Largest product in a grid
Largest product in a grid is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
- Task
The task description is taken from Project Euler:
(https://projecteuler.net/problem=11)
Given 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?
11l
F maxproduct(mat, length)
‘ find the largest product of len length horizontal or vertical length in matrix ’
V (nrow, ncol) = (mat.len, mat[0].len)
V (maxprod, maxrow, maxcol, arr) = (Int64(0), [0, 0], [0, 0], [0])
L(row) 0 .< nrow
L(col) 0 .< ncol
V (row2, col2) = (row + length, col + length)
I row < nrow - length
V array = mat[row .< row2].map(r -> r[@col])
V pro = product(array.map(Int64))
I pro > maxprod
(maxprod, maxrow, maxcol, arr) = (pro, [row, row2], [col], array)
I col < ncol - length
V pro = product(mat[row][col .< col2].map(Int64))
I pro > maxprod
(maxprod, maxrow, maxcol, arr) = (pro, [row], [col, col2], mat[row][col .< col2])
print(‘The max ’length‘-product is ’maxprod‘, product of ’arr‘ at row ’maxrow‘, col ’maxcol‘.’)
V MATRIX = [
[ 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]
]
L(n) 2..5
maxproduct(MATRIX, n)- Output:
The max 2-product is 9215, product of [95, 97] at row [7, 9], col [8]. The max 3-product is 776776, product of [91, 88, 97] at row [7, 10], col [15]. The max 4-product is 51267216, product of [66, 91, 88, 97] at row [6, 10], col [15]. The max 5-product is 2326829868, product of [62, 99, 69, 82, 67] at row [17], col [9, 14].
ALGOL 68
BEGIN # find the maximum product of 4 adjacent numbers in a row or column of a matrix #
[,]INT m = ( ( 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 )
);
INT elements = 4; # number of elements to multiply #
INT max product := - max int; # most negative integer #
INT row := 0, col := 0;
BOOL horizontal := TRUE;
FOR i FROM 1 LWB m TO 1 UPB m DO
FOR j FROM 2 LWB m TO ( 2 UPB m - elements ) + 1 DO
INT ij product := m[ i, j ] * m[ i, j + 1 ] * m[ i, j + 2 ] * m[ i, j + 3 ];
IF ij product > max product THEN
max product := ij product;
row := i;
col := j
FI
OD
OD;
FOR j FROM 2 LWB m TO 2 UPB m DO
FOR i FROM 1 LWB m TO ( 2 UPB m - elements ) + 1 DO
INT ij product := m[ i, j ] * m[ i + 1, j ] * m[ i + 2, j ] * m[ i + 3, j ];
IF ij product > max product THEN
max product := ij product;
row := i;
col := j;
horizontal := FALSE
FI
OD
OD;
print( ( "The maximum product of ", whole( elements, 0 )
, " elements: ", whole( max product, 0 )
, " is the ", IF horizontal THEN "row" ELSE "column" FI
, " of ", whole( elements, 0 )
, " numbers starting at: ", whole( row, 0 ), ", ", whole( col, 0 )
)
)
END- Output:
The maximum product of 4 elements: 51267216 is the column of 4 numbers starting at: 7, 16
AutoHotkey
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
)
oGrid := []
for r, line in StrSplit(grid, "`n", "`r")
for c, v in StrSplit(line, " ")
oGrid[r, c] := v
n := 4
Steps := []
for r, row in oGrid
{
for c, v in row
{
prodR := prodC := 1
strR := strC := ""
loop % n
{
prodR *= oGrid[r, c + A_Index - 1]
prodC *= oGrid[r + A_Index - 1, C]
strR .= oGrid[r, c + A_Index - 1] "*"
strC .= oGrid[r + A_Index - 1, C] "*"
}
Steps[prodR] .= "`n" Trim(strR, "*") " @ Row " r ", Col " c " - Col " c+n-1
Steps[prodC] .= "`n" Trim(strC, "*") " @ Row " r " - Row " r+n-1 ", Col " c
maxProd := maxProd > prodR ? maxProd : prodR
maxProd := maxProd > prodC ? maxProd : prodC
}
}
MsgBox, 262144, ,% result := "Max Product = " maxProd . Steps[maxProd]
- Output:
Max Product = 51267216 66*91*88*97 @ Row 7 - Row 10, Col 16
AWK
# syntax: GAWK -f LARGEST_PRODUCT_IN_A_GRID.AWK
BEGIN {
grid[++row] = "08,02,22,97,38,15,00,40,00,75,04,05,07,78,52,12,50,77,91,08"
grid[++row] = "49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48,04,56,62,00"
grid[++row] = "81,49,31,73,55,79,14,29,93,71,40,67,53,88,30,03,49,13,36,65"
grid[++row] = "52,70,95,23,04,60,11,42,69,24,68,56,01,32,56,71,37,02,36,91"
grid[++row] = "22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80"
grid[++row] = "24,47,32,60,99,03,45,02,44,75,33,53,78,36,84,20,35,17,12,50"
grid[++row] = "32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70"
grid[++row] = "67,26,20,68,02,62,12,20,95,63,94,39,63,08,40,91,66,49,94,21"
grid[++row] = "24,55,58,05,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72"
grid[++row] = "21,36,23,09,75,00,76,44,20,45,35,14,00,61,33,97,34,31,33,95"
grid[++row] = "78,17,53,28,22,75,31,67,15,94,03,80,04,62,16,14,09,53,56,92"
grid[++row] = "16,39,05,42,96,35,31,47,55,58,88,24,00,17,54,24,36,29,85,57"
grid[++row] = "86,56,00,48,35,71,89,07,05,44,44,37,44,60,21,58,51,54,17,58"
grid[++row] = "19,80,81,68,05,94,47,69,28,73,92,13,86,52,17,77,04,89,55,40"
grid[++row] = "04,52,08,83,97,35,99,16,07,97,57,32,16,26,26,79,33,27,98,66"
grid[++row] = "88,36,68,87,57,62,20,72,03,46,33,67,46,55,12,32,63,93,53,69"
grid[++row] = "04,42,16,73,38,25,39,11,24,94,72,18,08,46,29,32,40,62,76,36"
grid[++row] = "20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74,04,36,16"
grid[++row] = "20,73,35,29,78,31,90,01,74,31,49,71,48,86,81,16,23,57,05,54"
grid[++row] = "01,70,54,71,83,51,54,69,16,92,33,48,61,43,52,01,89,19,67,48"
for (r=1; r<=row; r++) { # build 2-dimensional array
col = split(grid[r],tmp_arr,",")
width_arr[col] = ""
for (c=1; c<=col; c++) {
arr[r][c] = tmp_arr[c]
}
}
if (length(width_arr) != 1) {
print("error: arrays must be same length")
exit(1)
}
delete grid
delete tmp_arr
delete width_arr
for (r=1; r<=row-3; r++) { # top-bottom / down
for (c=1; c<=col; c++) {
product = (p0=arr[r][c]) * (p1=arr[r+1][c]) * (p2=arr[r+2][c]) * (p3=arr[r+3][c])
if (product > ans) {
ans = product
cell_info = sprintf("%d*%d*%d*%d in column %d rows %d-%d",p0,p1,p2,p3,c,r,r+3)
}
}
}
for (c=1; c<=col-3; c++) { # left-right / across
for (r=1; r<=row; r++) {
product = (p0=arr[r][c]) * (p1=arr[r][c+1]) * (p2=arr[r][c+2]) * (p3=arr[r][c+3])
if (product > ans) {
ans = product
cell_info = sprintf("%d*%d*%d*%d in row %d columns %d-%d",p0,p1,p2,p3,r,c,c+3)
}
}
}
printf("%d = %s\n",ans,cell_info)
exit(0)
}
- Output:
51267216 = 66*91*88*97 in column 16 rows 7-10
F#
// Largest product in a grid. Nigel Galloway: December 30th., 2021
let N=[|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|]
printfn "%d" (seq{for n in 0..19 do for g in 0..16 do let n=n*20 in yield N.[n+g]*N.[n+g+1]*N.[n+g+2]*N.[n+g+3]; for n in 0..19 do for g in 0..16 do let g=g*20 in yield N.[n+g]*N.[n+g+20]*N.[n+g+40]*N.[n+g+60]}|>Seq.max)
- Output:
51267216
Factor
USING: grouping kernel math.matrices math.order prettyprint
sequences ;
: max-horizontal ( matrix m -- n )
[ <clumps> ] curry map [ product ] matrix-map mmax ;
: max-product ( matrix m -- n )
[ dup flip ] dip [ max-horizontal ] curry bi@ max ;
{
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
} 20 group
4 max-product .
- Output:
51267216
FreeBASIC
data 08,02,22,97,38,15,00,40,00,75,04,05,07,78,52,12,50,77,91,08
data 49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48,04,56,62,00
data 81,49,31,73,55,79,14,29,93,71,40,67,53,88,30,03,49,13,36,65
data 52,70,95,23,04,60,11,42,69,24,68,56,01,32,56,71,37,02,36,91
data 22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80
data 24,47,32,60,99,03,45,02,44,75,33,53,78,36,84,20,35,17,12,50
data 32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70
data 67,26,20,68,02,62,12,20,95,63,94,39,63,08,40,91,66,49,94,21
data 24,55,58,05,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72
data 21,36,23,09,75,00,76,44,20,45,35,14,00,61,33,97,34,31,33,95
data 78,17,53,28,22,75,31,67,15,94,03,80,04,62,16,14,09,53,56,92
data 16,39,05,42,96,35,31,47,55,58,88,24,00,17,54,24,36,29,85,57
data 86,56,00,48,35,71,89,07,05,44,44,37,44,60,21,58,51,54,17,58
data 19,80,81,68,05,94,47,69,28,73,92,13,86,52,17,77,04,89,55,40
data 04,52,08,83,97,35,99,16,07,97,57,32,16,26,26,79,33,27,98,66
data 88,36,68,87,57,62,20,72,03,46,33,67,46,55,12,32,63,93,53,69
data 04,42,16,73,38,25,39,11,24,94,72,18,08,46,29,32,40,62,76,36
data 20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74,04,36,16
data 20,73,35,29,78,31,90,01,74,31,49,71,48,86,81,16,23,57,05,54
data 01,70,54,71,83,51,54,69,16,92,33,48,61,43,52,01,89,19,67,48
dim as integer grid(1 to 20, 1 to 20), row, col, prod
dim as integer champ = 0, cr, cc
dim as boolean across = false
for row = 1 to 20
for col = 1 to 20
read grid(row, col)
next col
next row
'search down
for row = 1 to 17
for col = 1 to 20
prod = grid(row, col)*grid(row + 1, col)*grid(row + 2, col)*grid(row + 3, col)
if prod > champ then
cr = row
cc = col
champ = prod
end if
next col
next row
'search across
for row = 1 to 20
for col = 1 to 17
prod = grid(row, col)*grid(row, col + 1)*grid(row, col + 2)*grid(row, col + 3)
if prod > champ then
cr = row
cc = col
champ = prod
across = true
end if
next col
next row
print "The largest product was ";champ;" at row ";cr;" and column ";cc;", reading ";
if across then print "across." else print "down."- Output:
The largest product was 51267216 at row 7 and column 16, reading down.
Go
package main
import (
"fmt"
"rcu"
"strings"
)
var grid = [][]int {
{ 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},
}
func main() {
maxProd, maxR1, maxR2, maxC1, maxC2 := 0, 0, 0, 0, 0
var maxNums [4]int
h, w := len(grid), len(grid[0])
// right
for r := 0; r < h; r++ {
for c := 0; c < w-4; c++ {
prod := 1
for i := c; i < c+4; i++ {
prod *= grid[r][i]
}
if prod > maxProd {
maxProd = prod
for n := 0; n < 4; n++ {
maxNums[n] = grid[r][c+n]
}
maxR1, maxR2 = r, r
maxC1, maxC2 = c, c+3
}
}
}
// down
for c := 0; c < w; c++ {
for r := 0; r < h-4; r++ {
prod := 1
for i := r; i < r+4; i++ {
prod *= grid[i][c]
}
if prod > maxProd {
maxProd = prod
for n := 0; n < 4; n++ {
maxNums[n] = grid[r+n][c]
}
maxR1, maxR2 = r, r+3
maxC1, maxC2 = c, c
}
}
}
fmt.Println("The greatest product of four adjacent numbers in the same direction (down or right) in the grid is:")
var maxNumStrs [4]string
for i := 0; i < 4; i++ {
maxNumStrs[i] = fmt.Sprintf("%d", maxNums[i])
}
fmt.Printf(" %s = %s\n", strings.Join(maxNumStrs[:], " x "), rcu.Commatize(maxProd))
fmt.Print(" at indices (one based): ")
for r := maxR1; r <= maxR2; r++ {
for c := maxC1; c <= maxC2; c++ {
fmt.Printf("(%d, %d) ", r+1, c+1)
}
}
fmt.Println()
}
- Output:
The greatest product of four adjacent numbers in the same direction (down or right) in the grid is: 66 x 91 x 88 x 97 = 51,267,216 at indices (one based): (7, 16) (8, 16) (9, 16) (10, 16)
Julia
First, a quick method, which does not reveal the product locations:
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")
- Output:
The maximum product of 4 adjacent horizontal or vertical in the matrix is: 51267216
Alternatively, to get the position of the maximum product:
function maxprod(mat, len)
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 - len + 2
pro = prod(mat[row:row+len-1, col])
if pro > maxprod
maxprod, maxrow, maxcol, arr = pro, row:row+len-1, col:col, mat[row:row+len-1, col]
end
end
if col < ncol - len + 2
pro = prod(mat[row, col:col+len-1])
if pro > maxprod
maxprod, maxrow, maxcol, arr = pro, row:row, col:col+len-1, mat[row, col:col+len-1]
end
end
end
println("The maximum product is $maxprod, product of $arr at row $maxrow, col $maxcol")
end
maxprod(mat, 4)
- Output:
The maximum product is 51267216, product of [66, 91, 88, 97] at row 7:10, col 16:16
Mathematica / Wolfram Language
array = {
{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}
};
maxProduct[x_List, n_] := Max[Times @@@ Partition[x, n, 1]]
Max@Join[maxProduct[#, 4] & /@ array,
maxProduct[#, 4] & /@ Transpose[array]]
- Output:
51267216
ooRexx
/* REXX */
a.1=.array~of(08,02,22,97,38,15,00,40,00,75,04,05,07,78,52,12,50,77,91,08)
a.2=.array~of(49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48,04,56,62,00)
a.3=.array~of(81,49,31,73,55,79,14,29,93,71,40,67,53,88,30,03,49,13,36,65)
a.4=.array~of(52,70,95,23,04,60,11,42,69,24,68,56,01,32,56,71,37,02,36,91)
a.5=.array~of(22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80)
a.6=.array~of(24,47,32,60,99,03,45,02,44,75,33,53,78,36,84,20,35,17,12,50)
a.7=.array~of(32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70)
a.8=.array~of(67,26,20,68,02,62,12,20,95,63,94,39,63,08,40,91,66,49,94,21)
a.9=.array~of(24,55,58,05,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72)
a.10=.array~of(21,36,23,09,75,00,76,44,20,45,35,14,00,61,33,97,34,31,33,95)
a.11=.array~of(78,17,53,28,22,75,31,67,15,94,03,80,04,62,16,14,09,53,56,92)
a.12=.array~of(16,39,05,42,96,35,31,47,55,58,88,24,00,17,54,24,36,29,85,57)
a.13=.array~of(86,56,00,48,35,71,89,07,05,44,44,37,44,60,21,58,51,54,17,58)
a.14=.array~of(19,80,81,68,05,94,47,69,28,73,92,13,86,52,17,77,04,89,55,40)
a.15=.array~of(04,52,08,83,97,35,99,16,07,97,57,32,16,26,26,79,33,27,98,66)
a.16=.array~of(88,36,68,87,57,62,20,72,03,46,33,67,46,55,12,32,63,93,53,69)
a.17=.array~of(04,42,16,73,38,25,39,11,24,94,72,18,08,46,29,32,40,62,76,36)
a.18=.array~of(20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74,04,36,16)
a.19=.array~of(20,73,35,29,78,31,90,01,74,31,49,71,48,86,81,16,23,57,05,54)
a.20=.array~of(01,70,54,71,83,51,54,69,16,92,33,48,61,43,52,01,89,19,67,48)
max=0
Do row=1 To 20
Do col=1 To 17
ar=a.row
prod=ar[col]*ar[col+1]*ar[col+2]*ar[col+3]
If prod>max Then Do
max=prod
rc=row col
l=ar[col]'*'ar[col+1]'*'ar[col+2]'*'ar[col+3]'='prod
End
End
End
Parse Var rc row col
Say 'Maximum in row' row 'columns' col '...' (col+3) ':' l
Do i=1 To 20
b.i=.array~of(a.1[i],a.2[i],a.3[i],a.4[i],a.5[i],a.6[i],a.7[i],a.8[i],a.9[i],a.10[i],,
a.11[i],a.12[i],a.13[i],a.14[i],a.15[i],a.16[i],a.17[i],a.18[i],a.19[i],a.20[i])
End
Do col=1 to 20
Do row=1 To 17
bc=b.col
prod=bc[row]*bc[row+1]*bc[row+2]*bc[row+3]
If prod>max Then Do
max=prod
rc=row col
l=bc[row]'*'bc[row+1]'*'bc[row+2]'*'bc[row+3]'='prod
End
End
End
Parse Var rc row col
Say 'Maximum in column' col 'rows' row '...' (row+3)
Say l- Output:
Maximum in row 9 columns 11 ... 14 : 78*78*96*83=48477312 Maximum in column 16 rows 7 ... 10 : 66*91*88*97=51267216
Perl
#!/usr/bin/perl
use strict; # https://rosettacode.org/wiki/Largest_product_in_a_grid
use warnings;
use List::Util qw( max );
$_ = <<END;
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
END
my $score = 0;
for my $gap ( qr/ /, qr/.{58}/s )
{
$score = max $score, $1 * $2 * $3 * $4
while /(?=(\d\d)$gap(\d\d)$gap(\d\d)$gap(\d\d))/g;
}
print "max is $score\n";
- Output:
max is 51267216
Generalized
Handles non-square input (both narrow and wide).
use strict;
use warnings;
use feature 'say';
use List::AllUtils <max reduce>;
my $input = <<~END;
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
END
my(@m,@mt);
push @m, [ split /\s+/, s/\b0//gr ] for split "\n", $input;
for my $j (0..$#{$m[0]}) { push @mt, [ map $_->[$j], @m ] } # transpose
sub max_products {
my($terms,@matrix) = @_;
my @products;
my $columns = 1 + $#{$matrix[0]};
for my $row (@matrix) {
map { push @products, reduce { $a * $b } @$row[ $_ .. $_+$terms-1 ] } 0 .. $columns-$terms;
}
max @products
}
say "Largest product of $_ adjacent elements: " . max max_products($_,@m), max_products($_,@mt) for 1..6;
- Output:
Largest product of 1 adjacent elements: 99 Largest product of 2 adjacent elements: 9215 Largest product of 3 adjacent elements: 776776 Largest product of 4 adjacent elements: 51267216 Largest product of 5 adjacent elements: 2326829868 Largest product of 6 adjacent elements: 188210512710
Phix
with javascript_semantics function splint(string s) return apply(split(s),to_integer) end function constant grid = apply(split(""" 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 ""","\n"),splint) function gridmax(integer len) sequence gmax = {0,"???",0,0} integer height = length(grid), width = length(grid[1]) atom prod for row=1 to height do integer rmax = row+len-1 for col=1 to width do integer cmax = col+len-1 if cmax<=width then prod = product(grid[row][col..cmax]) gmax = max(gmax,{prod,"row",row,col}) end if if rmax<=height then prod = product(vslice(grid,col)[row..rmax]) gmax = max(gmax,{prod,"column",row,col}) end if end for end for return gmax end function for i=1 to 6 do printf(1,"The largest product of length %d is %,d in %s starting at %d,%d\n",i&gridmax(i)) end for
- Output:
The largest product of length 1 is 99 in row starting at 18,11 The largest product of length 2 is 9,215 in column starting at 8,9 The largest product of length 3 is 776,776 in column starting at 8,16 The largest product of length 4 is 51,267,216 in column starting at 7,16 The largest product of length 5 is 2,326,829,868 in row starting at 18,10 The largest product of length 6 is 188,210,512,710 in row starting at 18,11
Python
""" Rosetta code task: Largest_product_in_a_grid """
from math import prod
def maxproduct(mat, length):
""" find the largest product of len length horizontal or vertical length in matrix """
nrow, ncol = len(mat), len(mat[0])
maxprod, maxrow, maxcol, arr = 0, [0, 0], [0, 0], [0]
for row in range(nrow):
for col in range(ncol):
row2, col2 = row + length, col + length
if row < nrow - length:
array = [r[col] for r in mat[row:row2]]
pro = prod(array)
if pro > maxprod:
maxprod, maxrow, maxcol, arr = pro, [row, row2], col, array
if col < ncol - length:
pro = prod(mat[row][col:col2])
if pro > maxprod:
maxprod, maxrow, maxcol, arr = pro, row, [col, col2], mat[row][col:col2]
print(f"The max {length}-product is {maxprod}, product of {arr} at row {maxrow}, col {maxcol}.")
MATRIX = [
[ 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]
]
for n in range(2, 6):
maxproduct(MATRIX, n)
- Output:
The max 2-product is 9215, product of [95, 97] at row [7, 9], col 8. The max 3-product is 776776, product of [91, 88, 97] at row [7, 10], col 15. The max 4-product is 51267216, product of [66, 91, 88, 97] at row [6, 10], col 15. The max 5-product is 2326829868, product of [62, 99, 69, 82, 67] at row 17, col [9, 14].
Raku
General solution. No hard coded values. Works with any size matrix, configurable number of terms.
my @matrix = q:to/END/.lines».words;
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
END
my $terms = 4;
say "Largest product of $terms adjacent elements: " ~ max flat (^@matrix).map: {
@matrix.rotor($terms => -$terms+1).flat»[$_].batch($terms)».reduce(&[*]), # vertical
@matrix[$_].rotor($terms => -$terms+1)».reduce(&[*]); # horizontal
}
- Output:
Largest product of 4 adjacent elements: 51267216
REXX
/* REXX */
Call mk_a 1,08,02,22,97,38,15,00,40,00,75,04,05,07,78,52,12,50,77,91,08
Call mk_a 2,49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48,04,56,62,00
Call mk_a 3,81,49,31,73,55,79,14,29,93,71,40,67,53,88,30,03,49,13,36,65
Call mk_a 4,52,70,95,23,04,60,11,42,69,24,68,56,01,32,56,71,37,02,36,91
Call mk_a 5,22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80
Call mk_a 6,24,47,32,60,99,03,45,02,44,75,33,53,78,36,84,20,35,17,12,50
Call mk_a 7,32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70
Call mk_a 8,67,26,20,68,02,62,12,20,95,63,94,39,63,08,40,91,66,49,94,21
Call mk_a 9,24,55,58,05,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72
Call mk_a 10,21,36,23,09,75,00,76,44,20,45,35,14,00,61,33,97,34,31,33,95
Call mk_a 11,78,17,53,28,22,75,31,67,15,94,03,80,04,62,16,14,09,53,56,92
Call mk_a 12,16,39,05,42,96,35,31,47,55,58,88,24,00,17,54,24,36,29,85,57
Call mk_a 13,86,56,00,48,35,71,89,07,05,44,44,37,44,60,21,58,51,54,17,58
Call mk_a 14,19,80,81,68,05,94,47,69,28,73,92,13,86,52,17,77,04,89,55,40
Call mk_a 15,04,52,08,83,97,35,99,16,07,97,57,32,16,26,26,79,33,27,98,66
Call mk_a 16,88,36,68,87,57,62,20,72,03,46,33,67,46,55,12,32,63,93,53,69
Call mk_a 17,04,42,16,73,38,25,39,11,24,94,72,18,08,46,29,32,40,62,76,36
Call mk_a 18,20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74,04,36,16
Call mk_a 19,20,73,35,29,78,31,90,01,74,31,49,71,48,86,81,16,23,57,05,54
Call mk_a 20,01,70,54,71,83,51,54,69,16,92,33,48,61,43,52,01,89,19,67,48
max=0
Do row=1 To 20
Do col=1 To 17
Parse Value (col+1) (col+2) (col+3) With col1 col2 col3
prod=a.row.col*a.row.col1*a.row.col2*a.row.col3
If prod>max Then Do
max=prod
rc=row col
l=a.row.col'*'a.row.col1'*'a.row.col2'*'a.row.col3'='prod
End
End
End
Parse Var rc row col
Say 'Maximum in row' row 'columns' col '...' (col+3) ':' ö
Do col=1 to 20
Do row=1 To 17
Parse Value (row+1) (row+2) (row+3) With row1 row2 row3
prod=a.row.col*a.row1.col*a.row2.col*a.row3.col
If prod>max Then Do
max=prod
rc=row col
l=a.row.col'*'a.row1.col'*'a.row2.col'*'a.row3.col'='prod
End
End
End
Parse Var rc row col
Say 'Maximum in row' row 'columns' col '...' (col+3) ':' l
mk_a:
row=arg(1)
Do col=1 To 20
a.row.col=arg(col+1)
End
Return
- Output:
Maximum in row 9 columns 11 ... 14 : 78*78*96*83=48477312 Maximum in column 16 rows 7 ... 10 : 66*91*88*97=51267216
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- Output:
working... Largest product is: 66 * 91 * 88 * 97 = 51267216 Indices = (7,16)(8,16)(9,16)(10,16) done...
Sidef
var text = <<'EOT'
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
EOT
func horizontal(N, i, j, matrix) {
N.of {|k| matrix[i][j+k] }
}
func diagonal(N, i, j, matrix) {
N.of {|k| matrix[i+k][j+k] }
}
var matrix = Matrix(text.lines.map{ .nums }...)
var reversed_matrix = matrix.horizontal_flip
var transposed_matrix = matrix.transpose
define (
CHECK_DIAGONALS = false # true to also check diagonals
)
const e = matrix.end
for N in (1..6) {
var products = gather {
for i in (0..e), j in (0..e) {
(j+N < e) || next
# Horizontal and vertical
take(horizontal(N, i, j, matrix))
take(horizontal(N, i, j, transposed_matrix))
CHECK_DIAGONALS || next
(i+N < e) || next
# Left-to-right and right-to-left diagonals
take(diagonal(N, i, j, matrix))
take(diagonal(N, i, j, reversed_matrix))
}
}
var nums = products.max_by { .prod }
say "Largest product of #{N} adjacent elements: prod(#{nums}) = #{nums.prod}"
}
- Output:
Largest product of 1 adjacent elements: prod([99]) = 99 Largest product of 2 adjacent elements: prod([95, 97]) = 9215 Largest product of 3 adjacent elements: prod([91, 88, 97]) = 776776 Largest product of 4 adjacent elements: prod([66, 91, 88, 97]) = 51267216 Largest product of 5 adjacent elements: prod([62, 99, 69, 82, 67]) = 2326829868 Largest product of 6 adjacent elements: prod([99, 69, 82, 67, 59, 85]) = 188210512710
Wren
import "./fmt" for Fmt
var 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]
]
var maxProd = 0
var maxNums = [0, 0, 0, 0]
var maxR1 = 0
var maxR2 = 0
var maxC1 = 0
var maxC2 = 0
var h = grid.count
var w = grid[0].count
// right
for (r in 0...h) {
for (c in 0..w-5) {
var prod = 1
for (i in c..c+3) prod = prod * grid[r][i]
if (prod > maxProd) {
maxProd = prod
for (n in 0..3) maxNums[n] = grid[r][c+n]
maxR1 = maxR2 = r
maxC1 = c
maxC2 = c + 3
}
}
}
// down
for (c in 0...w) {
for (r in 0..h-5) {
var prod = 1
for (i in r..r+3) prod = prod * grid[i][c]
if (prod > maxProd) {
maxProd = prod
for (n in 0..3) maxNums[n] = grid[r+n][c]
maxR1 = r
maxR2 = r + 3
maxC1 = maxC2 = c
}
}
}
System.print("The greatest product of four adjacent numbers in the same direction (down or right) in the grid is:")
Fmt.print(" $s = $,d", maxNums.map{ |n| n.toString }.join(" x "), maxProd)
System.write(" at indices (one based): ")
for (r in maxR1..maxR2) {
for (c in maxC1..maxC2) Fmt.write("($d, $d) ", r+1, c+1)
}
System.print()- Output:
The greatest product of four adjacent numbers in the same direction (down or right) in the grid is: 66 x 91 x 88 x 97 = 51,267,216 at indices (one based): (7, 16) (8, 16) (9, 16) (10, 16)
XPL0
int Grid, Max, Prod, I, J, K;
[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]];
Max:= 0;
for J:= 0 to 20-1 do
for I:= 0 to 20-4 do
[Prod:= 1;
for K:= 0 to 4-1 do
[Prod:= Prod * Grid(J,I+K);
if Prod > Max then Max:= Prod;
];
];
for J:= 0 to 20-4 do
for I:= 0 to 20-1 do
[Prod:= 1;
for K:= 0 to 4-1 do
[Prod:= Prod * Grid(J+K,I);
if Prod > Max then Max:= Prod;
];
];
IntOut(0, Max);
]- Output:
51267216