Rod Cutting Problem
DP on Subsequences DSA practice problem on Onlearn.
Difficulty: hard.
Topics: Rod Cutting Problem (Unbounded Knapsack Variant): How to maximize profit by cutting a rod into pieces given prices for each possible length?, Dynamic Programming, Recursion, Memoization, Tabulation, Space Optimization, Time Complexity, Space Complexity, Greedy Algorithm, Arrays, complexity analysis, dynamic programming, memoization, tabulation, space optimization, recursion, greedy algorithm limitations.
Problem Statement Given a set of items, each with a specific weight and a corresponding value, and a knapsack with a maximum weight capacity, determine the maximum total value that can be obtained by filling the knapsack. Unlike the 0/1 Knapsack problem, you can take multiple instances of each item. This problem is also known as the Unbounded Knapsack Problem. Input Specification The first line contains an integer N, representing the number of items. The second line contains N integers, wt[0], wt[1], ..., wt[N 1], representing the weights of the items. The third line contains N integers, val[0], val[1], ..., val[N 1], representing the values of the items. The fourth line contains an integer W, representing the maximum weight capacity of the knapsack. Output Specification Output a single integer, the maximum total value that can be obtained. Sample Test Case Input: Output: