Here’s a pseudocode explanation of how this program functions. On line 21, we return the greater of profit1 and profit2 Then we recursively call the function, exclude the item, and save the result in the profit2 variable. If it is, we call the knapsack() function recursively with the item and save the result in profit1. On line 14, we start from the beginning of the weight array and check if the item is within the maximum capacity. Line numbers within explanation refer to the C++ version from above Int knapsackRecursive(int profits, int profitsLength, int weights, int capacity, int currentIndex) // The weight of eachĬout << "Total knapsack profit = " << knapSack(profits, 4, weights, 7) << endl Ĭout << "Total knapsack profit = " << knapSack(profits, 4, weights, 6) << endl Returns the maximum value that can be put in a knapsack of capacity W You can expect this question to be asked for any role that manages or creates automated optimization software. Automatically plan the best package delivery route.Optimize water distribution across a fixed pipe network.Determine the best programs to run on a limited resource cloud system.This has many practical applications in the workplace, as all combinatorial optimization problems seek maximum benefit within constraints.įor example, combinatorial optimization is used in solutions like: The knapsack problem also tests how well you approach combinatorial optimization problems. This is a popular choice because interviewers can see how well you shift from a recursive to a dynamic solution. Interviewers may ask you to produce both a recursive and dynamic solution if they value both skill sets. The interviewer can use this question to test your dynamic programming skills and see if you work for an optimized solution.Īnother popular solution to the knapsack problem uses recursion. The optimal solution for the knapsack problem is always a dynamic programming solution. In other words, you have to really understand the logic of the problem and code. This problem is so popular because it tests many desired skills at once and can be altered to throw interviewees off balance. In this case, each item also has a fixed volume, and the knapsack has a volume limit. When an element is selected, the program must decide if it should place it in the pack or leave it.Īt senior level interviews, you’ll encounter variants that add volume as a constrained attribute. The 0-1 variant does not allow you to break items.Īnother common variant is the constrained knapsack problem that restricts your program so you cannot select any item more than once. The fractional variant allows you to break items to maximize the value in the pack. There are two major variants of this question, fractional or 0-1. Create a function knapsack() that finds a subset or number of these items that will maximize value but whose total weight does not exceed the given number capacity. The weight and value are represented in an integer array. You have a set of items ( n items) each with fixed weight capacities and values. You’re a burglar with a knapsack that can hold a total weight of capacity. So, maximum possible value that can be put into the knapsack = 7.The knapsack problem is one of the top dynamic programming interview questions for computer science. ![]() ![]() The last entry represents the maximum possible value that can be put into the knapsack.T (i, j) = max Īfter all the entries are computed and filled in the table, we get the following table. ![]() Start filling the table row wise top to bottom from left to right.
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