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Computer Science Given an array of 1 2 , 0 0 0 integers, where the values range from 1 to 1 0 0 , 0

Computer Science Given an array of 12,000 integers, where the values range from 1 to 100,000, use a counting sort algorithm to sort the array. Determine the time complexity of counting sort and the space complexity of the counting array used for sorting. A binary search tree (BST) with 450 nodes has a maximum height of 45. If the BST is unbalanced, calculate the number of nodes in the longest path from the root to a leaf. For a graph with 110 vertices and 330 edges, calculate the number of Eulerian circuits using Fleurys algorithm, assuming the graph is Eulerian. Given a hash table with 5500 slots and a load factor of 0.6, estimate the number of elements in the hash table and the average number of elements per slot. A quicksort algorithm is applied to an array of 12,000 elements with a median-of-three pivot strategy. Determine the average number of comparisons made by the quicksort algorithm and its expected time complexity. A dynamic programming approach is used to solve the matrix chain multiplication problem for a sequence of 18 matrices. Calculate the time complexity of the algorithm and the size of the DP table used. For a graph with 140 vertices and 420 edges, use Prims algorithm to find the minimum spanning tree. Calculate the time complexity of the algorithm and the number of edges in the resulting spanning tree. A binary heap is used to implement a priority queue with 2400 elements. Determine the time complexity for inserting a new element and deleting the minimum element from the heap. Given a set of 100 tasks with start and end times, use the greedy algorithm for interval scheduling to determine the maximum number of non-overlapping tasks that can be scheduled. A depth-first search (DFS) is performed on a graph with 180 nodes and 600 edges. Calculate the space complexity of the DFS algorithm with respect to the number of nodes and edges. For a network flow problem with 150 nodes and 450 edges, apply the Ford-Fulkerson method to find the maximum flow. Determine the time complexity of the Ford-Fulkerson algorithm in terms of the number of nodes and edges. A set of 28 integers is sorted using radix sort. Calculate the time complexity of the radix sort algorithm and the maximum number of passes required for sorting. For a shortest path problem in a graph with 130 nodes and 390 edges, apply Dijkstras algorithm using a priority queue implemented as a binary heap. Calculate the time complexity of the algorithm and the maximum number of heap operations required.

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