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0/1 Knapsack Problem using Dynamic Programming in DAA in Hindi | Tabular Method |Shortcut method to fill the matrix table #daa #knapsack

In this video, I have explained 0/1 knapsack problem with dynamic programming approach.
Given a bag of a certain capacity, W. Given some items with their weights and profit(values). How do you fill this bag so that you get the maximum profit?

0/1 Knapsack Problem Dynamic Programming
Given a bag which can only take certain weight W. Given list of items with their weights and price. How do you fill this bag to maximize value of items in the bag.
0/1 Knapsack Problem Using Dynamic Programming Part-1 Explained With Solved Example in Hindi

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This video teaches how to solve the 0/1 Knapsack Problem using dynamic programming. The problem involves packing items with weights and values into a limited capacity knapsack. The goal is to maximize the total value while satisfying capacity constraints. The solution is to break the problem into smaller subproblems and solve them recursively, storing solutions in a tabular format.

What You Will Learn:

Dynamic Programming: An algorithmic technique to solve complex problems by breaking them down into smaller subproblems and solving them recursively.
Tabulation: Storing the solutions to subproblems in a tabular format to avoid solving the problem from scratch each time.
Memoization: A technique used in dynamic programming to store the solutions to subproblems in memory for faster computation. 💪 Tips and Tricks:
Break down the problem into smaller subproblems.
Use a recursive approach to solve the subproblems.
Store the solutions to subproblems in a tabular format.
Use memoization to avoid unnecessary computations.


Dynamic programming is based on the principle of optimality (also coined by Bellman). The principle of optimality states that no matter whatever the initial state and initial decision are, the remaining decision sequence must constitute an optimal decision sequence with regard to the state resulting from the first decision. The principle implies that an optimal decision sequence is comprised of optimal decision subsequence.
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 val[0..n-1] and wt[0..n-1] which represent values and weights associated with n items respectively. Also given an integer W which represents knapsack capacity, find out the maximum value subset of val[] such that sum of the weights of this subset is smaller than or equal to W. You cannot break an item, either pick the complete item, or do’t pick it (0-1 property).
Algorithm:
Dynamic-0-1-knapsack (v, w, n, W) for w = 0 to W do c[0, w] = 0 for i = 1 to n do c[i, 0] = 0
for w = 1 to W do if i ≤ the if vi + c[i-1, w-wi] then c[i, w] = vi + c[i-1, w-wi] else c[i, w] = c[i-1, w] else c[i, w] = c[i-1, w]

0/1 Knapsack problem | Dynamic Programming
Knapsack 0/1 problem by dynamic Programming in Hindi
0/1 knapsack problem-Dynamic Programming | Data structures and algorithms
0/1 Knapsack Problem
Dynamic Programming
Two Methods to solve the problem

Tabulation Method
Sets Method
Overview of the 0/1 Knapsack problem using dynamic programming
0/1 Knapsack Problem using Dynamic Programming || GATECSE || DAA