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Design and Analysis of Algorithms Explain the approximation algorithm for the travelling salesman problem.20257mFormal Language & Automata TheoryWrite a short note on: NP-hard problem20203.5mFormal Language & Automata TheoryWrite short notes on: NP-hard problem20227mDesign and Analysis of Algorithms Consider a TSP with 4 cities A, B, C, D and the following distance matrix: | | A | B | C | D | |---|---|---|---|---| | A | 0 | 10 | 15 | 20 | | B | 10 | 0 | 35 | 25 | | C | 15 | 35 | 0 | 30 | | D | 20 | 25 | 30 | 0 | Answer the following: (i) Use the branch-and-bound algorithm to find the shortest possible route that visits all cities exactly once and returns to the starting city. (ii) Show the branching steps and calculate lower bounds for each partial solution. (iii) Identify how the bounding helps prune the search tree.20247m