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Project Euler Problem 11

on project euler, erlang, python

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?

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
Link to original description
Source code examples on Github

Erlang version

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#!/usr/bin/env escript
%% -*- erlang -*-
%%! -smp enable -sname p9
% vim:syn=erlang

-mode(compile).

main(_) ->
    L = [
           [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]],
    io:format("Answer: ~p ~n", [c(L)]).

c(L) -> lists:max(lists:flatten([ prod(X,Y,L) || X <- lists:seq(1,20), Y <- lists:seq(1,20)])).

grid_ele(X,Y,L) -> lists:nth(X,(lists:nth(Y,L))).

prod(X,Y,_) when X > 17, Y > 17          -> [0];
prod(X,Y,L) when Y > 16, X =< 17         -> [f(X,Y,L)];
prod(X,Y,L) when X =< 3, Y < 17, X =< 17 -> [f(X,Y,L), d(X,Y,L), d_r(X,Y,L)];
prod(X,Y,L) when X > 3, X =< 17, Y =< 17 -> [f(X,Y,L), d(X,Y,L), d_r(X,Y,L), d_l(X,Y,L)];
prod(X,Y,L) when X > 17, Y < 17          -> [d(X,Y,L), d_l(X,Y,L)];
prod(X,Y,L) when Y >= 17, X > 17         -> [d_l(X,Y,L)].

f(X,Y,L)   -> grid_ele(X,Y,L) * grid_ele(X+1,Y,L) * grid_ele(X+2,Y,L) * grid_ele(X+3,Y,L).
d(X,Y,L)   -> grid_ele(X,Y,L) * grid_ele(X,Y+1,L) * grid_ele(X,Y+2,L) * grid_ele(X,Y+3,L).
d_r(X,Y,L) -> grid_ele(X,Y,L) * grid_ele(X+1,Y+1,L) * grid_ele(X+2,Y+2,L) * grid_ele(X+3,Y+3,L).
d_l(X,Y,L) -> grid_ele(X,Y,L) * grid_ele(X-1,Y+1,L) * grid_ele(X-2,Y+2,L) * grid_ele(X-3,Y+3,L).

Python version

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#!/usr/bin/python

def seqs(nums, row, col):
    if row + 4 <= len(nums):                                yield list(nums[i][col] for i in xrange(row, row+4))
    if col + 4 <= len(nums[row]):                           yield list(nums[row][i] for i in xrange(col, col+4))
    if row + 4 <= len(nums) and col + 4 <= len(nums[row]):  yield list(nums[row+i][col+i] for i in xrange(0,4))
    if row + 4 <= len(nums) and col >= 3:                   yield list(nums[row+i][col-i] for i in xrange(0,4))

def product(seq):
    n = 1
    for x in seq: n = n * x
    return n

def list_seqs(nums):
    for row in xrange(0, len(nums)):
        for col in xrange(0, len(nums[row])):
            for seq in seqs(nums, row, col):
                yield seq

nums = (
     ( 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)
)

print "Answer:" + str(max(product(seq) for seq in list_seqs(nums)))