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COP 3503 – Final Exam Review 1) Given the following items and a max weight of 5, solve the Knapsack problem: Item Weight Value A 2 3 B 3 4 C 4 5 D 5 6 Fill in the table below: Item/Weight A B C D 1 2 3 4 5 a. Algorithm in your own words: b. How do you know which items were chosen? 2) Find the LENGTH longest common subsequence between AGCAT and GAC. Fill in the table below: T C G A G T G C C T A G A C T T A G A T C A A C Give one longest common subsequence: ________________________________________ A 3) Binary Heap a. Show the result of inserting the value 7 into the heap shown below. (Note: The heap is shown in its array representation.) For your work, show the final result as a tree, not an array: index 1 value 1 2 2 3 8 4 17 5 6 6 14 7 20 8 31 9 19 10 11 11 9 12 20 b. Show the tree after deleteMin is run on the finished tree from above. c. Describe how a priority queue would be implemented. d. Describe how to do heap sort and the run time. 4) Draw the Disjoint Set that corresponds to the array representation shown below: index 1 2 3 4 5 6 7 value 1 1 6 8 8 1 8 8 8 5) (12 pts) Run Dijkstra's Algorithm to find the shortest distances in the graph H described below from vertex A to all other vertices. H contains vertices A, B, C, D, E, F, and G. H contains the following edges with the following weights: AB 3 AC 15 AG 40 BC 8 BD 13 CD 4 DE 10 DF 6 DG 20 EG 4 FE 2 Fill in the chart below as shown in class to receive full credit: Add to Set A A B C D E F G Note: Each row stores the estimates at that point in the algorithm from A to each of the vertices in the graph. 6) (10 pts) Consider doing a topological sort of ten items A, B, C, D, E, F, G, H, I and J with the following constraints: C before E J before G D before G B before D H before B H before A D before E D before I E before I B before F Start your Depth First Searches at A and go in alphabetical order. In any individual DFS, if you have a choice, first explore the letter that comes first alphabetically. Show your work and give the final answer of the topological sort with these rules. 7) Consider the world series problem with 5 games and 0.6 probability of winning a single game. Fill in the table below and determine the probability that your team wins the series: i/j 0 1 2 3 0 1 2 3 What is the formula for array[i][0]=____________________________ What is the formula for array[0][j]=____________________________ What is the formula for array[i][j] = ____________________________ 8) Consider the dynamic programming version of Subset Sum Given 4 values: 1,2,3,4, and a target 6, fill in the array isSubset after the algorithm is run. Then fill in the missing pseudocode below: int values[] = {1,2,3,4} Boolean[] isSubset = {true, false, false, false, false, false, false} after algorithm isSubset = { } // Determines if a subset of the elements of values adds to target // exactly. It is guaranteed that all the elements of values are // positive. public static boolean subsetSum(int[] values, int target) { // isSubset[x] stores true iff there is a subset of values // that adds up to x. boolean[] isSubset = new boolean[target+1]; isSubset[0] = true; // The only subset we have at first. // Consider each element in the array. for (int index=0; index<values.length; index++) { // Update whether or not this element helps for a // subset that adds upto check. for (______________________________________________________) { if (_____________________________________) isSubset[check] = true; } } // This is what we're interested in. return _____________________________; }