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• How can I best study a problem to determine whether recursion can/should be used?

  - by user10326

  In some cases, I fail to see that a problem could be solved by the divide and conquer method. To give a specific example, when studying the find max sub-array problem, my first approach is to brute force it by using a double loop to find the max subarray. When I saw the solution using the divide and conquer approach which is recursion-based, I understood it but ok. From my side, though, when I first read the problem statement, I did not think that recursion is applicable. When studying a problem, is there any technique or trick to see that a recursion based (i.e. divide and conquer) approach can be used or not?

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• How many copies are needed to enlarge an array?

  - by user10326

  I am reading an analysis on dynamic arrays (from the Skiena's algorithm manual). I.e. when we have an array structure and each time we are out of space we allocate a new array of double the size of the original. It describes the waste that occurs when the array has to be resized. It says that (n/2)+1 through n will be moved at most once or not at all. This is clear. Then by describing that half the elements move once, a quarter of the elements twice, and so on, the total number of movements M is given by: This seems to me that it adds more copies than actually happen. E.g. if we have the following: array of 1 element +--+ |a | +--+ double the array (2 elements) +--++--+ |a ||b | +--++--+ double the array (4 elements) +--++--++--++--+ |a ||b ||c ||c | +--++--++--++--+ double the array (8 elements) +--++--++--++--++--++--++--++--+ |a ||b ||c ||c ||x ||x ||x ||x | +--++--++--++--++--++--++--++--+ double the array (16 elements) +--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--+ |a ||b ||c ||c ||x ||x ||x ||x || || || || || || || || | +--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--+ We have the x element copied 4 times, c element copied 4 times, b element copied 4 times and a element copied 5 times so total is 4+4+4+5 = 17 copies/movements. But according to formula we should have 1*(16/2)+2*(16/4)+3*(16/8)+4*(16/16)= 8+8+6+4=26 copies of elements for the enlargement of the array to 16 elements. Is this some mistake or the aim of the formula is to provide a rough upper limit approximation? Or am I missunderstanding something here?

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• Is using build-in sorting considered cheating in practice tests?

  - by user10326

  I am using one of the practice online judges where a practice problem is asked and one submits the answer and gets back if it is accepted or not based on test inputs. My question is the following: In one of the practice tests, I needed to sort an array as part of the solution algorithm. If it matters the problem was: find 2 numbers in an array that add up to a specific target. As part of my algorithm I sorted the array, but to do that I used Java's quicksort and not implement sorting as part of the same method. To do that I had to do: java.util.Arrays.sort(array); Since I had to use the fully qualified name I am wondering if this is a kind of "cheating". (I mean perhaps an online judge does not expect this) Is it? In a formal interview (since these tests are practice for interview as I understand) would this be acceptable?

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