Skip to content

Commit e0cac03

Browse files
rubendelblancorubendelblanco
authored
Project Euler Problem 11 (#113)
* feat:first approach to the problem * feat:add Project euler problem 11
1 parent bb8747a commit e0cac03

File tree

3 files changed

+160
-1
lines changed

3 files changed

+160
-1
lines changed

‎DIRECTORY.md

Lines changed: 1 addition & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -46,6 +46,7 @@
4646
* [Problem7](./Maths/ProjectEuler/Problem7.php)
4747
* [Problem8](./Maths/ProjectEuler/Problem8.php)
4848
* [Problem9](./Maths/ProjectEuler/Problem9.php)
49+
* [Problem11](./Maths/ProjectEuler/Problem11.php)
4950

5051
## Searches
5152
* [Binarysearch](./Searches/BinarySearch.php)

‎Maths/ProjectEuler/Problem11.php

Lines changed: 153 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,153 @@
1+
<?php
2+
3+
4+
/*
5+
* This function solves the problem 11 of the Project Euler.
6+
*
7+
* Problem description:
8+
* In the 20×20 grid below, four numbers along a diagonal line have been marked in red.
9+
10+
08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
11+
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
12+
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
13+
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
14+
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
15+
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
16+
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
17+
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
18+
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
19+
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
20+
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
21+
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
22+
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
23+
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
24+
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
25+
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
26+
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
27+
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
28+
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
29+
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
30+
31+
The product of these numbers is 26 × 63 × 78 × 14 = 1788696.
32+
33+
What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?
34+
35+
Solution: 70600674
36+
*/
37+
38+
39+
function horizontalProduct($grid, $row, $col)
40+
{
41+
$product = 1;
42+
for ($i = 0; $i < 4; $i++) {
43+
$product *= $grid[$row][$col + $i];
44+
}
45+
return $product;
46+
}
47+
48+
function verticalProduct($grid, $row, $col)
49+
{
50+
$product = 1;
51+
for ($i = 0; $i < 4; $i++) {
52+
$product *= $grid[$row + $i][$col];
53+
}
54+
return $product;
55+
}
56+
57+
function diagonalRightProduct($grid, $row, $col)
58+
{
59+
$product = 1;
60+
for ($i = 0; $i < 4; $i++) {
61+
$product *= $grid[$row + $i][$col + $i];
62+
}
63+
return $product;
64+
}
65+
66+
function diagonalLeftProduct($grid, $row, $col)
67+
{
68+
$product = 1;
69+
for ($i = 0; $i < 4; $i++) {
70+
$product *= $grid[$row + $i][$col - $i];
71+
}
72+
return $product;
73+
}
74+
75+
function problem11()
76+
{
77+
$grid = "08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
78+
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
79+
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
80+
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
81+
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
82+
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
83+
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
84+
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
85+
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
86+
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
87+
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
88+
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
89+
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
90+
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
91+
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
92+
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
93+
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
94+
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
95+
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
96+
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48";
97+
98+
//Transform the grid string to a matrix data type (nested arrays)
99+
$grid = explode(' ', $grid);
100+
$grid_matrix = [];
101+
$row = [];
102+
$i = 0;
103+
$matrix_size = 20;
104+
105+
//Convert string $grid to a matrix
106+
foreach ($grid as $g) {
107+
$i++;
108+
$row[] = (int)trim($g);
109+
110+
if ($i == $matrix_size) {
111+
$grid_matrix[] = $row;
112+
$row = [];
113+
$i = 0;
114+
}
115+
}
116+
$maxProduct = 0;
117+
118+
for ($row = 0; $row < $matrix_size; $row++) {
119+
for ($col = 0; $col < $matrix_size; $col++) {
120+
// horizontal
121+
if ($col < $matrix_size - 3) {
122+
$product = horizontalProduct($grid_matrix, $row, $col);
123+
if ($product > $maxProduct) {
124+
$maxProduct = $product;
125+
}
126+
}
127+
// vertical
128+
if ($row < $matrix_size - 3) {
129+
$product = verticalProduct($grid_matrix, $row, $col);
130+
if ($product > $maxProduct) {
131+
$maxProduct = $product;
132+
}
133+
}
134+
// diagonal right
135+
if ($col < $matrix_size - 3 && $row < $matrix_size - 3) {
136+
$product = diagonalRightProduct($grid_matrix, $row, $col);
137+
if ($product > $maxProduct) {
138+
$maxProduct = $product;
139+
}
140+
}
141+
// diagonal left
142+
if ($col > 2 && $row < $matrix_size - 3) {
143+
$product = diagonalLeftProduct($grid_matrix, $row, $col);
144+
if ($product > $maxProduct) {
145+
$maxProduct = $product;
146+
}
147+
}
148+
}
149+
}
150+
151+
return $maxProduct;
152+
}
153+

‎tests/Maths/ProjectEulerTest.php

Lines changed: 6 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -13,6 +13,7 @@
1313
require_once __DIR__ . '/../../Maths/ProjectEuler/Problem8.php';
1414
require_once __DIR__ . '/../../Maths/ProjectEuler/Problem9.php';
1515
require_once __DIR__ . '/../../Maths/ProjectEuler/Problem10.php';
16+
require_once __DIR__ . '/../../Maths/ProjectEuler/Problem11.php';
1617

1718
class ProjectEulerTest extends TestCase
1819
{
@@ -61,10 +62,14 @@ public function testProblem9(): void
6162
{
6263
$this->assertSame(31875000, problem9());
6364
}
64-
65+
6566
public function testProblem10(): void
6667
{
6768
$this->assertSame(142913828922, problem10());
6869
}
6970

71+
public function testProblem11(): void
72+
{
73+
$this->assertSame(70600674, problem11());
74+
}
7075
}

0 commit comments

Comments
 (0)