Question 1: mergesort
Compute the number of inversions in an array of integers (mergesort based)
Question 2: quicksort
Compute the total number of comparisons used to sort the given input file by QuickSort
Question 3: minimum cut
Code up and run the randomized contraction algorithm for the min cut problem and use it on the above graph to compute the min cut.
Question 4: strong connected components
Code up the algorithm for computing strongly connected components (SCCs), and to run this algorithm on the given graph.
Question 5: heap-based Dijkstra's shortest path
Run Dijkstra's shortest-path algorithm on a given graph with O(mlog(n)) running time.
Question 6: median maintenance and hashing based 2-sum
Implement the "Median Maintainence" algorithm.
Implement a variant of the 2-SUM algorithm in a large data set.