2D Arrays - Hourglass-Problem

This problem involves using and navigating a 2-dimenstional array.

Learning Goals

By the end of this exercise we will be able to...

• Write code accessing elements in a 2D array
• Write code using loops to iterate through a 2D array

Problem Description

Given a 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

An hourglass in A is a 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. An hourglass sum is the sum of an hourglass' values. Calculate the hourglass sum for every hourglass in A, then print the maximum hourglass sum. The array will always be a 6 x 6 array.

Example

-9 -9 -9  1 1 1 
 0 -9  0  4 3 2
-9 -9 -9  1 2 3
 0  0  8  6 6 0
 0  0  0 -2 0 0
 0  0  1  2 4 0

The hourglass sums are:

-63, -34, -9, 12, 
-10,   0, 28, 23, 
-27, -11, -2, 10, 
  9,  17, 25, 18

The highest hourglass sum is 28 from the hourglass beginning at row 1, column 2:

0 4 3
  1
8 6 6

Method Description

Complete the hourglass_sum method.

hourglass_sum has the following parameter(s):

matrix: an array of integers

Returns

An Integer the maximum hourglass sum

Example

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

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

This problem was originally found on HackerRank.