Largest product in a grid: Difference between revisions
(julia example) |
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=={{header| |
=={{header|Julia}}== |
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First, a quick method, which does not reveal the product locations: |
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<lang julia>mat = [ |
<lang julia>mat = [ |
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08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 |
08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 |
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<lang julia>let |
<lang julia>let |
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nrow, ncol = size(mat) |
nrow, ncol = size(mat) |
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maxprod, maxrow, maxcol = 0, 0:0, 0:0 |
maxprod, maxrow, maxcol, arr = 0, 0:0, 0:0, [0] |
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for row in 1:nrow, col in 1:ncol |
for row in 1:nrow, col in 1:ncol |
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if row < nrow - 2 |
if row < nrow - 2 |
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pro = prod(mat[row:row+3, col]) |
pro = prod(mat[row:row+3, col]) |
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if pro > maxprod |
if pro > maxprod |
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maxprod, maxrow, maxcol = pro, row:row+3, col:col |
maxprod, maxrow, maxcol, arr = pro, row:row+3, col:col, mat[row:row+3, col] |
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end |
end |
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end |
end |
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pro = prod(mat[row, col:col+3]) |
pro = prod(mat[row, col:col+3]) |
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if pro > maxprod |
if pro > maxprod |
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maxprod, maxrow, maxcol = pro, row:row, col:col+3 |
maxprod, maxrow, maxcol, arr = pro, row:row, col:col+3, mat[row, col:col+3] |
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end |
end |
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end |
end |
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end |
end |
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println("The maxiumum product is $maxprod at row $maxrow, col $maxcol") |
println("The maxiumum product is $maxprod, product of $arr at row $maxrow, col $maxcol") |
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end |
end |
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</lang>{{out}} |
</lang>{{out}} |
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<pre>The maxiumum product is 51267216 at row 7:10, col 16:16</pre> |
<pre>The maxiumum product is 51267216, product of [66, 91, 88, 97] at row 7:10, col 16:16</pre> |
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=={{header|Ring}}== |
=={{header|Ring}}== |
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Revision as of 08:05, 22 October 2021
- Task
The task desciption is taken from Project Euler
(https://projecteuler.net/problem=11)
Let the 20×20 grid below:
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
What is the greatest product of four adjacent numbers in the same direction (down, right) in the 20×20 grid?
Julia
First, a quick method, which does not reveal the product locations: <lang julia>mat = [
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
]
x = max(maximum([prod(mat[j, i:i+3]) for i in 1:17, j in 1:20]),
maximum([prod(mat[i:i+3, j]) for i in 1:17, j in 1:20]))
println("The maximum product of 4 adjacent horizontal or vertical in the matrix is: $x")
</lang>
- Output:
The maximum product of 4 adjacent horizontal or vertical in the matrix is: 51267216
Alternatively, to get the position of the maximum product: <lang julia>let
nrow, ncol = size(mat)
maxprod, maxrow, maxcol, arr = 0, 0:0, 0:0, [0]
for row in 1:nrow, col in 1:ncol
if row < nrow - 2
pro = prod(mat[row:row+3, col])
if pro > maxprod
maxprod, maxrow, maxcol, arr = pro, row:row+3, col:col, mat[row:row+3, col]
end
end
if col < ncol - 2
pro = prod(mat[row, col:col+3])
if pro > maxprod
maxprod, maxrow, maxcol, arr = pro, row:row, col:col+3, mat[row, col:col+3]
end
end
end
println("The maxiumum product is $maxprod, product of $arr at row $maxrow, col $maxcol")
end
</lang>
- Output:
The maxiumum product is 51267216, product of [66, 91, 88, 97] at row 7:10, col 16:16
Ring
<lang ring> see "working..." + nl see "Largest product is:" + nl
Grid = [[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]]
Index = [] resTemp = [] prodNew = 0
for n = 1 to 17
prod = 0
for m = 1 to 20
prod = Grid[n][m] * Grid[n+1][m] * Grid[n+2][m] * Grid[n+3][m]
if prod > prodNew
prodNew = prod
res = 1000*Grid[n][m] + 100*Grid[n+1][m] + 10*Grid[n+2][m] + Grid[n+3][m]
resTemp = []
Index = []
add(Index,[n,m])
add(Index,[n+1,m])
add(Index,[n+2,m])
add(Index,[n+3,m])
add(resTemp,Grid[n][m])
add(resTemp,Grid[n+1][m])
add(resTemp,Grid[n+2][m])
add(resTemp,Grid[n+3][m])
ok
next
next
for n = 20 to 1 step -1
prod = 0
for m = 1 to 17
prod = Grid[n][m] * Grid[n][m+1] * Grid[n][m+2] * Grid[n][m+3]
if prod > prodNew
prodNew = prod
res = 1000*Grid[n][m] + 100*Grid[n][m+1] + 10*Grid[n][m+2] + Grid[n][m+3]
resTemp = []
Index = []
add(Index,[n,m])
add(Index,[n,m+1])
add(Index,[n,m+2])
add(Index,[n,m+3])
resTemp = []
add(resTemp,Grid[n][m])
add(resTemp,Grid[n][m+1])
add(resTemp,Grid[n+2][m+2])
add(resTemp,Grid[n][m+3])
ok
next
next
for n = 1 to len(resTemp)-1
see "" + resTemp[n] + " * "
next see "" + resTemp[len(resTemp)] + " = " + prodNew + nl
see "Indices = " for n = 1 to len(Index)
see "(" + Index[n][1] + "," + Index[n][2] + ")"
next
see nl + "done..." + nl </lang>
- Output:
working... Largest product is: 66 * 91 * 88 * 97 = 51267216 Indices = (7,16)(8,16)(9,16)(10,16) done...