A note to any readers : This will be the last post for a month.
In the 2020 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 2020 grid?
The solution to this problem is quite interesting because it demonstrates the use of a macro. A macro is a construct available within as which permits the same sort of abstraction as a procedure|subroutine|function would in a high-level language.
Inside the macro, the parameter a is accessed via \a and the construct \@ expands out to a unique value each time the macro is invoked; this allows the use in labels which are distinct for each macro invocation.
.syntax unified .align 2 .section .rodata buffer: .byte 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 .byte 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 .byte 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 .byte 0, 0, 0, 8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8, 0, 0, 0 .byte 0, 0, 0, 49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0, 0, 0, 0 .byte 0, 0, 0, 81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65, 0, 0, 0 .byte 0, 0, 0, 52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91, 0, 0, 0 .byte 0, 0, 0, 22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80, 0, 0, 0 .byte 0, 0, 0, 24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50, 0, 0, 0 .byte 0, 0, 0, 32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70, 0, 0, 0 .byte 0, 0, 0, 67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21, 0, 0, 0 .byte 0, 0, 0, 24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72, 0, 0, 0 .byte 0, 0, 0, 21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95, 0, 0, 0 .byte 0, 0, 0, 78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92, 0, 0, 0 .byte 0, 0, 0, 16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57, 0, 0, 0 .byte 0, 0, 0, 86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58, 0, 0, 0 .byte 0, 0, 0, 19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40, 0, 0, 0 .byte 0, 0, 0, 4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66, 0, 0, 0 .byte 0, 0, 0, 88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69, 0, 0, 0 .byte 0, 0, 0, 4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36, 0, 0, 0 .byte 0, 0, 0, 20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16, 0, 0, 0 .byte 0, 0, 0, 20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54, 0, 0, 0 .byte 0, 0, 0, 1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48, 0, 0, 0 .byte 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 .byte 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 .byte 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 resstring: .asciz "%d\n" .equ ocolumns, 26 .equ icolumns, 20 .equ colstart, 23 .equ border, 3 .equ offset, 2 .equ points, 4 .equ north, -ocolumns .equ north_east, -ocolumns+1 .equ east, 1 .equ south_east, ocolumns+1 .equ south, ocolumns .equ south_west, ocolumns - 1 .equ west, -1 .equ north_west, -ocolumns-1 .equ point_set, 1 tmp .req r2 pointv .req r3 data_ptr .req r4 icount .req r5 jcount .req r6 kcount .req r7 maxv .req r8 dpstore .req r9 .macro direction a mov data_ptr, dpstore mov kcount, points mov pointv, point_set kloop\@: ldrb tmp, [data_ptr], \a mul pointv, pointv, tmp subs kcount, kcount, 1 bne kloop\@ cmp maxv, pointv movlt maxv, pointv @ set maxv to max of maxv and pointv .endm .text .align 2 .global main .type main, %function main: stmfd sp!, {r4-r9, lr} mov icount, icolumns iloop: mov jcount, icolumns jloop: mov tmp, ocolumns add data_ptr, icount, offset mul tmp, tmp, data_ptr add tmp, tmp, jcount add tmp, tmp, offset ldr data_ptr, =buffer add dpstore, data_ptr, tmp @ data[i][j] direction north direction north_east direction east direction south_east direction south direction south_west direction west direction north_west subs jcount, jcount, 1 bne jloop subs icount, icount, 1 bne iloop printme: mov r1, maxv ldr r0, =resstring @ store address of start of string to r0 bl printf mov r0, 0 ldmfd sp!, {r4-r9, pc} mov r7, 1 @ set r7 to 1 - the syscall for exit swi 0 @ then invoke the syscall from linux
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