Day_11_2D_Arrays.md

Day 11: 2D Arrays

Problem

Objective

Today, we're building on our knowledge of Arrays by adding another dimension.

Context

Given a 6 X 6 2D Array, A:

1 1 1 0 0 0
0 1 0 0 0 0
1 1 1 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0

We define an hourglass in Ato be subset of values with indices falling in this pattern in A's graphical representation :

a b c
  d  
e f g

There are 16 hourglasses in A, and a hourglass sum is the sum of an hourglass' values.

Task

Calculate the hourglass sum for every hourglass in A, then print the maximum hourglass sum.

Input Format

There are 6 lines of input, where each line contains 6 space-seperated integers describing 2D Array A; every value in A will be in the inclusive range of -9 to 9.

Constraints

• -9 <= A[i][j] <= 9
• 0 <= i, j <= 5

Output Format

Print the largest (maximum) hourglass sum found in A.

Sample Input

1 1 1 0 0 0
0 1 0 0 0 0
1 1 1 0 0 0
0 0 2 4 4 0
0 0 0 2 0 0
0 0 1 2 4 0

Sample Output

19

Explanation

A contains the following hourglasses:

1 1 1   1 1 0   1 0 0   0 0 0
  1       0       0       0
1 1 1   1 1 0   1 0 0   0 0 0

0 1 0   1 0 0   0 0 0   0 0 0
  1       1       0       0
0 0 2   0 2 4   2 4 4   4 4 0

1 1 1   1 1 0   1 0 0   0 0 0
  0       2       4       4
0 0 0   0 0 2   0 2 0   2 0 0

0 0 2   0 2 4   2 4 4   4 4 0
  0       0       2       0
0 0 1   0 1 2   1 2 4   2 4 0

The hourglass with the maximum sum (19) is :

2 4 4
  2
1 2 4

Given code

import math
import os
import random
import re
import sys



if __name__ == '__main__':
    arr = []

    for _ in range(6):
        arr.append(list(map(int, input().rstrip().split())))

Solution 1

import math
import os
import random
import re
import sys



if __name__ == '__main__':
    arr = []

    for _ in range(6):
        arr.append(list(map(int, input().rstrip().split())))

        def maxsumofhourglasses(thearray):
            sums = []

    for x in range(len(thearray)-2):
        for y in range(len(thearray)-2):
            sums.append(sum([arr[x][y],
                             arr[x][y+1],
                             arr[x][y+2],
                             arr[x+1][y+1],
                             arr[x+2][y],
                             arr[x+2][y+1],
                             arr[x+2][y+2]]))

    return max(sums)


print(maxsumofhourglasses(arr))

Solution 2

import math
import os
import random
import re
import sys



if __name__ == '__main__':
    arr = []

    for _ in range(6):
        arr.append(list(map(int, input().rstrip().split())))

    sums = []

    for x in range(len(arr)-2):
        for y in range(len(arr)-2):
            sums.append(sum([arr[x][y], arr[x][y+1], arr[x][y+2], arr[x+1][y+1], arr[x+2][y], arr[x+2][y+1], arr[x+2][y+2]]))

    print(max(sums))

Solution 3

import math
import os
import random
import re
import sys



if __name__ == '__main__':
    arr = []

    for _ in range(6):
        arr.append(list(map(int, input().rstrip().split())))

    max_sum = None

    for i in range(len(arr)-2) :
        for n in range(len(arr)-2):
            lst = [arr[i][n], arr[i][n+1], arr[i][n+2], arr[i+1][n+1], arr[i+2][n], arr[i+2][n+1], arr[i+2][n+2]]
            if max_sum == None:
                max_sum = sum(lst)
            elif sum(lst) > max_sum:
                max_sum = sum(lst)
            else:
                continue

    print(max_sum)