[2016-04-04] Challenge #261 [Easy] verifying 3x3 magic squares

magic-square.R

#
# [2016-04-04] Challenge #261 [Easy] verifying 3x3 magic squares
# https://www.reddit.com/r/dailyprogrammer/comments/4dccix/20160404_challenge_261_easy_verifying_3x3_magic/
# Demo at http://www.r-fiddle.org/#/fiddle?id=AgVxiDgU&version=1
#
# Kory Becker 4/4/2016
# http://primaryobjects.com
#

magicSquare <- function(input) {
  # Determine the sum of a magic square row, column, diagonal.
  n <- sqrt(length(input))
  (n * (n ^ 2 + 1)) / 2
}

diagSums <- function(grid) {
  # Verify diagonals.
  y1 <- 1
  y2 <- nrow(grid)
  a <- c()
  b <- c()
  
  for (x in seq(ncol(grid))) {
    # Top-left diagonal.
    a <- c(a, grid[y1, x])
    # Bottom-left diagonal.
    b <- c(b, grid[y2, x])
    
    y1 <- y1 + 1
    y2 <- y2 - 1
    
    if (y1 > nrow(grid))
      break
  }
  
  c(sum(a), sum(b))
}

isMagicSquare <- function(input) {
  sum <- magicSquare(input)
  grid <- t(as.data.frame(split(input, ceiling(seq_along(input) / sqrt(length(input))))))
  
  # Verify rows, columns, diagonals.
  (length(which(rowSums(grid) == sum)) == nrow(grid) &&
   length(which(colSums(grid) == sum)) == ncol(grid) &&
   length(which(diagSums(grid) == sum)) == 2)
}

isMagicSquare(c(8, 1, 6, 3, 5, 7, 4, 9, 2))
isMagicSquare(c(2, 7, 6, 9, 5, 1, 4, 3, 8))
isMagicSquare(c(3, 5, 7, 8, 1, 6, 4, 9, 2))
isMagicSquare(c(8, 1, 6, 7, 5, 3, 4, 9, 2))
isMagicSquare(c(16,2,3,13,5,11,10,8,9,7,6,12,4,14,15,1))
isMagicSquare(1:16)
isMagicSquare(c(1,2,62,61,60,59,7,8,9,10,54,53,52,51,15,16,48,47,19,20,21,22,42,41,40,39,27,28,29,30,34,33,32,31,35,36,37,38,26,25,24,23,43,44,45,46,18,17,49,50,14,13,12,11,55,56,57,58,6,5,4,3,63,64))

output.txt

> isMagicSquare(c(8, 1, 6, 3, 5, 7, 4, 9, 2))
[1] TRUE

> isMagicSquare(c(2, 7, 6, 9, 5, 1, 4, 3, 8))
[1] TRUE

> isMagicSquare(c(3, 5, 7, 8, 1, 6, 4, 9, 2))
[1] FALSE

> isMagicSquare(c(8, 1, 6, 7, 5, 3, 4, 9, 2))
[1] FALSE

> isMagicSquare(c(16,2,3,13,5,11,10,8,9,7,6,12,4,14,15,1))
[1] TRUE

> isMagicSquare(1:16)
[1] FALSE

> isMagicSquare(c(1,2,62,61,60,59,7,8,9,10,54,53,52,51,15,16,48,47,19,20,21,22,42,41,40,39,27,28,29,30,34,33,32,31,35,36,37,38,26,25,24,23,43,44,45,46 .... [TRUNCATED] 
[1] TRUE