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Author: Manasi2001

Arrays/Hourglass_Sum.py

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+'''
+Given a 6X6 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, and an hourglass sum is the sum of an hourglass' 
+values. Like here, the maximum hourglass sum is 7 for the hourglass in the top 
+left corner.
+
+Aim: Check all such hourglasses and print the maximum hourglass sum for the 
+2D array entered by user.
+
+'''
+
+# getting the 2D array as input
+arr = []
+for _ in range(6):
+    arr.append(list(map(int, input().rstrip().split())))
+
+res = []
+# looping through the 2D array
+for x in range(0, 4):
+    for y in range(0, 4):
+        # selecting combinations that make an hourglass
+        s = sum(arr[x][y:y+3]) + arr[x+1][y+1] + sum(arr[x+2][y:y+3])
+        res.append(s)
+# printing out the maximum hourglass sum        
+print(max(res))
+
+'''
+
+COMPLEXITY:
+	
+	 Time Complexity -> O(N^2)
+	 Space Complexity -> O(N)
+     
+Sample Input:
+0 0 1 2 3 0
+0 0 0 5 0 0
+1 0 0 7 1 0
+0 0 0 0 0 0
+0 1 1 1 0 1
+0 0 4 0 0 4
+
+Sample Output:
+19
+
+Explanation:
+The hourglass with the maximum sum is,
+1 2 3
+  5 
+0 7 1
+with the sum being 1 + 2 + 3 + 5 + 0 + 7 + 1 = 19
+    
+'''