r - R中二进制序列的函数

Question

如何在 R 中编写一个函数，给定一个整数 n，它找到所有长度为 2n 的二进制序列，使得前 n 位的总和与后 n 位的总和相同。

Example:
For   n = 2, the sequences are:
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    0    1    1    0    0    1
[2,]    0    0    0    1    1    1
[3,]    0    1    0    1    0    1
[4,]    0    0    1    0    1    1

Answer 1

以下函数是this GeeksforGeeks post中函数的R翻译.

findAllSeq2n <- function(n){
  f <- function(d, out, start, end){
    if (abs(d) > (end - start + 1) / 2) return(NULL)
    if (start > end) { 
      if (d == 0) {
        #cat(out, "\n")
        return(out)
      }
    }

    out[start] <- 0L
    out[end] <- 1L
    s01 <- f(d + 1L, out, start + 1L, end - 1L)
    
    out[start] <- 1L
    out[end] <- 1L
    s11 <- f(d, out, start + 1L, end - 1L)
    
    out[start] <- 0L
    out[end] <- 0L
    s00 <- f(d, out, start + 1L, end - 1L)
    
    out[start] <- 1L
    out[end] <- 0L
    s10 <- f(d - 1L, out, start + 1L, end - 1L)

    do.call(cbind, list(s01, s11, s00, s10))
  }
  out <- integer(2*n)
  f(0, out, 1, 2*n)
}

findAllSeq2n(2)
#     [,1] [,2] [,3] [,4] [,5] [,6]
#[1,]    0    1    1    0    0    1
#[2,]    1    1    0    1    0    0
#[3,]    0    1    0    1    0    1
#[4,]    1    1    1    0    0    0

findAllSeq2n(3)
findAllSeq2n(4)