Intro to Algorithms from MIT Press qualifies QuickSort as in-place – it sorts the elements within the array with at most a constant amount of them outside the array at any given time. At the end of the day, people will always have differing opinions (is Top-Down Memoization considered Dynamic Programming? Not to some “classical” folks), side with who you … Read more
(I’m assuming that this is just some kind of thought exercise, or even a trick homework/interview question, but I suppose I could imagine some bizarre scenario where you’re not allowed any heap space for some reason [some really bad custom memory manager? some bizarre runtime/OS issues?] while you still have access to the stack…) Breadth-first … Read more
Using Commons Lang (to convert) + Collections (to min/max) Note that Arrays.asList() wraps the underlying array, so it should not be too memory intensive and it should not perform a copy on the elements of the array.
I’ll do my best to explain it here on simple terms, but be warned that this topic takes my students a couple of months to finally grasp. You can find more information on the Chapter 2 of the Data Structures and Algorithms in Java book. There is no mechanical procedure that can be used to get the BigOh. As … Read more
The worst case of merge sort will be the one where merge sort will have to do maximum number of comparisons. So I will try building the worst case in bottom up manner: Suppose the array in final step after sorting is {0,1,2,3,4,5,6,7} For worst case the array before this step must be {0,2,4,6,1,3,5,7} because here left subarray={0,2,4,6} and right … Read more
You’ve got it, just keep going! And be careful with the indexes… To simplify a bit I’ll assume that N and M are > k, so the complexity here is O(log k), which is O(log N + log M). Pseudo-code: For the demonstration you can use the loop invariant i + j = k, but … Read more
I want to know what will be the best case for a bubble sort ? There may be a case wherein there may be no swapping for the say last 2 passes for example. I’m doing my program in C language. Suppose i have an array of 5 elements and i give the elements as … Read more
There you go. This is probably the most trivial example of a function that runs in O(n!) time (where n is the argument to the function):
It says A* is faster than using dijkstra and uses best-first-search to speed things up. A* is basically an informed variation of Dijkstra.A* is considered a “best first search” because it greedily chooses which vertex to explore next, according to the value of f(v) [f(v) = h(v) + g(v)] – where h is the heuristic and g is the cost so … Read more
Selection Sort: Given a list, take the current element and exchange it with the smallest element on the right hand side of the current element. Insertion Sort: Given a list, take the current element and insert it at the appropriate position of the list, adjusting the list every time you insert. It is similar to … Read more