I approached this from the way I expect someone with a great deal of experience designing complex enterprise-grade systems. It is modular in design and allows for changes in the business needs. The actual "shape" is isolated so that this system can be used to detect other similar problems with different parameters.
Given a 2D Array, :
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 to be a subset of values with indices falling in this pattern in 's graphical representation:
a b c
d
e f g
There are hourglasses in , and an hourglass sum is the sum of an hourglass' values. Calculate the hourglass sum for every hourglass in , then print the maximum hourglass sum.
For example, given the 2D array:
-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
We calculate the following hourglass values:
-63, -34, -9, 12,
-10, 0, 28, 23,
-27, -11, -2, 10,
9, 17, 25, 18
Our highest hourglass value is from the hourglass:
0 4 3
1
8 6 6
Note: If you have already solved the Java domain's Java 2D Array challenge, you may wish to skip this challenge.
Function Description
Complete the function hourglassSum in the editor below. It should return an integer, the maximum hourglass sum in the array.
hourglassSum has the following parameter(s):
arr: an array of integers Input Format
Each of the lines of inputs contains space-separated integers .
Constraints
Output Format
Print the largest (maximum) hourglass sum found in .
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 () is:
2 4 4
2
1 2 4