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

最新推荐文章于 2021-07-02 11:15:42 发布

转载最新推荐文章于 2021-07-02 11:15:42 发布 · 82 阅读

0 ·

CC 4.0 BY-SA版权

原文链接：http://www.cnblogs.com/caiyishuai/p/9721655.html

在20x20的数字网格中，寻找四个相邻数字（水平、垂直或对角）的最大乘积。通过编程算法遍历所有可能的组合，最终找到最大乘积为70600674。

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

转载于:https://www.cnblogs.com/caiyishuai/p/9721655.html