The use of prompt engineering in large language models involves carefully crafting the initial input to produce a specific and desired output, with optimization techniques such as the greedy 0/1 knapsack algorithm being used to improve accuracy and relevance. The algorithm selects the most valuable items that can be added to a prompt without exceeding its capacity, considering factors such as code context tokens, their value, and the overall quality of generated code. By applying this approach, developers can optimize the selection of prompt tokens for code generation, achieving high-quality results while staying within predetermined limits.