dynamic-programming

问题 Given a value N, if we want to make change for N cents, and we have infinite supply of each of S = { S1, S2, .. , Sm} valued coins, how many ways can we make the change? The order of coins doesn’t matter. For example, for N = 4 and S = {1,2,3}, there are four solutions: {1,1,1,1},{1,1,2},{2,2},{1,3}. So output should be 4. For N = 10 and S = {2, 5, 3, 6}, there are five solutions: {2,2,2,2,2}, {2,2,3,3}, {2,2,6}, {2,3,5} and {5,5}. So the output should be 5. I found the 3 approaches HERE. But

问题 Suppose I have numbers 1 to N and I want to divide them into subsets based on following criteria: Each number can be present in only 1 subset. The elements of the subsets must be mutually coprime. Minimizing the total number of subsets. My approach to it is by finding all primes up to N using Sieve of Eratosthenes and then dividing them accordingly in subsets. For example for N=5, I can have two subsets at minimum {1,2,3,5} and {4}. But I am unsure how to distribute the elements in subsets so

问题 I was going through the question on LeetCode linked here. Given a string containing only three types of characters: '(', ')' and '*', write a function to check whether this string is valid. We define the validity of a string by these rules: Any left parenthesis '(' must have a corresponding right parenthesis ')'. Any right parenthesis ')' must have a corresponding left parenthesis '('. Left parenthesis '(' must go before the corresponding right parenthesis ')'. '*' could be treated as a

问题 I have an array of n positive real numbers And I have to find out the Maximum Product Subarray for this given array. How to implement DP Solution for the problem ? Explain in detail the DP formulation of the solution. 回答1: Since the solution for maximal sum is known, you can compute log of each array's item into another array apply the known algorithm to the new array exp of the result is the answer. (But you can just trivially adjust the existing algorithm, which is already mentioned in

问题 I have an array of n positive real numbers And I have to find out the Maximum Product Subarray for this given array. How to implement DP Solution for the problem ? Explain in detail the DP formulation of the solution. 回答1: Since the solution for maximal sum is known, you can compute log of each array's item into another array apply the known algorithm to the new array exp of the result is the answer. (But you can just trivially adjust the existing algorithm, which is already mentioned in

问题 There is a grid of size N x M . Some cells are islands denoted by '0' and the others are water . Each water cell has a number on it denoting the cost of a bridge made on that cell. You have to find the minimum cost for which all the islands can be connected. A cell is connected to another cell if it shares an edge or a vertex. What algorithm can be used to solve this problem? What can be used as a brute force approach if the values of N, M are very small, say NxM <= 100? Example : In the

问题 Closed . This question needs to be more focused. It is not currently accepting answers. Want to improve this question? Update the question so it focuses on one problem only by editing this post. Closed 4 days ago . found this question in geeksforgeeks related to dynamic programming with bitmasking : https://www.geeksforgeeks.org/sum-subsets-dynamic-programming/ I am trying for weeks but not able to understand how the answer is formulated. Please provide any links, that may help to understand

问题 I'm writing a variation of knapsack 0-1 with multiple constraints. In addition to a weight constraint I also have a quantity constraint, but in this case I want to solve the knapsack problem given that I'm required to have exactly n items in my knapsack, with a weight less than or equal to W. I'm currently implementing a dynamic programming ruby solution for the simple 0-1 case based off of the code at Rosetta Code at http://rosettacode.org/wiki/Knapsack_problem/0-1#Ruby. What's the best way

问题 There is a classic Knapsack problem. My version of this problem is a little different. Given set of items, each with a mass, determine the number of combinations to pack items so that the total weight is less than or equal to a given limit. For example, there is 5 items with mass: 1, 1, 3, 4, 5 . There is a bug with limit = 7 . There are the following combinations: 1 + 3 1 + 4 1 + 5 1 + 1 + 3 1 + 1 + 4 1 + 1 + 5 3 3 + 4 4 5 Is there a way to count number of combinations without brute? 回答1:

问题 I will be happy to get some help. I have the following problem: I'm given a list of numbers seq and a target number and I need to write 2 things: A recursive solution that returns True if there is a sum of a subsequence that equals the target number and False otherwise. example: subset_sum([-1,1,5,4],0) # True subset_sum([-1,1,5,4],-3) # False Secondly, I need to write a solution using what I wrote in the previous solution but now with memoization that uses a dictionary in which the keys are