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.
Tag: Recursive
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.
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.
Count the number of paths in a matrix with a given cost to reach the destination cell
Given an M × N matrix where each cell has a non-negative cost associated with it, count the number of paths to reach the last cell (M-1, N-1) of the matrix from its first cell (0, 0) such that the path has given cost.
Find the longest sequence formed by adjacent numbers in the matrix
Given an N × N matrix where each cell has a 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 in its value.
Find minimum cost to reach the last cell of a matrix from its first cell
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 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.
Find the size of the largest square submatrix of 1’s present in a binary matrix
Given an M × N binary matrix, find the size of the largest square submatrix of 1’s present.