'''
Project Euler Problem #11

From the 20 x 20 grid, What is the greatest product of four adjacent numbers
in the same direction(up, down, left, right, or diagonally) in the 20x20 grid?
'''

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'

GRID_SIZE = 20

TEST_GRID = '01 02 03 04 \
01 02 03 04 \
01 02 03 04 \
01 02 03 04'

def gridToList(g):
    '''
    input: g, string
    output: input g divided into rows and columns
    '''
    sg = g.split()
    l = [sg[i*GRID_SIZE:(i+1)*GRID_SIZE] for i in range(GRID_SIZE)]
    return l

def getSubGrids(g, n):
    '''
    input: g, list of list of number strings
            n, int
    return list of starting points for n x ns from grid
    '''
    points = []
    for row in range(len(g) - n + 1):
        for col in range(len(g) - n + 1):
            points.append((row, col))
    
    grids = []
    for r,c in points:
        grid = [[g[r+rOffset][c+cOffset] for cOffset in range(n)] for rOffset in range(n)]
        grids.append(grid)
    return grids

def printGrid(g):
    print('--------')
    for r in g: print(r)
    print('--------')

def calculate(g):
    '''
    input: nxn grid
    returns max from list of multiplications of  vertical, horizontal, and diagonal
    '''
    #1 get horizontal sums
    import operator
    from functools import reduce
    sums = []
    l = len(g)
    
    for row in g:
        m = reduce(operator.mul, map(int, row))
        sums.append(m)
    #print(sums)

    #2 get vertical sums
    for i in range(l):
        m = reduce(operator.mul, map(int, [g[j][i] for j in range(l)]))
        sums.append(m)
    #print(sums)

    #3 get diagonal sum
    m = reduce(operator.mul, map(int, [g[i][i] for i in range(l)]))
    m = reduce(operator.mul, map(int, [g[i][l-i-1] for i in range(l)]))
    sums.append(m)
    #print(sums)
    return max(sums)

def test():
    l = gridToList(TEST_GRID)
    printGrid(l)

    subGrids = getSubGrids(l, 3)
    
    sums = []
    for grid in subGrids:
        printGrid(grid)
        sums.append(calculate(grid))
    print(max(sums))

if __name__=='__main__':
    # test()
    l = gridToList(GRID)
    printGrid(l)

    subGrids = getSubGrids(l, 4)
    print(len(subGrids))
    sums = []
    for grid in subGrids:
        printGrid(grid)
        sums.append(calculate(grid))
    print(max(sums))
