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C++ Program for the Fractional Knapsack Problem

Last updated: 19 July 2020

Pre-requisite: Fractional Knapsack ProblemGiven two arrays weight[] and profit[] the weights and profit of N items, we need to put these items in a knapsack of capacity W ...read more

Competitive Programming

Greedy Algorithms

0/1 Knapsack using Least Cost Branch and Bound

Last updated: 26 June 2023

Given N items with weights W[0..n-1], values V[0..n-1] and a knapsack with capacity C, select the items such that:The sum of weights taken into the knapsack is less than o...read more

Dynamic Programming

Branch and Bound

Greedy approach vs Dynamic programming

Last updated: 13 March 2023

Greedy approach and dynamic programming are two different algorithmic approaches that can be used to solve optimization problems. Here are the main differences between the ...read more

Dynamic Programming

Difference Between

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Printing Items in 0/1 Knapsack

Last updated: 23 June 2022

Given weights and values of n items, put these items in a knapsack of capacity W to get the maximum total value in the knapsack. In other words, given two integer arrays, ...read more

Dynamic Programming

Unbounded Knapsack (Repetition of items allowed)

Last updated: 11 September 2023

Given a knapsack weight W and a set of n items with certain value vali and weight wti, we need to calculate the maximum amount that could make up this quantity exactly. Th ...read more

Dynamic Programming

Minimum cost to fill given weight in a bag

Last updated: 17 April 2023

You are given a bag of size W kg and you are provided costs of packets different weights of oranges in array cost[] where cost[i] is basically the cost of 'i' kg packet of ...read more

Dynamic Programming

A Space Optimized DP solution for 0-1 Knapsack Problem

Last updated: 24 April 2023

Given the weights and values of n items, put these items in a knapsack of capacity W to get the maximum total value in the knapsack. In other words, given two integer arra ...read more

Dynamic Programming

Last updated: 20 September 2023

Given an array arr[] of length N and an integer target. You want to build an expression out of arr[] by adding one of the symbols '+' and '-' before each integer in arr[] ...read more

Implementation of 0/1 Knapsack using Branch and Bound

Last updated: 21 September 2023

We strongly recommend to refer below post as a prerequisite for this. Branch and Bound | Set 1 (Introduction with 0/1 Knapsack) We discussed different approaches to solve ...read more

Branch and Bound

0/1 Knapsack using Branch and Bound

Last updated: 23 June 2023

Branch and bound is an algorithm design paradigm which is generally used for solving combinatorial optimization problems. These problems typically exponential in terms of ...read more

Branch and Bound

Fractional Knapsack Problem

Last updated: 03 April 2023

Given the weights and profits of N items, in the form of {profit, weight} put these items in a knapsack of capacity W to get the maximum total profit in the knapsack. In F ...read more

Pseudo-polynomial Algorithms

Last updated: 22 August 2021

What is a pseudo-polynomial algorithm?A pseudo-polynomial algorithm is an algorithm whose worst-case time complexity is polynomial in the numeric value of input (not numbe ...read more

Java Program 0-1 Knapsack Problem

Last updated: 13 February 2023

Recursive Solution[tabby title="Java"][sourcecode language="java"]/* A Naive recursive implementation of 0-1 Knapsack problem */class Knapsack { // A utility function t ...read more

Python Program for 0-1 Knapsack Problem

Last updated: 23 October 2019

[sourcecode highlight="" language="Python"]# A naive recursive implementation of 0-1 Knapsack Problem# Returns the maximum value that can be put in a knapsack of# capacity ...read more

Python Programs

0/1 Knapsack Problem

Last updated: 31 July 2023

Prerequisites: Introduction to Knapsack Problem, its Types and How to solve themGiven N items where each item has some weight and profit associated with it and also given ...read more

Dynamic Programming