Select all binary neighbors of decimal number - r

Question

Let's say I have a number in decimal format: 5
its binary version is: 00101
I would like to write a function that takes the decimal number x
and returns all other decimal numbers that have a single digit difference (in their binary forms) from the original one:
so for the example above the neighbors are:
10101 01101 00111 00001 00100
and the corresponding decimals are:
21 13 7 1 4
I would like a solution that is computationally efficient and doesn't take a long time even if I have say a million digits.
Is this possible to do?

Answer 1

I've no idea how trial and error got me here, but it looks valid unless I've messed up binaries and decimals:
bin_neighs = function(x, n) bitwXor(x, (2 ^ (0:(n - 1))))
bin_neighs(5, 5)
#[1] 4 7 1 13 21

Answer 2

I think you're asking how to take as input a number 5 and to return all neighboring binary values. To do this, you need to convert the number to a useful binary format (just the bits you want to flip), flip each bit, and return the result:
library(R.utils)
bin.neighbors <- function(x, num.neighbors=NA) {
# Get the bits with the appropriate amount of padding
bits <- as.numeric(unlist(strsplit(intToBin(x), "")))
if (!is.na(num.neighbors) & num.neighbors > length(bits)) {
bits <- c(rep(0, num.neighbors-length(bits)), bits)
}
# Build a matrix where each column is a bit vector of a neighbor
mat <- matrix(bits, length(bits), length(bits))
diag(mat) <- 1-diag(mat)
# Return the decimal values of the neighbors using strtoi
apply(mat, 2, function(x) strtoi(paste0(x, collapse=""), 2))
}
bin.neighbors(5, 5)
# [1] 21 13 1 7 4
Because each number has a number of binary representations with different numbers of leading 0s (e.g. 5 can be represented as 101, 0101, 00101, 000101, 0000101, etc.), I added an argument num.neighbors to specify the length of the output vector from the function. You can pass NA to obtain an output vector equal to the number of bits in the binary representation of the input with no leading zeros.

Answer 3

Here's another way using magrittr's pipe:
binNeighbours <- function(a, numNeighbours = ceiling(log2(a))) {
rep(a, numNeighbours) %>%
outer(., seq(.) - 1, function(x, y) x %/% (2 ^ y) %% 2) %>%
`diag<-`(., 1 - diag(.)) %>%
`%*%`(2 ^(0:(nrow(.) - 1))) %>%
`[`(, 1)
}