Value of optimal combination of objects

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SUMMARY

The forum discussion centers on the Knapsack problem, specifically the optimal combination of objects given a weight capacity $W$ and an infinite supply of each object. The algorithm discussed uses the formula $$K(w)=\max_{w_i \leq w} \{ K(w-w_i)+v_i\}$$ to determine the maximum value of items that can fit in the knapsack. Participants explore the reasoning behind the formula and provide examples to illustrate its application, including calculating values for specific weights and creating a table to visualize the optimal combinations.

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  • #31
I like Serena said:
Suppose we had 2 identical objects with place for only 1 of them.
Then we would have 2 solutions.

Of suppose we had objects with weights 1 and 4, and also objects with weights 2 and 3, both adding up to the same value.
Then, if we only had a weight allowance of 5, we would still have 2 solutions. (Nerd)

I understand! Thank you very much! (Clapping)(Smirk)
 

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