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Hello friends my name is too short and today I am going to talk about zero-one knapsack problem so I have an old video on this question but I felt that I missed few things in that videos I'm creating a new video to fill those gaps so what is 0-1 knapsack problem suppose I have a total weight and then I have certain items with their weights and values how do you pick items from this set such that the sum of their values is maximum but some of their weights is less than or equal to total weight also we have just one quantity of each item so what does 1 means 1 means that either you pick the item or you don't pick the item it means that you cannot split the item so if it was not a zero-one knapsack problems just say that you could have split the item there is a greedy solution to solve that question all you have to do is solve the item by the value 2 weight sort the item by value to weight in a non increasing order and then keep picking the items and then if the last item cannot be picked totally split it up and pick whatever ratio you can so but here we are you doing a knapsack problem it means that we cannot split the item so how do we do it yes we will use dynamic programming to solve this question in the next section let's see how so how do we solve this problem so the question is very simple whenever a new item comes in you have to decide you have to pick this item or not and you have to find which gives you the maximum value if you pick the item the maximum value will be the value of the item plus whatever we can get by subtracting subtracting this value the this value from the total weight and excluding this item or the best you can do without including this item all together let's try to understand on with this example so here I have a 2-dimensional matrix and this is my total number of columns is same as a total weight plus 1 and my number of rows is same as the total items so our first column is it means that if the total weight is no matter what items I have my maximum value I can get is always zero so this is why this all is zero so let's start from here so if my total weight was one and if I just had one item one the best I can do is one so this is the weight of the item the total weight is one so the maximum value I can get is just one if my total weight is 2 if I just had one item of weight 1 and whose value is 1 the.