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  2. Continuous knapsack problem - Wikipedia

    en.wikipedia.org/wiki/Continuous_knapsack_problem

    The continuous knapsack problem may be solved by a greedy algorithm, first published in 1957 by George Dantzig, [2] [3] that considers the materials in sorted order by their values per unit weight. For each material, the amount x i is chosen to be as large as possible:

  3. Knapsack problem - Wikipedia

    en.wikipedia.org/wiki/Knapsack_problem

    The most common problem being solved is the 0-1 knapsack problem, which restricts the number of copies of each kind of item to zero or one. Given a set of items numbered from 1 up to , each with a weight and a value , along with a maximum weight capacity ,

  4. List of knapsack problems - Wikipedia

    en.wikipedia.org/wiki/List_of_knapsack_problems

    The knapsack problem is one of the most studied problems in combinatorial optimization, with many real-life applications. For this reason, many special cases and generalizations have been examined. For this reason, many special cases and generalizations have been examined.

  5. Bin packing problem - Wikipedia

    en.wikipedia.org/wiki/Bin_packing_problem

    The bin packing problem can also be seen as a special case of the cutting stock problem. When the number of bins is restricted to 1 and each item is characterized by both a volume and a value, the problem of maximizing the value of items that can fit in the bin is known as the knapsack problem.

  6. Karmarkar–Karp bin packing algorithms - Wikipedia

    en.wikipedia.org/wiki/Karmarkar–Karp_bin...

    The knapsack problem can be solved by dynamic programming in pseudo-polynomial time: (), where m is the number of inputs and V is the number of different possible values. To get a polynomial-time algorithm, we can solve the knapsack problem approximately, using input rounding.

  7. Change-making problem - Wikipedia

    en.wikipedia.org/wiki/Change-making_problem

    One variation of this problem assumes that the people making change will use the "greedy algorithm" for making change, even when that requires more than the minimum number of coins. Most current currencies use a 1-2-5 series , but some other set of denominations would require fewer denominations of coins or a smaller average number of coins to ...

  8. Puzzle solutions for Friday, Nov. 29, 2024

    www.aol.com/news/puzzle-solutions-friday-nov-29...

    Note: Most subscribers have some, but not all, of the puzzles that correspond to the following set of solutions for their local newspaper. CROSSWORDS

  9. Cutting stock problem - Wikipedia

    en.wikipedia.org/wiki/Cutting_stock_problem

    For the one-dimensional case, the new patterns are introduced by solving an auxiliary optimization problem called the knapsack problem, using dual variable information from the linear program. The knapsack problem has well-known methods to solve it, such as branch and bound and dynamic programming. The Delayed Column Generation method can be ...