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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 n {\displaystyle n} items numbered from 1 up to n {\displaystyle n} , each with a weight w i {\displaystyle w_{i}} and a value v i {\displaystyle v_{i}} , along with a maximum weight capacity ...
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.
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.
For example, bin packing is strongly NP-complete while the 0-1 Knapsack problem is only weakly NP-complete. Thus the version of bin packing where the object and bin sizes are integers bounded by a polynomial remains NP-complete, while the corresponding version of the Knapsack problem can be solved in pseudo-polynomial time by dynamic programming.
It is a special case of the integer knapsack problem, and has applications wider than just currency. It is also the most common variation of the coin change problem , a general case of partition in which, given the available denominations of an infinite set of coins, the objective is to find out the number of possible ways of making a change ...
The parents of a 10-year-old boy who hanged himself in May after “horrific bullying” are suing their son’s school, claiming staff covered up complaints and punished victims who spoke up ...
The S&P 500 slipped less than 0.1% Thursday, its first loss after three straight gains. The Dow Jones Industrial Average added 0.1%, and the Nasdaq composite fell 0.1%. How major US stock indexes ...
Alabama athletics director Greg Byrne makes a case for the Crimson Tide to make the College Football Playoff despite not winning a conference championship and having three losses.