搜搜做题作业网谁能帮我翻译一下这段话,急用 谢谢了
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谁能帮我翻译一下这段话,急用 谢谢了
n is the number of items, and m is the number of knapsack constraints with
capacities bj (j = 1, 2, · · ·,m). Each item xi requires aij units of resource consumption
of jth knapsack (j = 1, 2, · · ·,m) and yields ci units of profit upon inclusion.
The goal is to find a subset of items that yields maximum profit without
exceeding the resource capacities. The much simpler case with single constraint
(m = 1) is known as the single knapsack problem, which is not strongly NPhard,
and effective approximate algorithms have been developed for obtaining its
near-optimal solutions. The general case corresponding to m ≥ 2 is known as the
multidimensional knapsack problem (MKP), which is strongly NP-hard. Many
practical problems can be formulated as the MKP, for example, the capital budgeting
problem, allocating processors and databases in a distributed computer
system, and the project selection and cargo loading. Many algorithms, such as
the dynamic programming method, the enumerative method, the branch-andbound
method and the heuristic algorithms, are proposed for solving the MKP.
n is the number of items, and m is the number of knapsack constraints with
capacities bj (j = 1, 2, · · ·,m). Each item xi requires aij units of resource consumption
of jth knapsack (j = 1, 2, · · ·,m) and yields ci units of profit upon inclusion.
The goal is to find a subset of items that yields maximum profit without
exceeding the resource capacities. The much simpler case with single constraint
(m = 1) is known as the single knapsack problem, which is not strongly NPhard,
and effective approximate algorithms have been developed for obtaining its
near-optimal solutions. The general case corresponding to m ≥ 2 is known as the
multidimensional knapsack problem (MKP), which is strongly NP-hard. Many
practical problems can be formulated as the MKP, for example, the capital budgeting
problem, allocating processors and databases in a distributed computer
system, and the project selection and cargo loading. Many algorithms, such as
the dynamic programming method, the enumerative method, the branch-andbound
method and the heuristic algorithms, are proposed for solving the MKP.
n是项目的数量,和m是背包约束数
北京（J = 1的能力,2,···,M）.每个项目需要的资源消耗AIJ单位西
的第j个背包（J = 1,2,···,M）和产量的单位利润对夹杂物的词.
我们的目标是找到的产量最大的利润没有项目的子集
超过资源的能力.单约束情况下的简单的多
（M = 1）被称为单一的背包问题,这是不强烈NPhard,
有效的近似算法已经被开发用于获得其
接近最优的解决方案.对应的M≥2一般情况下,被称为
多维背包问题（MKP）,这是强NP困难的.许多
实际问题都可以归结为MKP,例如,资本预算
的问题,分配处理器和数据库在分布式计算机
系统,和项目的选择和装载货物.许多算法,如
动态规划法,枚举法,分andbound
法和启发式算法,给出了求解MKP.
再问： 能不能不要这么随便啊？期待大神啊
北京（J = 1的能力,2,···,M）.每个项目需要的资源消耗AIJ单位西
的第j个背包（J = 1,2,···,M）和产量的单位利润对夹杂物的词.
我们的目标是找到的产量最大的利润没有项目的子集
超过资源的能力.单约束情况下的简单的多
（M = 1）被称为单一的背包问题,这是不强烈NPhard,
有效的近似算法已经被开发用于获得其
接近最优的解决方案.对应的M≥2一般情况下,被称为
多维背包问题（MKP）,这是强NP困难的.许多
实际问题都可以归结为MKP,例如,资本预算
的问题,分配处理器和数据库在分布式计算机
系统,和项目的选择和装载货物.许多算法,如
动态规划法,枚举法,分andbound
法和启发式算法,给出了求解MKP.
再问： 能不能不要这么随便啊？期待大神啊