Refer to page 60 for solving the Knapsack problem using dynamic programming. Instructions: • Implement the dynamic programming approach for the 0/1 Knapsack problem. Clearly define the recurrence relation and show the construction of the DP table. Verify your solution by tracing the selected items for a given weight limit. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]

[a] Prove that the "Bin Packing Problem" (BPP) is NP-Complete. Like the rest of the exam, you may use online resources but should cite your source and summarize the proof in your own words. [b] Write an approximation algorithm for the online version of BPP that randomly considers up to three partially filled bins, and if none have room, then create a new bin and use that. [c] What modification to your solution in [b] would you recommend to solve the offline version of BPP. [d] In light of your prior knowledge of and experience with approximation algorithms for BPP, provide a reasonable estimate of the error bound

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Write the recurrence relation for the recursive binary search algorithm and explain it. Express that using Big-O notation. Show all your work.

Given below is the implementation of the bellman ford and dijkstras algorithm. Please complete the code for the time_shortest_path_algs() function according to the instructions in the 1st screenshot provided. Done in python 3.10 or later please   def bellman_ford(self,s) :        """Bellman Ford Algorithm for single source shortest path.         Keyword Arguments:        s - The source vertex.        """        distances = {v: float('inf') for v in self.adjacency_list}        distances[s] = 0        parents = {v: None for v in self.adjacency_list}         for _ in range(len(self.adjacency_list) - 1):            for from_vertex in self.adjacency_list:                for to_vertex in self.adjacency_list[from_vertex]:                    if distances[from_vertex] + self.weights[(from_vertex, to_vertex)] < distances[to_vertex]:                        distances[to_vertex] = distances[from_vertex] + self.weights[(from_vertex, to_vertex)]                        parents[to_vertex] =…

Question 4 Full explain this question and text typing work only thanks

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I’m meeting help with part C of this problem which is finding a recursive solution. The first picture shows you the problem and the second picture is the recursive solution that I have developed which is not working. Any help would be appreciated.

Provide an example of a recursive function in which the amount of work on each activation is constant. Provide the recurrence equation and the initial condition that counts the number of operations executed. Specify which operations you are counting and why they are the critical ones to count to assess its execution time. Draw the recursion tree for that function and determine the Big-© by determining a formula that counts the number of nodes in the tree as a function of n.-Use course material of   CMSC 451 and additional sources.  Need reference also . Note dont copy from any other sites

Provide an example of a recursive function in which the amount of work on each activation is constant. Provide the recurrence equation and the initial condition that counts the number of operations executed. Specify which operations you are counting and why they are the critical ones to count to assess its execution time. Draw the recursion tree for that function and determine the Big-© by determining a formula that counts the number of nodes in the tree as a function of n.-Use course material of   CMSC 451 and additional sources.  Need reference also . Note dont copy from any other sites including chat gpt also . Previous ans here was also copy from chat gpt .