Find the maximum sum of a subsequence with no adjacent elements
Given an integer array, find the maximum sum of subsequence where the subsequence contains no adjacent elements.
Tag: Bottom-up
Find optimal cost to construct a binary search tree
Find the optimal cost to construct a binary search tree where each key can repeat several times. We are given each key’s frequency in the same order as corresponding keys in the inorder traversal of a binary search tree.
Collect maximum points in a matrix by satisfying given constraints
Given an M × N matrix where each cell can have a value of 1, 0, or -1, where -1 denotes an unsafe cell, collect the maximum number of ones starting from the first cell and by visiting only safe cells (i.e., 0 or 1).
Count the number of times a pattern appears in a given string as a subsequence
Given a string, count the number of times a given pattern appears in it as a subsequence.
Longest Alternating Subsequence Problem
The 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
Given an unlimited supply of coins of given denominations, find the total number of distinct ways to get the desired change.
Coin change-making problem
Coin change-making problem: Given an unlimited supply of coins of given denominations, find the minimum number of coins required to get the desired change.
Maximum Product Rod Cutting
Given a rod of length n, find the optimal way to cut the rod into smaller rods to maximize the product of each of the smaller rod’s price. Assume each rod of length i has price i.
Rod Cutting Problem
Given a rod of length n and a list of prices of rods of length i, where 1 <= i <= n, find the optimal way to cut the rod into smaller rods to maximize profit.
Find all n-digit binary numbers without any consecutive 1’s
Given a positive integer n, count all n–digit binary numbers without any consecutive 1’s.
Minimum Sum Partition Problem
Given a set of positive integers S, partition set S into two subsets, S1 and S2, such that the difference between the sum of elements in S1 and the sum of elements in S2 is minimized.
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.