Hardik gupta - 3 years ago 126

R Question

I have a large data frame with more than 100 000 records where the values are sorted

For example, consider the following dummy data set

`df <- data.frame(values = c(1,1,2,2,3,4,5,6,6,7))`

I want to create 3 groups of above values (in sequence only) such that the sum of each group is more or less the same

So for the above group, if I decide to divide the sorted

`df`

`1. 1 + 1 + 2 +2 + 3 + 4 = 13`

2. 5 + 6 = 11

3. 6 + 7 = 13

How can create this optimization in R? any logic?

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Answer Source

So, let's use pruning. I think other solutions are giving a good solution, but not the best one.

First, we want to minimize where S_n is the cumulative sum of the first n elements.

```
computeD <- function(p, q, S) {
n <- length(S)
S.star <- S[n] / 3
if (all(p < q)) {
(S[p] - S.star)^2 + (S[q] - S[p] - S.star)^2 + (S[n] - S[q] - S.star)^2
} else {
stop("You shouldn't be here!")
}
}
```

I think the other solutions optimize over p and q independently, which won't give a global minima (expected for some particular cases).

```
optiCut <- function(v) {
S <- cumsum(v)
n <- length(v)
S_star <- S[n] / 3
# good starting values
p_star <- which.min((S - S_star)^2)
q_star <- which.min((S - 2*S_star)^2)
print(min <- computeD(p_star, q_star, S))
count <- 0
for (q in 2:(n-1)) {
S3 <- S[n] - S[q] - S_star
if (S3*S3 < min) {
count <- count + 1
D <- computeD(seq_len(q - 1), q, S)
ind = which.min(D);
if (D[ind] < min) {
# Update optimal values
p_star = ind;
q_star = q;
min = D[ind];
}
}
}
c(p_star, q_star, computeD(p_star, q_star, S), count)
}
```

This is as fast as the other solutions because it prunes a lot the iterations based on the condition `S3*S3 < min`

. But, it gives the optimal solution, see `optiCut(c(1, 2, 3, 3, 5, 10))`

.

For the solution with K >= 3, I basically reimplemented trees with nested tibbles, that was fun!

```
optiCut_K <- function(v, K) {
S <- cumsum(v)
n <- length(v)
S_star <- S[n] / K
# good starting values
p_vec_first <- sapply(seq_len(K - 1), function(i) which.min((S - i*S_star)^2))
min_first <- sum((diff(c(0, S[c(p_vec_first, n)])) - S_star)^2)
compute_children <- function(level, ind, val) {
# leaf
if (level == 1) {
val <- val + (S[ind] - S_star)^2
if (val > min_first) {
return(NULL)
} else {
return(val)
}
}
P_all <- val + (S[ind] - S[seq_len(ind - 1)] - S_star)^2
inds <- which(P_all < min_first)
if (length(inds) == 0) return(NULL)
node <- tibble::tibble(
level = level - 1,
ind = inds,
val = P_all[inds]
)
node$children <- purrr::pmap(node, compute_children)
node <- dplyr::filter(node, !purrr::map_lgl(children, is.null))
`if`(nrow(node) == 0, NULL, node)
}
compute_children(K, n, 0)
}
```

This gives you all the solution that are least better than the greedy one:

```
v <- sort(sample(1:1000, 1e5, replace = TRUE))
test <- optiCut_K(v, 9)
```

You need to unnest this:

```
full_unnest <- function(tbl) {
tmp <- try(tidyr::unnest(tbl), silent = TRUE)
`if`(identical(class(tmp), "try-error"), tbl, full_unnest(tmp))
}
print(test <- full_unnest(test))
```

And finally, to get the best solution:

```
test[which.min(test$children), ]
```

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