Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.

Wikipedia for more information

For example you can be given a max weight of 15 and objects with value/masses as [5,2], [7,4] [1,1] and you would output [7,0,1] which is 7 [5 <value>, 2 <mass>] objects and 1 [1 <value>, 1 <mass>] object for a score of 36. #Rules Input can be taken in any reasonable format

Output is also flexible format,

You may not use libraries that are non-standard. If you have to install or download any library to use it separate from the initial setup then it is not allowed

Objects may have negative mass and value (i.e -1,-1)

Optimal answers required #Winning Shortest code wins

#Negative mass and value? This is a key part of this challenge. Lets say you have a object with items (mass, value) such as [4,3],[-1,-1] and a bag with capacity of 15. You could put 3 of the first ones and score 9 or put 4 of the first ones and one of the -1,-1 object for a score of 11.

Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.

Wikipedia for more information

For example you can be given a max weight of 15 and objects with value/masses as [5,2], [7,4] [1,1] and you would output [7,0,1] which is 7 [5 <value>, 2 <mass>] objects and 1 [1 <value>, 1 <mass>] object for a score of 36.

Rules

Input can be taken in any reasonable format

Output is also flexible format,

You may not use libraries that are non-standard. If you have to install or download any library to use it separate from the initial setup then it is not allowed

Objects may have negative mass and value (i.e -1,-1)

Optimal answers required

Winning

Shortest code wins

Negative mass and value?

This is a key part of this challenge. Lets say you have a object with items (mass, value) such as [4,3],[-1,-1] and a bag with capacity of 15. You could put 3 of the first ones and score 9 or put 4 of the first ones and one of the -1,-1 object for a score of 11.

Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.

Wikipedia for more information

For example you can be given a max weight of 15 and objects with value/masses as [5,2], [7,4] [1,1] and you would output [7,0,1] which is 7 [5 <value>, 2 <mass>] objects and 1 [1 <value>, 1 <mass>] object for a score of 36. #Rules Input can be taken in any reasonable format

Output is also flexible format,

You may not use libraries that are non-standard. If you have to install or download any library to use it separate from the initial setup then it is not allowed

Objects may have negative mass and value (i.e -1,-1)

Optimal answers required #Winning Shortest code wins

#Negative mass and value? This is a key part of this challenge. Lets say you have a object with items (mass, value) such as [4,3],[-1,-1] and a bag with capacity of 13. You could put 3 of the first ones and score 9 or put 4 of the first ones and one of the -1,-1 object for a score of 15.

Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.

Wikipedia for more information

For example you can be given a max weight of 15 and objects with value/masses as [5,2], [7,4] [1,1] and you would output [7,0,1] which is 7 [5 <value>, 2 <mass>] objects and 1 [1 <value>, 1 <mass>] object for a score of 36. #Rules Input can be taken in any reasonable format

Output is also flexible format,

You may not use libraries that are non-standard. If you have to install or download any library to use it separate from the initial setup then it is not allowed

Objects may have negative mass and value (i.e -1,-1)

Optimal answers required #Winning Shortest code wins

#Negative mass and value? This is a key part of this challenge. Lets say you have a object with items (mass, value) such as [4,3],[-1,-1] and a bag with capacity of 15. You could put 3 of the first ones and score 9 or put 4 of the first ones and one of the -1,-1 object for a score of 11.

Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.

Wikipedia for more information

For example you can be given a max weight of 15 and objects with value/masses as [5,2], [7,4] [1,1] and you would output [7,0,1] which is 7 [5 <value>, 2 <mass>] objects and 1 [1 <value>, 1 <mass>] object for a score of 36. #Rules Input can be taken in any reasonable format

Output is also flexible format,

You may not use libraries that are non-standard. If you have to install or download any library to use it separate from the initial setup then it is not allowed

Objects may have negative mass and value (i.e -1,-1)

Optimal answers required #Winning Shortest code wins

#Negative mass and value? This is a key part of this challenge. Lets say you have a object with items (mass, value) such as [4,3],[-1,-1] and a bag with capacity of 13. You could put 3 of the first ones and score 9 or put 4 of the first ones and one of the -1,-1 object for a score of 11.

Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.

Wikipedia for more information

For example you can be given a max weight of 15 and objects with value/masses as [5,2], [7,4] [1,1] and you would output [7,0,1] which is 7 [5 <value>, 2 <mass>] objects and 1 [1 <value>, 1 <mass>] object for a score of 36. #Rules Input can be taken in any reasonable format

Output is also flexible format,

You may not use libraries that are non-standard. If you have to install or download any library to use it separate from the initial setup then it is not allowed

Objects may have negative mass and value (i.e -1,-1)

Optimal answers required #Winning Shortest code wins

#Negative mass and value? This is a key part of this challenge. Lets say you have a object with items (mass, value) such as [4,3],[-1,-1] and a bag with capacity of 13. You could put 3 of the first ones and score 9 or put 4 of the first ones and one of the -1,-1 object for a score of 15.