R:尽可能均匀地分配金额 II [英] R: Distributing an amount as evenly as possible II

问题描述

我们有一定数量的，例如300 台.该数量应尽可能均匀地分布在 40 个槽"或箱"上.如果每个插槽都相同，那就很容易了 - 所以每个插槽都是 7,5.但是，插槽的大小各不相同，我们不能填充"超过其大小"允许的范围，例如如果只有 4.我们不能填写"超过 4 的.因此，我们必须在其他的上分配更多.

We have have a certain amount e.g. 300 units. This amount should be as evenly as possible distributed over 40 "slots" or "bins". It would be easy if each slot would be the same - so it would be 7,5 at each slot. However, the slots vary in size and we cannot "fill in" there more than its "size" allows for e.g. if its only 4. What we cannot "fill in" more than 4. Hence, we have to distribute more over the other ones.

让我们假设还有另一个限制:一般填写限制，例如5. 那就是说，即使我们的槽有足够的大小来填充 12 个，剩余的单元也足够多，例如 11，我们也只能填充 5.所有槽被填充后多余的值应该放在一个单独的位置剩余槽.对于每个填充过程，我们还应该获得一个数字，以百分比为单位使用了多少最大填充容量.IE.如果我们填写4和5是一般的填写限制.我们使用了 80%.

Lets assume that there is another limitation: A general filling in limit of e.g. 5. That would mean that even if we have enough size in the slot to fill in say 12 and enough units remaining say 11, we can only fill in 5. The value that is excess after all slots are filled should be placed in a seperated remainder slot. With each filling in process we should also get a number how much of the maximum-filling in capacity in percent is used. I.e. if we fill in 4 and 5 is the general filling limit. We used 80%.

我们之前已经在另一个问题中讨论过这个问题:尽可能均匀地分配金额

We discussed this already earlier in anohter question: Distributing an amount as evenly as possible

我有一些想法如何进一步开发这个公式，但它仍然存在部分问题.感谢您的帮助！

I have some ideas how do develop this formula further, however partially it still stucks. Thanks for your help!

# developing slots and their "size" 
a <- rnorm(40,10,4) 
sum(a) 

# overall sum to distribute 
b <- 300  
# general filling in limit
c <- 8

optimal.fill <- function(a, b) 
{ 
  stopifnot(sum(a) >= b) 

  d <- rep(0, length(a))
  info <- rep(0, length(a))  
  while(b > 0) { 
    has.room  <- a > 0 
    num.slots <- sum(has.room) 
    min.size  <- min(a[has.room]) 
    add.size  <- min(b / num.slots, min.size)
    #maximum limitation
    add.size[add.size>c]  <- c
    #percentage info
    info[has.room] <- add.size/c
    d[has.room] <- d[has.room] + add.size 
    a[has.room] <- a[has.room] - add.size 
    b <- b - num.slots * add.size 
    } 
  return(d) 
} 
optimal.fill(a,b)

推荐答案

这个怎么样

optimal.fill <- function(a, b, generalLimit = 8){
  a <- pmax(0, pmin(a, generalLimit))
  if(sum(a) < b){
    stop("not enough room")
  }
  if(length(a) * min(a) <= b){
    result <- rep(min(a), length(a))
  } else {
    result <- rep(floor(b / length(a)), length(a))
  }
  while(floor((b - sum(result)) / sum(result < a)) >= 1){
    if(min(a[result < a]) * sum(result < a) <= b - sum(result)){
      result[result < a] <- 
        result[result < a] + rep(min(a[result < a]), sum(result < a))
    } else {
      result[result < a] <- 
        result[result < a] + 
        rep(floor((b - sum(result)) / sum(result < a)), sum(result < a))
    }
  }
  extra <- sample(which(result < a), (b - sum(result)), replace = FALSE)
  result[extra] <- result[extra] + 1
  return(cbind(result,  result / a))
}
optimal.fill(ceiling(rnorm(40,10,4)), 300, 8)

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