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01 knapsack how to#
01 knapsack code#
01 knapsack plus#

heappush (heap, ) if len (heap ) = 0 : print ( "%d Status of items (1 is loaded in backpack, 0 is not loaded in backpack):%s" % (n ,bests ) ) print ( "The best price value is: %d" %bestv ) break #print("heap:") #print(heap) # Upper bound function: calculating the upper bound of value under the current node def maxbound (i ) : global cweightīestv =cvalue +value #print("bestv=%d"%bestv) # The optimal path to store the current optimal valueīests =bests + '0' * (n - len (bests ) ) # In the heap: because python has only a small root heap, the upper bound value is large and the priority is high by inverting the upper bound value if i + 1 =bestv : if i + 1

01 knapsack code#

This code is the branch limit 01 knapsack code under python3 When the right son node satisfies the upper bound constraint, it is added to the subset tree and the priority queue of the nodes.If the left son node is a feasible node, it is added to the subset tree and the priority queue of the nodes The algorithm first checks the feasibility of the left son node of the current extension node.

01 knapsack plus#

The priority of the node is the sum of the value of the bagged items plus the value of the remaining maximum unit weight of the items filled with the remaining capacity.

First of all, the input data should be preprocessed to arrange the items according to their unit weight value from large to small.

branches of subset tree) will be cut off until all nodes in the heap are popped up. Otherwise, all paths under the node (i.e. If the upper bound of value under the current node is larger than the current optimal value, the current node will be added to the heap. The upper bound function maxbound() is constructed to calculate the upper bound of value under the current node. The priority queue method is used to rank the items according to their unit value from large to small, and the big root heap structure is used to store the item data. The backtracking method searches the solution space tree in the way of depth first, while the branch and bound method searches the solution space tree in the way of breadth first or minimum cost first.Ġ1 knapsack problem under branch and bound The goal of backtracking method is to find all the solutions satisfying the constraints in the solution space tree, while the goal of branch and bound method is to find a solution satisfying the constraints, or to find the optimal solution in a certain sense in the solution satisfying the constraints.

The difference between backtracking method and backtracking method.

This process continues until the required solution or activity table is found to be empty. After that, a node is taken from the node table to become the current extension node, and the above node extension process is repeated. In these son nodes, the son nodes that lead to infeasible solutions or non optimal solutions are discarded, and the rest of the son nodes are added to the activity node table.

Once a node becomes an extension node, all its child nodes are generated at once. In branch and bound method, each active node has only one chance to become an extended node. The problem that items can be partially packed into a backpack is called the backpack problem Branch and boundīranch and bound method often searches the solution space tree of the problem in the way of breadth first or minimum cost (maximum benefit) first. Items cannot be split into smaller units for loading, that is, they cannot be partially loaded.

Note: 01 the knapsack problem requires that an item has only two states of 0 / 1, that is, loading knapsack or not loading knapsack.

01 knapsack how to#

For a given capacity backpack, how to make the items in the backpack have the maximum total value? There are N items, each of which has its own weight and value.