Given a positive integer N, count all N-digit binary strings without any consecutive 1’s.
Given a set of positive integers S, partition the set S into two subsets S1, S2 such that the difference between the sum of elements in S1 and the sum of elements in S2 is minimized.
Given a set of positive integers and an integer s, is there any non-empty subset whose sum to s.
Given a set of positive integers, find if it can be divided into two subsets with equal sum.
Given an array A, maximize value of the expression (A[s] – A[r] + A[q] – A[p]) where l, k, j and i are indexes of the input array and s > r > q > p.
Given a set of items, each with a weight and a value, 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. Items are indivisible; you either take an item or …
Given a M x N matrix where each cell have non-negative cost associated with it, count number of paths to reach last cell (M-1, N-1) of the matrix from its first cell (0, 0) such that path has given cost. We can only move one unit right or one unit down from any cell. i.e. …
Given a N x N matrix where each cell has distinct value in the 1 to N * N. Find the longest sequence formed by adjacent numbers in the matrix such that for each number, the number on the adjacent neighbor is +1 its value.
Given a M x N matrix where each cell has a cost associated with it, find the minimum cost to reach 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 …
Determine optimal parenthesization of a product of n matrices.
Given a M x N binary matrix, find the size of largest square sub-matrix of 1’s present in it.
Edit distance is a way of quantifying how dissimilar two strings are to 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 subsequence sum is as high as possible and 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 in increasing order, then in decreasing order, and the subsequence is as long as possible.