Largest product in a grid
2014-09-11
Problem 011: Largest product in a grid
In the 20×20 grid below, four numbers along a diagonal line have been marked in red.
...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?
Solution:
v v <
>"4"2/:*1-00p > 000g: "4"2/ %"?"+\ "4"2/ /1+ p 00g:1-00p #^_v++++++++++++++++++++++++++
++++++++++++++++++++++++++
++++++++++++++++++++++++++
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 | +++####################+++
vp00-1*:*45 p1++1550p0++1551p1+55-10p0+551p19-10p090 p010<++++++++++++++++++++++++++ >10pv
>00g:54*%3*1+\54*/4+g"0"-52**00g:54*%3*2+\54*/4+g"0"-+00g:54*%v++++++++++++++++++++++++++ >$> v
| p00-1:g00p+4/*45\+"B"<++++++++++++++++++++++++++ ^_^#`g01:< v <
>54*:*1-00p>220p>20g9+:0g30p1g40p00g:54*%50p54*/60p50g"B"+60g4+g50g30g+50p60g40g+60p>50g"B"+60g4+g50g30g+50p60g40g+60pv >20g:1-20p#v_00g:1-00p#^_10g. @
^ _^# <vp06+g04g06p05+g03g05g+4g06+"B"g05<^ < v 0<
>50g"B"+60g4+g50g30g+50p60g40g+60p***^
^ <<
>"4"2/:*1-00p > 000g: "4"2/ %"?"+\ "4"2/ /1+ p 00g:1-00p #^_v++++++++++++++++++++++++++
++++++++++++++++++++++++++
++++++++++++++++++++++++++
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 | +++####################+++
vp00-1*:*45 p1++1550p0++1551p1+55-10p0+551p19-10p090 p010<++++++++++++++++++++++++++ >10pv
>00g:54*%3*1+\54*/4+g"0"-52**00g:54*%3*2+\54*/4+g"0"-+00g:54*%v++++++++++++++++++++++++++ >$> v
| p00-1:g00p+4/*45\+"B"<++++++++++++++++++++++++++ ^_^#`g01:< v <
>54*:*1-00p>220p>20g9+:0g30p1g40p00g:54*%50p54*/60p50g"B"+60g4+g50g30g+50p60g40g+60p>50g"B"+60g4+g50g30g+50p60g40g+60pv >20g:1-20p#v_00g:1-00p#^_10g. @
^ _^# <vp06+g04g06p05+g03g05g+4g06+"B"g05<^ < v 0<
>50g"B"+60g4+g50g30g+50p60g40g+60p***^
^ <<
Start
??
Pause
Reset
Output:
Stack: (0)
Explanation:
The idea here was to first move the numbers into a real 20x20 grid where every field represents a single number, the rest was just brute-forcing all possible products and outputting the biggest.
| Interpreter steps: | 323 945 |
| Execution time (BefunExec): | 78ms (4.15 MHz) |
| Program size: | 151 x 31 |
| Solution: | 70600674 |
| Solved at: | 2014-09-11 |