Subset Sum Problem – Dynamic Programming Solution
Given a set of positive integers and an integer s, is there any non-empty subset whose sum to s.
Tag: Algorithm
Partition Problem using Dynamic Programming
Given a set of positive integers, find if it can be divided into two subsets with equal sum. The partition problem is a special case of the subset sum problem, which itself is a special case of the knapsack problem.
0–1 Knapsack Problem
In the 0–1 Knapsack problem, we are given a set of items, each with a weight and a value, and we need to determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.
Matrix Chain Multiplication using Dynamic Programming
Matrix chain multiplication is an optimization problem that to find the most efficient way to multiply a given sequence of matrices. The problem is not actually to perform the multiplications but merely to decide the sequence of the matrix multiplications involved.
The Levenshtein distance (Edit distance) Problem
Edit distance is a way of quantifying how different two strings are from one another by counting the minimum number of operations required to transform one string into the other.
Maximum Sum Increasing Subsequence Problem
Find a subsequence of a given sequence such that the subsequence sum is as high as possible and the subsequence’s elements are in sorted order, from lowest to highest. This subsequence is not necessarily contiguous or unique.
Longest Bitonic Subsequence
The longest bitonic subsequence problem is to find a subsequence of a given sequence in which the subsequence’s elements are first sorted in increasing order, then in decreasing order, and the subsequence is as long as possible.
Longest Increasing Subsequence using Dynamic Programming
The longest increasing subsequence problem is to find a subsequence of a given sequence in which the subsequence’s elements are in sorted order, lowest to highest, and in which the subsequence is as long as possible. This subsequence is not necessarily contiguous or unique.
Shortest Common Supersequence Problem
The Shortest Common Supersequence (SCS) is finding the shortest supersequence Z of given sequences X and Y such that both X and Y are subsequences of Z.
Longest Repeated Subsequence Problem
The Longest Repeating Subsequence (LRS) problem is finding the longest subsequences of a string that occurs at least twice.
Longest Palindromic Subsequence using Dynamic Programming
The Longest Palindromic Subsequence (LPS) problem is finding the longest subsequences of a string that is also a palindrome.
Longest Common Substring Problem
The longest common substring problem is the problem of finding the longest string (or strings) that is a substring (or are substrings) of two strings.