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Get StartedGiven 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.
Given an array A, maximize value of expression (A[s] – A[r] + A[q] – A[p]), where p, q, r, and s are indices of the array and s > r > q > p.
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.
Given an M × N matrix where each cell has a cost associated with it, find the minimum cost to reach the last cell (M-1, N-1) of the matrix from its first cell (0, 0). We can only move one unit right or one unit down from any cell, i.e., from cell (i, j), we can move to (i, j+1) or (i+1, j).
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.
Given an M × N binary matrix, find the size of the largest square submatrix of 1’s present.
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.
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.
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.
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.
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.
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.