Solution to Project Euler Problem 18: Maximum path sum I - By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. 3 7 4 2 4 6 8 5 9 3 That is, 3 + 7 + 4 + 9 = 23. Find the maximum total from top to bottom of the triangle below:
Updated: Sept. 25, 2023 — Training Time: 4 minutes
Overseen by: Archangel Macsika
Difficulty: Easy.
Objective: By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.
3
7 4
2 4 6
8 5 9 3
That is, 3 + 7 + 4 + 9 = 23.
Find the maximum total from top to bottom of the triangle below: 75
95 64
17 47 82
18 35 87 10
20 04 82 47 65
19 01 23 75 03 34
88 02 77 73 07 63 67
99 65 04 28 06 16 70 92
41 41 26 56 83 40 80 70 33
41 48 72 33 47 32 37 16 94 29
53 71 44 65 25 43 91 52 97 51 14
70 11 33 28 77 73 17 78 39 68 17 57
91 71 52 38 17 14 91 43 58 50 27 29 48
63 66 04 68 89 53 67 30 73 16 69 87 40 31
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23
NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)
Input: None.
Expected Output: 1074.
Sikademy Solution in Java Programming Language
package sikademy;
/**
*
* @author Archangel Macsika
* Copyright (c) Sikademy. All rights reserved
*/
public class SikademyEulerSolution {
public String run() {
for (int i = triangle.length - 2; i >= 0; i--) {
for (int j = 0; j < triangle[i].length; j++)
triangle[i][j] += Math.max(triangle[i + 1][j], triangle[i + 1][j + 1]);
}
return Integer.toString(triangle[0][0]);
}
private int[][] triangle = { // Mutable
{75},
{95,64},
{17,47,82},
{18,35,87,10},
{20, 4,82,47,65},
{19, 1,23,75, 3,34},
{88, 2,77,73, 7,63,67},
{99,65, 4,28, 6,16,70,92},
{41,41,26,56,83,40,80,70,33},
{41,48,72,33,47,32,37,16,94,29},
{53,71,44,65,25,43,91,52,97,51,14},
{70,11,33,28,77,73,17,78,39,68,17,57},
{91,71,52,38,17,14,91,43,58,50,27,29,48},
{63,66, 4,68,89,53,67,30,73,16,69,87,40,31},
{ 4,62,98,27,23, 9,70,98,73,93,38,53,60, 4,23},
};
public static void main(String[] args) {
SikademyEulerSolution solution = new SikademyEulerSolution();
System.out.println(solution.run());
}
}
Sikademy Solution in Python Programming Language
#
# @author Archangel Macsika
# Copyright (c) Sikademy. All rights reserved.
#
def compute():
for i in reversed(range(len(triangle) - 1)):
for j in range(len(triangle[i])):
triangle[i][j] += max(triangle[i + 1][j], triangle[i + 1][j + 1])
return str(triangle[0][0])
triangle = [ # Mutable
[75],
[95,64],
[17,47,82],
[18,35,87,10],
[20, 4,82,47,65],
[19, 1,23,75, 3,34],
[88, 2,77,73, 7,63,67],
[99,65, 4,28, 6,16,70,92],
[41,41,26,56,83,40,80,70,33],
[41,48,72,33,47,32,37,16,94,29],
[53,71,44,65,25,43,91,52,97,51,14],
[70,11,33,28,77,73,17,78,39,68,17,57],
[91,71,52,38,17,14,91,43,58,50,27,29,48],
[63,66, 4,68,89,53,67,30,73,16,69,87,40,31],
[ 4,62,98,27,23, 9,70,98,73,93,38,53,60, 4,23],
]
if __name__ == "__main__":
print(compute())