R语言学习——欧拉计划（11）Largest product in a grid

Posted 2021-01-09 caiyishuai

Problem 11

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?

这些数字的乘积是26×63×78×14 = 1788696。

在20×20网格中，相同方向（上，下，左，右或对角）的四个相邻数字的最大乘积是多少？

f<-function(){
  N<-20
  grid<-matrix(c(8,2,22,97,38,15,0,40,0,75,4,5,7,78,52,12,50,77,91,8,
              49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48,4,56,62,0,
              81,49,31,73,55,79,14,29,93,71,40,67,53,88,30,3,49,13,36,65,
              52,70,95,23,4,60,11,42,69,24,68,56,1,32,56,71,37,2,36,91,
              22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80,
              24,47,32,60,99,3,45,2,44,75,33,53,78,36,84,20,35,17,12,50,
              32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70,
              67,26,20,68,2,62,12,20,95,63,94,39,63,8,40,91,66,49,94,21,
              24,55,58,5,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72,
              21,36,23,9,75,0,76,44,20,45,35,14,0,61,33,97,34,31,33,95,
              78,17,53,28,22,75,31,67,15,94,3,80,4,62,16,14,9,53,56,92,
              16,39,5,42,96,35,31,47,55,58,88,24,0,17,54,24,36,29,85,57,
              86,56,0,48,35,71,89,7,5,44,44,37,44,60,21,58,51,54,17,58,
              19,80,81,68,5,94,47,69,28,73,92,13,86,52,17,77,4,89,55,40,
              4,52,8,83,97,35,99,16,7,97,57,32,16,26,26,79,33,27,98,66,
              88,36,68,87,57,62,20,72,3,46,33,67,46,55,12,32,63,93,53,69,
              4,42,16,73,38,25,39,11,24,94,72,18,8,46,29,32,40,62,76,36,
              20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74,4,36,16,
              20,73,35,29,78,31,90,1,74,31,49,71,48,86,81,16,23,57,5,54,
              1,70,54,71,83,51,54,69,16,92,33,48,61,43,52,1,89,19,67,48),20,20,byrow=TRUE)
  print(grid)
  m<-0
  for (i in 1:16){
    #print(i)
    for(j in 1:16){
      #print(j)
      #print(grid[i,j])
      h<-grid[i,j] * grid[i,j+1] * grid[i,j+2] * grid[i,j+3] #行 
      #print(h)
      v<-grid[j,i] * grid[j+1,i] * grid[j+2,i] * grid[j+3,i] #列
      #print(v)
      d1<-grid[i,j] * grid[i+1,j+1] * grid[i+2,j+2] * grid[i+3,j+3] #右下斜
      #print(d1)
      d2<-grid[i,N-j-1] * grid[i+1,N-j-2] * grid[i+2,N-j-3] * grid[i+3,N-j-4] #左下斜 
      #print(d2)
      m<-max(m, max(h, max(v, max(d1, d2))))
    }
  }
  print(m)
}

Answer: 70600674 Completed on Fri, 28 Sep 2018, 17:41