divide-and-conquer

问题 Given an array arr[] of integers, find out the difference between any two elements such that larger element appears after the smaller number in arr[]. Max Difference = Max { arr[x] - arr[y] | x > y } Examples: If array is [2, 3, 10, 6, 4, 8, 1, 7] then returned value should be 8 (Diff between 10 and 2). If array is [ 7, 9, 5, 6, 3, 2 ] then returned value should be 2 (Diff between 7 and 9) My Algorithm: I thought of using D&C algorithm. Explanation 2, 3, 10, 6, 4, 8, 1, 7 then 2,3,10,6 and 4

问题 I am trying to write a divide & conquer algorithm for trees. For the divide step I need an algorithm that partitions a given undirected Graph G=(V,E) with n nodes and m edges into sub-trees by removing a node . All subgraphs should have the property that they don't contain more than n/2 nodes (the tree should be split as equal as possible). First I tried to recursively remove all leaves from the tree to find the last remaining node, then I tried to find the longest path in G and remove the

问题 I was reading notes on Dynamic programming, and I encountered the following comment. If the subproblems are not independent, i.e. subproblems share subsubproblems, then a divideand-conquer algorithm repeatedly solves the common subsubproblems. Thus, it does more work than necessary What does this mean ? Can you give me examples to make the above point clear ? 回答1: The author refers to the fact that many divide-and-conquer algorithms have subproblems that overlap with one another. Consider,

问题 I was reading notes on Dynamic programming, and I encountered the following comment. If the subproblems are not independent, i.e. subproblems share subsubproblems, then a divideand-conquer algorithm repeatedly solves the common subsubproblems. Thus, it does more work than necessary What does this mean ? Can you give me examples to make the above point clear ? 回答1: The author refers to the fact that many divide-and-conquer algorithms have subproblems that overlap with one another. Consider,

问题 I'm looking for an efficient polynomial-time solution to the following problem: Implement a recursive function node x y for calculating the (x,y)-th number in a number triangle defined as g(x,y) = 0 if |x| > y = 1 if (x,y) = (0,0) = sum of all incoming paths otherwise The sum of all incoming paths to a node is defined as the sum of the values of all possible paths from the root node (x, y) = (0, 0) to the node under consideration, where at each node (x,y) a path can either continue diagonally

问题 Assume that we are given 'n' objects and a subroutine that takes two inputs and says if they are equivalent or not (e.g. it can give output as 1 if they are equal). I need to come up with an algorithm that calls the above function O(n log n) times and decides if the input has more than 'n/2' items that are equivalent to each other. 回答1: You can use the Boyer-Moore majority voting algorithm, which does at most n-1 comparisons. function find_majority(A) majority = None count = 0 for a in A: if

问题 It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center. Closed 7 years ago . We have two databases of size n containing numbers without repeats. So, in total we have 2n elements. They can be accessed through a query to one database at a time. The query is such that you give it a k and it

问题 What is the difference between Divide and Conquer Algorithms and Dynamic Programming Algorithms? How are the two terms different? I do not understand the difference between them. Please take a simple example to explain any difference between the two and on what ground they seem to be similar. 回答1: Divide and Conquer Divide and Conquer works by dividing the problem into sub-problems, conquer each sub-problem recursively and combine these solutions. Dynamic Programming Dynamic Programming is a

问题 I'm looking for an efficient algorithm for computing the multiplicative partitions for any given integer. For example, the number of such partitions for 12 is 4, which are 12 = 12 x 1 = 4 x 3 = 2 x 2 x 3 = 2 x 6 I've read the wikipedia article for this, but that doesn't really give me an algorithm for generating the partitions (it only talks about the number of such partitions, and to be honest, even that is not very clear to me!). The problem I'm looking at requires me to compute

问题 I wonder if the technique of divide and conquer always divide a problem into subproblems of same type? By same type, I mean one can implement it using a function with recursion. Can divide and conquer always be implemented by recursion? Thanks! 回答1: "Always" is a scary word, but I can't think of a divide-and-conquer situation in which you couldn't use recursion. It is by definition that divide-and-conquer creates subproblems of the same form as the initial problem - these subproblems are