I think you can solve this using the dynamic programming longest increasing subsequence algorithm: http://www.algorithmist.com/index.php/Longest_Increasing_Subsequence Accounting for the rotations is easy enough: for every tower all you have to check is what happens if you use its height as the length of the base and its width as the height and what happens if you … Read more
Here is a sketch of an O(n^2 log n) solution. First, the preliminaries shared with other answers. When we have a line passing through some rectangles, we can translate it to any of the two sides until it passes through a corner of some rectangle. After that, we fix that corner as the center of … Read more
Be aware that there’s a small mistake in the explanation of the algorithm in the book, look in the errata for the text “(*) Page 297”. About your questions: No, the items don’t need to be sorted, only contiguous (that is, you can’t rearrange them) I believe the easiest way to visualize the algorithm is … Read more
There’s a beautiful algorithm for solving this problem in time O(n + Sort), where Sort is the amount of time required to sort the input array. The idea behind the algorithm is to sort the array and then ask the following question: what is the smallest positive integer you cannot make using the first k … Read more
To build up to how you’d use the longest increasing subsequence algorithm to solve this problem, let’s start off with some intuition and then build up to a solution. Since you can only build bridges between cities at matching indices, you can think of the set of bridges that you end up building as the … Read more
The term “cut and paste” shows up in algorithms sometimes when doing dynamic programming (and other things too, but that is where I first saw it). The idea is that in order to use dynamic programming, the problem you are trying to solve probably has some kind of underlying redundancy. You use a table or … Read more
This question can be easily solved with the help of set in O(N) time and space complexity.First add all the elements of array into set and then traverse each element of array and check whether K-ar[i] is present in set or not. Here is the code in java with O(N) complexity : boolean flag=false; HashSet<Long> … Read more
AC stands for ‘Accepted’ solution.
I agree with the logic of your method but there is no need to do recursive processing or global maxima searches. To find the sell/buy days you just need to look at each day once: The trick is to start from the end. Stock trade is easy if your travel backwards in time! If you … Read more
This can be solved in O(n^2) using dynamic programming. Basically, the problem is about building the longest palindromic subsequence in x[i…j] using the longest subsequence for x[i+1…j], x[i,…j-1] and x[i+1,…,j-1] (if first and last letters are the same). Firstly, the empty string and a single character string is trivially a palindrome. Notice that for a … Read more