0/1 Knapsack problem | Dynamic Programming
WilliamFiset・2 minutes read
The zero-one knapsack problem in computer science involves selecting objects with values and weights to maximize the total value within a given weight capacity using dynamic programming. By creating a table to store values for different states, one can determine the best value for each capacity by including or excluding items, ultimately providing the optimal solution.
Insights
- The zero-one knapsack problem in computer science involves selecting objects with values and weights to maximize total value within a given weight capacity, solved through dynamic programming by creating a table of values for different states.
- Dynamic programming for the knapsack problem includes considering each item, calculating the best value for each capacity by including or excluding the item, and filling a table incrementally with blue arrows indicating optimal values, leading to the determination of the best achievable value and selected items.
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Recent questions
What is the knapsack problem?
A widely encountered computer science issue involving dynamic programming.
How is the knapsack problem solved?
By creating a table to store values for different states.
What is the role of dynamic programming in solving the knapsack problem?
Dynamic programming helps calculate the optimal value for each capacity.
How is the optimal value determined in the knapsack problem solution?
By considering each item and including or excluding it based on the best value.
How are the selected items determined in the knapsack problem solution?
By starting from the bottom right corner of the table and working backward.
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Summary
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Solving the Zero-One Knapsack Problem
- The knapsack problem in computer science, specifically the zero-one knapsack problem, is a widely encountered issue that can be solved using dynamic programming.
- The problem involves selecting objects with values and weights to maximize the total value within a given weight capacity.
- An example with five items of varying weights and values, along with a knapsack capacity of seven kilograms, is used to illustrate the solution process.
- Dynamic programming involves creating a table to store values for different states, with rows representing items and columns representing knapsack capacities.
- The process entails considering each item, determining the best value for each capacity by including or excluding the item, and using previous information to calculate the optimal value.
- The table is filled incrementally, with blue arrows indicating the best value for each cell based on including or excluding the current item.
- The final table provides the best value achievable, and to determine the selected items, one starts from the bottom right corner and works backward, including items where the values differ between rows.
