Project Euler: Problem 11 – Largest product in a grid

Problem 11:

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 x 63 x 78 x 14 = 1788696.

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

Idea:

At first, the problem seemed daunting for all the directions they wanted to find the maximum product. However, finding the product upwards is the same as downwards, as is left and right; diagonally requires two directions even though only one is listed.

Finding the maximum product of any 4 adjacent numbers horizontally or vertically is relatively trivial as only one index is being modified. Finding the diagonals is only slightly more complicated in that both indices are being modified, but the modification is the same for both. The hardest part is making sure you stay within the appropriate array boundaries.

```long answer = -1;
int[] numbers = new int[4];

int ROWS = 20;
int COLS = 20;

int[][] grid = problem11grid();  //recreates the grid above

//vertical
for(int i = 0; i < ROWS-4; i++) {
for(int j = 0; j < COLS; j++) {
long tmp = grid[i][j]* grid[i+1][j]* grid[i+2][j]* grid [i+3][j];
numbers[0] = grid[i][j];
numbers[1] = grid[i+1][j];
numbers[2] = grid[i+2][j];
numbers[3] = grid[i+3][j];
}
}
}

//horizontal
for(int i = 0; i < ROWS; i++) {
for(int j = 0; j < COLS-4; j++) {
long tmp = grid[i][j]* grid[i][j+1]* grid[i][j+2]* grid [i][j+3];
numbers[0] = grid[i][j];
numbers[1] = grid[i][j+1];
numbers[2] = grid[i][j+2];
numbers[3] = grid[i][j+3];
}
}
}

//diagonal right
for(int i = 0; i < ROWS-4; i++) {
for(int j = 0; j < COLS-4; j++) {
long tmp = grid[i][j]* grid[i+1][j+1]* grid[i+2][j+2]* grid [i+3][j+3];
numbers[0] = grid[i][j];
numbers[1] = grid[i+1][j+1];
numbers[2] = grid[i+2][j+2];
numbers[3] = grid[i+3][j+3];
}
}
}

//diagonal left
for(int i = 3; i < ROWS; i++) {
for(int j = 0; j < COLS-4; j++) {
long tmp = grid[i][j]* grid[i-1][j+1]* grid[i-2][j+2]* grid [i-3][j+3];
numbers[0] = grid[i][j];
numbers[1] = grid[i-1][j+1];
numbers[2] = grid[i-2][j+2];
numbers[3] = grid[i-3][j+3];
}
}
}
The text passage describes a mathematical problem from Project Euler, specifically Problem 11, which involves finding the greatest product of four adjacent numbers in a 20x20 grid in any direction (up, down, left, right, or diagonally). The passage provides the grid and a sample calculation but does not provide the final answer to the problem.
single_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Project Euler: Problem 11 – Largest product in a grid

Problem 11:

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 x 63 x 78 x 14 = 1788696.

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

Idea:

At first, the problem seemed daunting for all the directions they wanted to find the maximum product. However, finding the product upwards is the same as downwards, as is left and right; diagonally requires two directions even though only one is listed.

Finding the maximum product of any 4 adjacent numbers horizontally or vertically is relatively trivial as only one index is being modified. Finding the diagonals is only slightly more complicated in that both indices are being modified, but the modification is the same for both. The hardest part is making sure you stay within the appropriate array boundaries.

```long answer = -1;
int[] numbers = new int[4];

int ROWS = 20;
int COLS = 20;

int[][] grid = problem11grid();  //recreates the grid above

//vertical
for(int i = 0; i < ROWS-4; i++) {
for(int j = 0; j < COLS; j++) {
long tmp = grid[i][j]* grid[i+1][j]* grid[i+2][j]* grid [i+3][j];
numbers[0] = grid[i][j];
numbers[1] = grid[i+1][j];
numbers[2] = grid[i+2][j];
numbers[3] = grid[i+3][j];
}
}
}

//horizontal
for(int i = 0; i < ROWS; i++) {
for(int j = 0; j < COLS-4; j++) {
long tmp = grid[i][j]* grid[i][j+1]* grid[i][j+2]* grid [i][j+3];
numbers[0] = grid[i][j];
numbers[1] = grid[i][j+1];
numbers[2] = grid[i][j+2];
numbers[3] = grid[i][j+3];
}
}
}

//diagonal right
for(int i = 0; i < ROWS-4; i++) {
for(int j = 0; j < COLS-4; j++) {
long tmp = grid[i][j]* grid[i+1][j+1]* grid[i+2][j+2]* grid [i+3][j+3];
numbers[0] = grid[i][j];
numbers[1] = grid[i+1][j+1];
numbers[2] = grid[i+2][j+2];
numbers[3] = grid[i+3][j+3];
}
}
}

//diagonal left
for(int i = 3; i < ROWS; i++) {
for(int j = 0; j < COLS-4; j++) {
long tmp = grid[i][j]* grid[i-1][j+1]* grid[i-2][j+2]* grid [i-3][j+3];
numbers[0] = grid[i][j];
numbers[1] = grid[i-1][j+1];
numbers[2] = grid[i-2][j+2];
numbers[3] = grid[i-3][j+3];
}
}
}
user
The text passage describes a mathematical problem from Project Euler, specifically Problem 11, which involves finding the greatest product of four adjacent numbers in a 20x20 grid in any direction (up, down, left, right, or diagonally). The passage provides the grid and a sample calculation but does not provide the final answer to the problem.

TYPE: SINGLE_QUESTION