SimplyStats thanksgiving Rubik's Cube solution

simplystats_thanksgiving.R

## transform the input to the output using rubiks-cube transformations and dplyr
require(dplyr)

## provided input
input <- data.frame(matrix(c("h","a","t","t","i","v","i","g","k","s","g","n","n","g","n","i"),
                           4,
                           4,
                           byrow=TRUE,
                           dimnames=list(NULL,paste0("col",1:4))), 
                    stringsAsFactors=FALSE)

## requested output
output <- data.frame(matrix(c("t","h","a","n","k","s","g","i","v","i","n","g"),
                            4,
                            3,
                            byrow=TRUE,
                            dimnames=list(NULL,paste0("col",1:3))), 
                     stringsAsFactors=FALSE)

## construct the column rotating function using dplyr commands
## taking care of wrap-around
## allows forwards or backwards rotation through + or - operator
rotate_col <- function(df, colnum) {
  if(colnum > 0) {
    ## rotate the cube 1->4 by 1 step (row3->row4, row2->row3, etc...)
    ## row4->row1
    rotdfcol <- df %>% slice(c(2,3,4,1)) %>% select(colnum)
  } else {
    ## rotate the cube 4->1 by 1 step (row4->row3, row3->row2, etc...)
    ## row1->row4
    colnum <- -colnum
    rotdfcol <- df %>% slice(c(4,1,2,3)) %>% select(colnum)
  }
  newdf <- df
  newdf[, colnum] <- rotdfcol
  return(newdf)
}

## construct the row rotating function using dplyr commands
## using the same conventions as rotate_col
rotate_row <- function(df, rownum) {
  if (rownum > 0) {
    rotdfrow <- df %>% select(c(4,1,2,3)) %>% slice(rownum)
  } else {
    rownum <- -rownum
    rotdfrow <- df %>% select(c(2,3,4,1)) %>% slice(rownum)
  }
  newdf <- df
  newdf[rownum, ] <- rotdfrow
  
  return(newdf)
}

## perform rubiks-cube operations to achieve the desired result, utilising row 4 as free spaces
## in no way guaranteed to be the fastest method, just the first one that worked
input %>%
  rotate_row(+1) %>%
  rotate_col(+4) %>% rotate_col(+4) %>%
  rotate_col(-1) %>% rotate_row(+4) %>% rotate_col(-1) %>% rotate_row(-4) %>% rotate_col(+1) %>% rotate_col(+1) %>%
  rotate_col(-2) %>% rotate_row(+4) %>% rotate_col(-2) %>% rotate_row(-4) %>% rotate_col(+2) %>% rotate_col(+2) %>%
  rotate_col(-3) %>% rotate_row(-4) %>% rotate_col(-3) %>% rotate_row(+4) %>% rotate_col(+3) %>% rotate_col(+3) %>%
  rotate_row(+4) %>% rotate_col(-1) %>% rotate_row(-4) %>% rotate_col(+1) %>%
  rotate_col(-2) %>% rotate_row(+4) %>% rotate_col(+2) %>%
  rotate_row(+4) %>% rotate_col(-3) %>% rotate_row(-4) %>% rotate_col(+3) %>%
  rotate_col(-4) %>% rotate_row(+4) %>% rotate_col(+4) %>% 
  slice(c(1,2,3)) -> solved ## still a 3x4 matrix

## re-shape the solution into a 4x3 matrix
final <- solved %>% 
  t %>% 
  c %>% 
  matrix(4, 
         3, 
         byrow=TRUE, 
         dimnames=list(NULL,paste0("col",1:3))) %>% 
  data.frame(stringsAsFactors=FALSE)

## check the solution is correct
identical(final, output) # TRUE

http://simplystatistics.org/2015/11/25/a-thanksgiving-dplyr-rubiks-cube-puzzle-for-you/