R中的洗牌向量，但相同的元素应该有最小距离
Shuffle Vector in R, But Identical Elements Should Have Minimum Distance
我想要randomize/shuffle一个向量。一些矢量元素是相同的。洗牌后，相同元素的最小距离应为三（即其他两个元素应位于相同元素之间）。
考虑 R 中的以下示例向量：
x <- rep(LETTERS[1:5], 3) # Create example vector
x
# [1] "A" "B" "C" "D" "E" "A" "B" "C" "D" "E" "A" "B" "C" "D" "E"
如果我使用 sample 函数打乱我的向量，一些相同的元素可能靠得太近。例如，如果我使用以下 R 代码，元素“C”将紧接着出现在位置 5 和 6 处：
set.seed(53135)
sample(x) # sample() function puts same elements too close
# [1] "B" "A" "E" "D" "C" "C" "E" "A" "B" "C" "D" "E" "A" "D" "B"
如何确保相同元素的最小距离为三？
所以基本上我们需要有条件地从 x 向量中抽取一个在 min.dist-1 运行中未被选择的元素。使用 purrr 的 reduce 我们可以实现这个：
min.dist <- 2
reduce(integer(length(x)-1), ~c(.x, sample(x[!x %in% tail(.x, min.dist)], 1)), .init=sample(x,1))
[1] "A" "E" "D" "B" "A" "D" "E" "C" "D" "A" "C" "E" "B" "A" "E"
捆绑在一个函数中
shuffle <- function(x, min.dist=2){
stopifnot(min.dist < length(unique(x)))
reduce(integer(length(x)-1), ~c(.x, sample(x[!x %in% tail(.x, min.dist)], 1)), .init=sample(x,1))
}
> shuffle(x, 3)
[1] "A" "C" "B" "D" "E" "A" "B" "C" "E" "D" "A" "B" "C" "E" "A"
> shuffle(x, 3)
[1] "A" "B" "D" "E" "C" "A" "B" "D" "E" "C" "A" "D" "E" "C" "A"
> shuffle(x, 4)
[1] "C" "E" "D" "A" "B" "C" "E" "D" "A" "B" "C" "E" "D" "A" "B"
> shuffle(x, 4)
[1] "A" "B" "D" "E" "C" "A" "B" "D" "E" "C" "A" "B" "D" "E" "C"
> shuffle(x, 2)
[1] "E" "A" "D" "E" "B" "D" "A" "E" "C" "D" "A" "E" "C" "A" "B"
> shuffle(x, 2)
[1] "B" "A" "D" "C" "B" "A" "E" "B" "A" "E" "B" "C" "D" "A" "E"
在 @27ϕ9 评论后：
shuffle <- function(x, min.dist=2){
stopifnot(min.dist < length(unique(x)))
reduce(integer(length(x)-1), ~ c(.x, sample(x[!x %in% tail(.x, min.dist) &( x %in% names(t <- table(x[x%in%.x]) > table(.x))[t] | !x %in% .x)], 1)), .init=sample(x,1))
}
> table(shuffle(rep(LETTERS[1:5], 3),2))
A B C D E
3 3 3 3 3
> table(shuffle(rep(LETTERS[1:5], 3),2))
Error in sample.int(length(x), size, replace, prob) :
invalid first argument
更新
经过反复试验，考虑到并非总是有足够的元素来 space 出 min.dist 这一事实，我想出了一个解决方案，这段代码解释得最多来自上面的：
shuffle <- function(x, min.dist=2){
stopifnot(min.dist < length(unique(x)))
reduce(integer(length(x)-1), function(.x, ...){
# whether the value is in the tail of the aggregated vector
in.tail <- x %in% tail(.x, min.dist)
# whether a value still hasn't reached the max frequency
freq.got <- x %in% names(t<-table(x[x%in%.x]) > table(.x))[t]
# whether a value isn't in the aggregated vector
yet <- !x %in% .x
# the if is there basically to account for the cases when we don't have enough vars to space out the vectors
c(.x, if(any((!in.tail & freq.got) | yet )) sample(x[(!in.tail & freq.got) | yet ], 1) else x[which(freq.got)[1]] )
}, .init=sample(x,1))
}
现在 运行 table(shuffle(rep(LETTERS[1:5], 3),2)) 对于所有变量总是 return 3 我们可以肯定地说在向量中变量是 spaced最小距离为 2。保证没有元素重复的唯一方法是使用 min.dist=length(unique(x))-1，否则会出现最大 r < min.dist 元素与其最后一次出现的距离不 min.dist 的情况，如果存在这样的元素，它们将位于结果向量的 length(x) + 1 - 1:min.dist 子集中。
只是为了完全确定使用循环来检查输出向量的尾部是否具有唯一值：（删除打印语句我只是为了演示目的使用它）
shuffler <- function(x, min.dist=2){
while(!length(unique(print(tail(l<-shuffle(x, min.dist=min.dist), min.dist+1))))==min.dist+1){}
l
}
table(print(shuffler(rep(LETTERS[1:5], 3),2)))
[1] "A" "B" "C" "E" "B" "C" "D" "A" "C" "D" "A" "E" "B" "D" "E"
A B C D E
3 3 3 3 3
table(print(shuffler(rep(LETTERS[1:5], 3),2)))
[1] "D" "C" "C"
[1] "C" "C" "E"
[1] "C" "A" "C"
[1] "D" "B" "D"
[1] "B" "E" "D"
[1] "C" "A" "E" "D" "A" "B" "C" "E" "A" "B" "D" "C" "B" "E" "D"
A B C D E
3 3 3 3 3
更新：
shuffler <- function(x, min.dist=2){
while(any(unlist(lapply(unique(tl<-tail(l<-shuffle(x, min.dist=min.dist), 2*min.dist)), function(x) diff(which(tl==x))<=min.dist)))){}
l
}
这个新版本对向量尾部的元素是否min.dist进行了严格的测试，之前的版本适用于min.dist=2，但是这个新版本做了更好的测试。
我希望这个答案对你有用。它是用 base R 完成的，但它有效。如果你想逐行检查，我离开打印：
x <- rep(LETTERS[1:5], 3) # Create example vector
shuffle <- function(x, min_dist=3){
#init variables
result<-c() # result vector
count<-0
vec_use<-x
vec_keep<-c()
for(i in 1:length(x)){
# print(paste0("iteration =", i))
if (count>min_dist){
valback<-vec_keep[1]
# print(paste0("value to be returned:", valback))
ntimes_valback<-(table(vec_keep)[valback])
vec_use<- c(vec_use,rep(valback,ntimes_valback))
# print(paste0("vec_use after giving back valbak =", valback))
# print(paste0(vec_use,","))
vec_keep <- vec_keep[!vec_keep %in% valback]
# print(paste0("vec_keep after removing valback =", valback))
# print(paste0(vec_keep,","))
}
val<-sample(vec_use,1)
# print(paste0("val = ",val))#remove value
vec_keep<- c(vec_keep,x[x %in% val])
vec_keep<-vec_keep[1:(length(vec_keep)-1)]#removing 1 letter
# print(paste0("vec_keep ="))
# print(paste0(vec_keep,","))
vec_use <- vec_use[!vec_use %in% val]
# print(paste0("vec_use ="))
# print(paste0(vec_use,","))
result[i]<-val
count<-count+1
}
return(result)
}
shuffle(x)
"C" "D" "B" "E" "C" "A" "B" "D" "E" "A" "C" "D" "B" "E" "C"
如果您的数据很大，那么依靠概率来完成这类任务可能会（方式）更快。
这是一个例子：
prob_shuffler = function(x, min.dist = 2){
n = length(x)
res = sample(x)
OK = FALSE
# We loop until we have a solution
while(!OK){
OK = TRUE
for(i in 1:min.dist){
# We check if identical elements are 'i' steps away
pblm = res[1:(n-i)] == res[-(1:i)]
if(any(pblm)){
if(sum(pblm) >= (n - i)/2){
# back to square 1
res = sample(x)
} else {
# we pair each identical element with
# an extra one
extra = sample(which(!pblm), sum(pblm))
id_reshuffle = c(which(pblm), extra)
res[id_reshuffle] = sample(res[id_reshuffle])
}
# We recheck from the beginning
OK = FALSE
break
}
}
}
res
}
尽管 while 循环看起来很可怕，但实际上收敛速度很快。当然，两个字符在 min.dist 远的概率越低，收敛越快。
@Abdessabour Mtk 和@Carles Sans Fuentes 的当前解决方案有效，但根据输入数据的大小，速度很快会变得非常慢。这是一个基准：
library(microbenchmark)
x = rep(c(letters, LETTERS), 10)
length(x)
#> [1] 520
microbenchmark(prob_shuffler(x, 1), shuffler_am(x, 1), shuffler_csf(x, 1), times = 10)
#> Unit: microseconds
#> expr min lq mean median uq max neval
#> prob_shuffler(x, 1) 87.001 111.501 155.071 131.801 192.401 264.401 10
#> shuffler_am(x, 1) 17218.100 18041.900 20324.301 18740.351 22296.301 26495.200 10
#> shuffler_csf(x, 1) 86771.401 88550.501 118185.581 95582.001 98781.601 341826.701 10
microbenchmark(prob_shuffler(x, 2), shuffler_am(x, 2), shuffler_csf(x, 2), times = 10)
#> Unit: microseconds
#> expr min lq mean median uq max neval
#> prob_shuffler(x, 2) 140.1 195.201 236.3312 245.252 263.202 354.101 10
#> shuffler_am(x, 2) 18886.2 19526.901 22967.6409 21021.151 26758.800 29133.400 10
#> shuffler_csf(x, 2) 86078.1 92209.901 97151.0609 97612.251 99850.101 107981.401 10
microbenchmark(prob_shuffler(x, 3), shuffler_am(x, 3), shuffler_csf(x, 3), times = 10)
#> Unit: microseconds
#> expr min lq mean median uq max neval
#> prob_shuffler(x, 3) 318.001 450.402 631.5312 573.352 782.2 1070.401 10
#> shuffler_am(x, 3) 19003.501 19622.300 23314.4808 20784.551 28281.5 32885.101 10
#> shuffler_csf(x, 3) 87692.701 96152.202 101233.5411 100925.201 108034.7 113814.901 10
我们可以注意到两点：a) 在所有逻辑中，prob_shuffler 的速度取决于 min.dist 而其他方法则没有那么多，b) prob_shuffler 大约是 100 - 仅 520 次观察（并且它可以缩放）更快。
当然，如果 min.dist 处有两个相同字符的概率非常高，那么递归方法应该更快。但在大多数实际情况下，概率法更快。
我想要randomize/shuffle一个向量。一些矢量元素是相同的。洗牌后，相同元素的最小距离应为三（即其他两个元素应位于相同元素之间）。
考虑 R 中的以下示例向量：
x <- rep(LETTERS[1:5], 3) # Create example vector
x
# [1] "A" "B" "C" "D" "E" "A" "B" "C" "D" "E" "A" "B" "C" "D" "E"
如果我使用 sample 函数打乱我的向量，一些相同的元素可能靠得太近。例如，如果我使用以下 R 代码，元素“C”将紧接着出现在位置 5 和 6 处：
set.seed(53135)
sample(x) # sample() function puts same elements too close
# [1] "B" "A" "E" "D" "C" "C" "E" "A" "B" "C" "D" "E" "A" "D" "B"
如何确保相同元素的最小距离为三？
所以基本上我们需要有条件地从 x 向量中抽取一个在 min.dist-1 运行中未被选择的元素。使用 purrr 的 reduce 我们可以实现这个：
min.dist <- 2
reduce(integer(length(x)-1), ~c(.x, sample(x[!x %in% tail(.x, min.dist)], 1)), .init=sample(x,1))
[1] "A" "E" "D" "B" "A" "D" "E" "C" "D" "A" "C" "E" "B" "A" "E"
捆绑在一个函数中
shuffle <- function(x, min.dist=2){
stopifnot(min.dist < length(unique(x)))
reduce(integer(length(x)-1), ~c(.x, sample(x[!x %in% tail(.x, min.dist)], 1)), .init=sample(x,1))
}
> shuffle(x, 3)
[1] "A" "C" "B" "D" "E" "A" "B" "C" "E" "D" "A" "B" "C" "E" "A"
> shuffle(x, 3)
[1] "A" "B" "D" "E" "C" "A" "B" "D" "E" "C" "A" "D" "E" "C" "A"
> shuffle(x, 4)
[1] "C" "E" "D" "A" "B" "C" "E" "D" "A" "B" "C" "E" "D" "A" "B"
> shuffle(x, 4)
[1] "A" "B" "D" "E" "C" "A" "B" "D" "E" "C" "A" "B" "D" "E" "C"
> shuffle(x, 2)
[1] "E" "A" "D" "E" "B" "D" "A" "E" "C" "D" "A" "E" "C" "A" "B"
> shuffle(x, 2)
[1] "B" "A" "D" "C" "B" "A" "E" "B" "A" "E" "B" "C" "D" "A" "E"
在 @27ϕ9 评论后：
shuffle <- function(x, min.dist=2){
stopifnot(min.dist < length(unique(x)))
reduce(integer(length(x)-1), ~ c(.x, sample(x[!x %in% tail(.x, min.dist) &( x %in% names(t <- table(x[x%in%.x]) > table(.x))[t] | !x %in% .x)], 1)), .init=sample(x,1))
}
> table(shuffle(rep(LETTERS[1:5], 3),2))
A B C D E
3 3 3 3 3
> table(shuffle(rep(LETTERS[1:5], 3),2))
Error in sample.int(length(x), size, replace, prob) :
invalid first argument
更新
经过反复试验，考虑到并非总是有足够的元素来 space 出 min.dist 这一事实，我想出了一个解决方案，这段代码解释得最多来自上面的：
shuffle <- function(x, min.dist=2){
stopifnot(min.dist < length(unique(x)))
reduce(integer(length(x)-1), function(.x, ...){
# whether the value is in the tail of the aggregated vector
in.tail <- x %in% tail(.x, min.dist)
# whether a value still hasn't reached the max frequency
freq.got <- x %in% names(t<-table(x[x%in%.x]) > table(.x))[t]
# whether a value isn't in the aggregated vector
yet <- !x %in% .x
# the if is there basically to account for the cases when we don't have enough vars to space out the vectors
c(.x, if(any((!in.tail & freq.got) | yet )) sample(x[(!in.tail & freq.got) | yet ], 1) else x[which(freq.got)[1]] )
}, .init=sample(x,1))
}
现在 运行 table(shuffle(rep(LETTERS[1:5], 3),2)) 对于所有变量总是 return 3 我们可以肯定地说在向量中变量是 spaced最小距离为 2。保证没有元素重复的唯一方法是使用 min.dist=length(unique(x))-1，否则会出现最大 r < min.dist 元素与其最后一次出现的距离不 min.dist 的情况，如果存在这样的元素，它们将位于结果向量的 length(x) + 1 - 1:min.dist 子集中。
只是为了完全确定使用循环来检查输出向量的尾部是否具有唯一值：（删除打印语句我只是为了演示目的使用它）
shuffler <- function(x, min.dist=2){
while(!length(unique(print(tail(l<-shuffle(x, min.dist=min.dist), min.dist+1))))==min.dist+1){}
l
}
table(print(shuffler(rep(LETTERS[1:5], 3),2)))
[1] "A" "B" "C" "E" "B" "C" "D" "A" "C" "D" "A" "E" "B" "D" "E"
A B C D E
3 3 3 3 3
table(print(shuffler(rep(LETTERS[1:5], 3),2)))
[1] "D" "C" "C"
[1] "C" "C" "E"
[1] "C" "A" "C"
[1] "D" "B" "D"
[1] "B" "E" "D"
[1] "C" "A" "E" "D" "A" "B" "C" "E" "A" "B" "D" "C" "B" "E" "D"
A B C D E
3 3 3 3 3
更新：
shuffler <- function(x, min.dist=2){
while(any(unlist(lapply(unique(tl<-tail(l<-shuffle(x, min.dist=min.dist), 2*min.dist)), function(x) diff(which(tl==x))<=min.dist)))){}
l
}
这个新版本对向量尾部的元素是否min.dist进行了严格的测试，之前的版本适用于min.dist=2，但是这个新版本做了更好的测试。
我希望这个答案对你有用。它是用 base R 完成的，但它有效。如果你想逐行检查，我离开打印：
x <- rep(LETTERS[1:5], 3) # Create example vector
shuffle <- function(x, min_dist=3){
#init variables
result<-c() # result vector
count<-0
vec_use<-x
vec_keep<-c()
for(i in 1:length(x)){
# print(paste0("iteration =", i))
if (count>min_dist){
valback<-vec_keep[1]
# print(paste0("value to be returned:", valback))
ntimes_valback<-(table(vec_keep)[valback])
vec_use<- c(vec_use,rep(valback,ntimes_valback))
# print(paste0("vec_use after giving back valbak =", valback))
# print(paste0(vec_use,","))
vec_keep <- vec_keep[!vec_keep %in% valback]
# print(paste0("vec_keep after removing valback =", valback))
# print(paste0(vec_keep,","))
}
val<-sample(vec_use,1)
# print(paste0("val = ",val))#remove value
vec_keep<- c(vec_keep,x[x %in% val])
vec_keep<-vec_keep[1:(length(vec_keep)-1)]#removing 1 letter
# print(paste0("vec_keep ="))
# print(paste0(vec_keep,","))
vec_use <- vec_use[!vec_use %in% val]
# print(paste0("vec_use ="))
# print(paste0(vec_use,","))
result[i]<-val
count<-count+1
}
return(result)
}
shuffle(x)
"C" "D" "B" "E" "C" "A" "B" "D" "E" "A" "C" "D" "B" "E" "C"
如果您的数据很大，那么依靠概率来完成这类任务可能会（方式）更快。
这是一个例子：
prob_shuffler = function(x, min.dist = 2){
n = length(x)
res = sample(x)
OK = FALSE
# We loop until we have a solution
while(!OK){
OK = TRUE
for(i in 1:min.dist){
# We check if identical elements are 'i' steps away
pblm = res[1:(n-i)] == res[-(1:i)]
if(any(pblm)){
if(sum(pblm) >= (n - i)/2){
# back to square 1
res = sample(x)
} else {
# we pair each identical element with
# an extra one
extra = sample(which(!pblm), sum(pblm))
id_reshuffle = c(which(pblm), extra)
res[id_reshuffle] = sample(res[id_reshuffle])
}
# We recheck from the beginning
OK = FALSE
break
}
}
}
res
}
尽管 while 循环看起来很可怕，但实际上收敛速度很快。当然，两个字符在 min.dist 远的概率越低，收敛越快。
@Abdessabour Mtk 和@Carles Sans Fuentes 的当前解决方案有效，但根据输入数据的大小，速度很快会变得非常慢。这是一个基准：
library(microbenchmark)
x = rep(c(letters, LETTERS), 10)
length(x)
#> [1] 520
microbenchmark(prob_shuffler(x, 1), shuffler_am(x, 1), shuffler_csf(x, 1), times = 10)
#> Unit: microseconds
#> expr min lq mean median uq max neval
#> prob_shuffler(x, 1) 87.001 111.501 155.071 131.801 192.401 264.401 10
#> shuffler_am(x, 1) 17218.100 18041.900 20324.301 18740.351 22296.301 26495.200 10
#> shuffler_csf(x, 1) 86771.401 88550.501 118185.581 95582.001 98781.601 341826.701 10
microbenchmark(prob_shuffler(x, 2), shuffler_am(x, 2), shuffler_csf(x, 2), times = 10)
#> Unit: microseconds
#> expr min lq mean median uq max neval
#> prob_shuffler(x, 2) 140.1 195.201 236.3312 245.252 263.202 354.101 10
#> shuffler_am(x, 2) 18886.2 19526.901 22967.6409 21021.151 26758.800 29133.400 10
#> shuffler_csf(x, 2) 86078.1 92209.901 97151.0609 97612.251 99850.101 107981.401 10
microbenchmark(prob_shuffler(x, 3), shuffler_am(x, 3), shuffler_csf(x, 3), times = 10)
#> Unit: microseconds
#> expr min lq mean median uq max neval
#> prob_shuffler(x, 3) 318.001 450.402 631.5312 573.352 782.2 1070.401 10
#> shuffler_am(x, 3) 19003.501 19622.300 23314.4808 20784.551 28281.5 32885.101 10
#> shuffler_csf(x, 3) 87692.701 96152.202 101233.5411 100925.201 108034.7 113814.901 10
我们可以注意到两点：a) 在所有逻辑中，prob_shuffler 的速度取决于 min.dist 而其他方法则没有那么多，b) prob_shuffler 大约是 100 - 仅 520 次观察（并且它可以缩放）更快。
当然，如果 min.dist 处有两个相同字符的概率非常高，那么递归方法应该更快。但在大多数实际情况下，概率法更快。