problem011.py

# First let's store the grid somewhere
gridStr = """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
""".replace('\n',' ')

print(gridStr)

gridList = gridStr.split()
print("confirm total elements:",len(gridList))

# create a 20 x 20 array
grid = [[0 for _ in range(20)] for _ in range(20)]
#print(grid)

# replace grid with our numbers
for i in range(20):
    for j in range(20):
        grid[i][j] = int(gridList[i*20+j])


# a debug print out to highlight a particular number
def highlightGrid(x,y):
    for i in range(20):
        for j in range(20):
            if (x,y) == (i,j):
                print(f"*{grid[i][j]:2}*",end='')
            else:
                print(f" {grid[i][j]:2} ",end='')
        print()


print(grid)

def checkUp(i,j):
    # must have at least 3 more rows above it
    # rows 0,1,2 not eligible
    if i <= 2:
        return -1

    return grid[i][j] * grid[i-1][j] * grid[i-2][j] * grid[i-3][j] 

def checkDown(i,j):
    # must have at least 3 more rows below it
    if i >= 17:
        return -1

    return grid[i][j] * grid[i+1][j] * grid[i+2][j] * grid[i+3][j] 


def checkLeft(i,j):
    # must have at least 3 more columns to the left
    # cols 0,1,2 not eligible
    if j <= 2:
        return -1

    return grid[i][j] * grid[i][j-1] * grid[i][j-2] * grid[i][j-3] 


def checkRight(i,j):
    # must have at least 3 more columns to the right
    if j >= 17:
        return -1

    return grid[i][j] * grid[i][j+1] * grid[i][j+2] * grid[i][j+3] 

def checkUpLeft(i,j):
    if i <= 2 or j <= 2:
        return -1
    return grid[i][j] * grid[i-1][j-1] * grid[i-2][j-2] * grid[i-3][j-3]

def checkUpRight(i,j):
    if i <= 2 or j >= 17:
        return -1
    return grid[i][j] * grid[i-1][j+1] * grid[i-2][j+2] * grid[i-3][j+3]

def checkDownLeft(i,j):
    if i >= 17 or j <= 2:
        return -1
    return grid[i][j] * grid[i+1][j-1] * grid[i+2][j-2] * grid[i+3][j-3]

def checkDownRight(i,j):
    if i >= 17 or j >= 17:
        return -1
    return grid[i][j] * grid[i+1][j+1] * grid[i+2][j+2] * grid[i+3][j+3]



largest = 0
I = 0
J = 0
direction = ''

def updateLargest(L, directionStr, i, j):
    global largest, I, J, direction
    if L > largest:
        largest = L
        direction = directionStr
        I = i
        J = j

        print(f"largest found at {grid[i][j]} loc (i,j)=({i},{j}) direction {directionStr}: {largest}")


checks = [
        (checkUp, "up"),
        (checkDown, "down"),
        (checkLeft, "left"),
        (checkRight, "right"),
        (checkUpLeft, "up left"),
        (checkUpRight, "up right"),
        (checkDownLeft, "down left"),
        (checkDownRight, "down right")
        ]


# Method 1: check all 8 directions
print("--- Method 1: check all 8 directions ---")
for i in range(20):
    for j in range(20):
        for func, name in checks:
            updateLargest(func(i,j), name, i, j)

highlightGrid(I,J)
print(f"Largest product is {largest} found at grid[{I},{J}]={grid[I][J]} in direction {direction}")


# Method 2: use 4 directional vectors

print("--- Method 2: check 4 vectors ---")
# reset globals

largest = 0
I = 0
J = 0
direction = ''

vectors = [
        ("right", 0, 1),
        ("down", 1, 0),
        ("down right", 1, 1),
        ("up right", -1, 1)
        ]

# define what "out of bounds" mean
def outOfBounds(i,j):
    return i <= 2 or i >= 17 or j <= 2 or j >= 17


for i in range(20):
    for j in range(20):
        for name, dx, dy in vectors:
            if not outOfBounds(i+dx, j+dy):
                product = grid[i][j] * grid[i+dx][j+dy] * grid[i+2*dx][j+2*dy] * grid[i+3*dx][j+3*dy]
                updateLargest(product,name,i,j)

highlightGrid(I,J)
print(f"Largest product is {largest} found at grid[{I},{J}]={grid[I][J]} in direction {direction}")