Project Euler Problem 11

2014年03月10日

Q

In the 20×20 grid below, four numbers along a diagonal line have been marked in red.

 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48

The product of these numbers is 26 × 63 × 78 × 14 = 1788696.
What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?

first version:

setwd('/home/dorothy/HelloWorld/R/')
n <- 20
pm <- matrix(scan('11.txt'),nrow=n,ncol=n,byrow=TRUE)
pl <- numeric()
for(i in 1:n)
{
  for(j in 1:n)
  {
    if(i+3<=n)
      {
        if(j+3<=n) pl <- c(pl,prod(diag(pm[i+(0:3),j+(0:3)])))
        if(j-3>=1) pl <- c(pl,prod(pm[i,j],pm[i+1,j-1],pm[i+2,j-2],pm[i+3,j-3]))
        pl <- c(pl,prod(pm[i+(0:3),j]))
      }
    if(i-3>=1) 
      {
        if(j+3<=n) pl <- c(pl,prod(pm[i,j],pm[i-1,j+1],pm[i-2,j+2],pm[i-3,j+3]))
        if(j-3>=1) pl <- c(pl,prod(diag(pm[i-(0:3),j-(0:3)])))
        pl <- c(pl,prod(pm[i+(0:-3),j]))
      }
    if(j+3<=n) pl <- c(pl,prod(pm[i,j+(0:3)]))
    if(j-3>=1) pl <- c(pl,prod(pm[i,j+(0:-3)]))
  }
}
print(max(pl))

# [1] 70600674