Project Euler | Problem 11 | Largest product in a grid

Problem Description:

In the 20×20 grid below, four numbers along a diagonal line have been marked in red.

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

The product of these numbers is 26 × 63 × 78 × 14 = 1788696.

What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?

Figure1

Concept:

Store 20 X 20 grid in two-dimensional array and consider following 8 cases to solve this problem.

1. When i <  3 && j < 3 - Get product of four adjacent numbers in right, bottom and bottom right diagonal side.
2. When i <  3 && (j  >= 3 && j < 17) -  Get product of four adjacent numbers in right, left, bottom, bottom right diagonal and bottom left diagonal side.
3. When i < 3 && j >= 17  - Get product of four adjacent numbers in left, bottom and bottom left diagonal side.
4. When (i >= 3 && i < 17) && j < 3 - Get product of four adjacent numbers in right, bottom, up, bottom right diagonal and up right diagonal side.
5. When i >= 17 && j < 3 - Get product of four adjacent numbers in right, up, up right diagonal side.
6. When (i >= 3 && i < 17) && (j >= 3 && j < 17) - Get product of four adjacent numbers in right, left, bottom, up, bottom right diagonal, bottom left diagonal, up right diagonal and up left diagonal side.
7. When i >= 17 && (j >= 3 && j < 17) - Get product of four adjacent numbers in right, left, up, up right diagonal and up left diagonal side.
8. When i >= 17 && j >= 17 -  Get product of four adjacent numbers in left, up and up left diagonal side.

Now w.r.t each case we need to find greatest product in particular direction and finally we will get greatest product of four adjacent numbers in same direction (up, down, left, right, or diagonally) in the 20 X 20 grid.

Java Program :

Output:

Figure2

References:

https://projecteuler.net/problem=11
https://docs.oracle.com/javase/7/docs/api/java/util/Collections.html#sort(java.util.List)

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