, lst    Output: the list of integers in lst that are multiples of both 3 and 7    """    res = []    for i in range(len(lst)):        if lst[i]%3 == 0 and lst[i]%7 == 0:            res.append(lst[i])        # Identify the loop invariant here    return res Question 17 (Invariant 2) This function checks if a given list (of comparable elements) is sorted in ascending order. Identify the loop exit condition, the loop post-condition, and the loop invariant at the end of each iteration of the loop, which…

*Data Structures and Algorithm Sliding (or k 2 − 1) puzzle using A* algorithm A sliding puzzle is a puzzle that challenges a player to slide flat pieces along certain routes on a k × k board to establish a certain end-configuration. The fifteen puzzle is the oldest type of sliding block puzzle and it was invented by Noyes Chapman in 1880s. It is played on a 4-by-4 grid with 15 square blocks labeled 1 through 15 and a blank square. The goal is to rearrange the blocks so that they are in order, using as few moves as possible. Blocks are permitted to be slid horizontally or vertically into the blank square. Search time for the goal state can be shortened by adding a priority for the direction of the search to proceed. A* algorithm is commonly used as an efficient alternative to find an answer to the sliding puzzle with the minimum number of steps.  you will implement A* algorithm to solve the sliding puzzle problem.   A* Algorithm  A* (pronounced A-star) is an informed search algorithm,…

Python Big-O Notation/Time Complexity Pls answer only if u know big-o Thanks!  Item #3.

Algorithms in pseudo code ** MUST** be placed in code blocks/fences, and use `cpp` as the syntax highlighter. - Algorithms should follow the pseudo code standard described in *Pseudocode Handout*. - Do NOT change the template except the answer portion. Formulas and equations should be in math mode using Latex math symbols. - Markdown math tutorial: http://tug.ctan.org/info/undergradmath/undergradmat h.pdf - Two ways to enter math mode: - Insert a pair of dollar signs: \$your equations go here\$. This is the inline math mode. *Notice that there is no space between the \$ and the letter*. - Insert a pair of double-dollar signs: \$\$ your equations go here \$\$, which produces a standalone equation/formula set. le for s ## Problem Set ### Problem 1 Design an algorithm in pseudo code for computing $\lfloor \sqrt n \rfloor$ for any *positive* integer $n$. Besides assignment and comparison, your algorithm may only use the four basic arithmetical operations, namely: - addition subtraction -…