## Longest Alternating Subsequence Problem

Longest Alternating Subsequence is a problem of finding a subsequence of a given sequence in which the elements are in alternating order, and in which the sequence is as long as possible.

## Coin Change Problem (Total number of ways to get the denomination of coins)

Given an unlimited supply of coins of given denominations, find the total number of distinct ways to get a desired change.

## Coin change-making problem (unlimited supply of coins)

Given an unlimited supply of coins of given denominations, find the minimum number of coins required to get a desired change.

## Maximum Product Rod Cutting

Given a rod of length n, find the optimal way to cut rod into smaller rods in order to maximize product of price of each of the smaller rod. Assume each rod of length i has price i.

## Rod Cutting Problem

Given a rod of length n and list of prices of rod of length i where 1 < = i

## Find all N-digit binary strings without any consecutive 1’s

Given a positive integer N, count all N-digit binary strings without any consecutive 1’s.

## Minimum Sum Partition Problem

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.

## Subset Sum Problem

Given a set of positive integers and an integer s, is there any non-empty subset whose sum to s.

## Partition problem | Dynamic Programming Solution

Given a set of positive integers, find if it can be divided into two subsets with equal sum.

## Maximize the Value of an Expression

Given an array A, maximize value of the expression (A[s] – A[r] + A[q] – A[p]) where p, q, r and s are indices of the input array and s > r > q > p.

## 0-1 Knapsack problem

In 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 …

## Count number of paths in a matrix with given cost to reach destination cell

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. …