#'@title Dynamic Knapsack Algorithm
#'@description Calculates best values and weights for given capacity.
#'@param x Dataframe with variables v and w.
#'@param W Integer as capacity.
#'@export
#'@return Returns a list with best value and combination.
knapsack_dynamic <- function(x,W){
if(!is.data.frame(x) || W < 0){
stop("errounous input")
}
# Creating empty matrix
combinationMatrix <- matrix(NA, ncol = W + 1, nrow = nrow(x) + 1)
combinationMatrix[1,] <- 0
combinationMatrix[,1] <- 0
el_order <- order(x$w)
wt <- x[order(x$w), 1]
val <- x[order(x$w), 2]
elements <- c()
for (i in 1:(nrow(x) + 1)) {
for (j in 1:(W + 1)) {
if (i == 1 || j == 1) {
combinationMatrix[i, j] <- 0
} else if (wt[i - 1] < j - 1 | wt[i - 1] == j - 1) {
if(combinationMatrix[i - 1, j - wt[i - 1]] == 0){
tal <- 0
} else {
tal <- combinationMatrix[i - 1, j - wt[i - 1]]
}
combinationMatrix[i, j] <- max(val[i - 1]+tal, combinationMatrix[i-1,j])
} else{
combinationMatrix[i, j] <- combinationMatrix[i-1, j]
}
}
}
i <- nrow(x)+1
j <- W+1
n <- 1
while (i >= 2 && j >= 1) {
if (combinationMatrix[i, j] > combinationMatrix[i-1,j]) {
elements[n] <- el_order[i-1]
n <- n + 1
j <- j-wt[i-1]
}
i <- i-1
}
list_ret <- list(value = round(max(combinationMatrix)), elements = sort(elements))
return(list_ret)
}
# set.seed(42)
# n <- 16
# knapsack_objects <-
# data.frame(
# w=sample(1:4000, size = n, replace = TRUE),
# v=runif(n = n, 0, 10000)
# )
# library(lineprof)
# dynamic <- lineprof(knapsack_dynamic(x = knapsack_objects[1:11,], W = 3500))
# shine(dynamic)
# ptm <- proc.time()
# knapsack_dynamic(x = knapsack_objects[1:8,], W = 3500)
# proc.time() - ptm
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