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The 0/1 knapsack problem is a typical problem in the field of operational research and combinatorial optimization, and it belongs to the NP problem. Research on the solutions of the 0/1 knapsack problem algorithm has very important practical value. This paper first described the 0/1 knapsack problem, and then presented the algorithm analysis, design and implementation of the 0/1 knapsack problem using the brute force algorithm, the greedy algorithm, the genetic algorithm and the dynamic programming algorithm, and compared the four algorithms in terms of algorithm complexity and accuracy. On this basis, the future research directions of the 0/1 knapsack problem were analysed, and we proposed to use the rough set theory to solve the 0/1 knapsack problem. This paper can provide insight for solving the 0/1 knapsack problem and applications.