Which of the following is the size of the state space? Ο ΜΝ Ο ΜΝΤ Ο ΜΝB Ο ΜΝΤB O (MN)B+1 O 2MN MN O (MN)B+12B Save Answer Q8.3 Which of the following heuristics are admissible (if any)? Cost of optimal path to target in the simpler problem that has no birds. Manhattan distance from the insect's current position to the target. Manhattan distance from the insect's current position to the nearest bird. Manhattan distance from the insect's current position to the target divided by three.

3. A thief robbing a store finds n items. The i" item is worth v; dollars and weighs w; pounds, where v; and wi are integers. The thief wants to take as valuable a load as possible, but he can carry at most W pounds in his knapsack, for some integer W. Which items should he take? This problem is called 0-1 knapsack problem because for each item, the thief either take it or leave behind. No fractional amount from an item can be taken. Consider the most valuable load that weighs at most W pounds. If we remove item j from this load, the remaining load must be the most valuable load weighing at most W-w; that the thief can take from the n - I original items excluding j. Write a simple pseudo code for the given greedy algorithm description first and show how using this greedy algorithm to solve the problem of Knapsack problem below. Assume that maximum weight that can be carried is 7 lbs. Does it your code find the optimal solution? Show the optimal solution if it exists. Item Value ($)…

You solve a non-singular system of 10,000 linear equations with 10,000 unknowns using the Gauss-Jordan algorithm without pivoting with single precision numbers and arithmetics on a computer that natively can do single precision operations very fast, but can operate in double and half precision as well. Your solution has a residual infinity-norm that is unacceptably large. In which order should you apply the following strategies to lower the residual norm? If a strategy is not / no longer helpful, do not list it as an option. a) use half precision numbers and arithmetics instead of single precision; b) use double precision numbers and arithmetics instead of single precision; c) use partial pivoting; d) use pivoting when encountering a zero in the pivot position.

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