min {wi，W - w}在背包算法中的作用

Question

Algorithm FractionalKnapsack(S, W ):
Input: Set S of items, such that each item i ∈ S has a positive benefit bi and a
positive weight wi; positive maximum total weight W
Output: Amount xi of each item i ∈ S that maximizes the total benefit while
not exceeding the maximum total weight W
for each item i ∈ S do 
 xi ← 0
 vi ← bi/wi // value index of item i 
w ← 0 // total weight
while w < W and S ̸= ∅ do
 remove from S an item i with highest value index
 a ← min{wi, W − w} // more than W − w causes a weight overflow 
 xi ← a
 w←w+a

我正在尝试在Ruby中实现上面的伪代码，我已成功实现了优先级队列，但我只需要有人为我解释这一行：

  

a←min {wi，W - w} //大于W - w导致重量溢出

min函数究竟应该做什么？以及如何实施？

Answer 1

线a←min {wi，W-w}实际上给出'a'的值，该值是w [i]和W-w的最小值。

$product->test

您可以执行

if w[i] < W-w then a ← w[i]
otherwise a ← W-w