0/1 Knapsack Problem: Branch and Bound with FIFO and LC

Full transcript

The zero one Knapsack Problem is an optimization problem: given a delivery bag with capacity five kilograms, we must include each package completely or exclude it, maximizing total profit. Using Branch and Bound, we branch into include and exclude nodes, bound each node's best possible profit, and prune infeasible branches. FIFO expands nodes in queue order, while LC picks the highest bound first; both find the optimal solution: Item A and Item B, weight five kilograms, profit ninety. This method has exponential worst case time and space, approximately O of two to the n, yet it's widely applied in cargo loading, budget allocation, project selection, and resource allocation. Branch and Bound, through FIFO or LC strategies, efficiently finds the optimal knapsack solution by pruning branches that cannot improve the best known profit.