I need the algorithm, proof of correctness and runtime analysis for the problem. No code necessary ONLY algorithm. And runtime should be O(m log m) as stated in the question.

[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

MATLAB PROBLEM

4. Develop a Python code to implement bisection method to solve the problem-2. That is for: f(x) = 5?3 ―5?2 + 6?―2 find roots of this equation using bisection method. Employ initial guesses of xl = 0 and xu = 1 and iterate until the estimate error ɛa falls below a level of ɛs = 1%. Compare your answers from problem 2. Report the following: a) Estimated Roots b) Number of iterations required