/* 
 * Solution to Project Euler problem 18
 * Copyright (c) Project Nayuki. All rights reserved.
 * 
 * https://www.nayuki.io/page/project-euler-solutions
 * https://github.com/nayuki/Project-Euler-solutions
 */


public final class p018 implements EulerSolution {
	
	public static void main(String[] args) {
		System.out.println(new p018().run());
	}
	
	
	/* 
	 * We create a new blank triangle with the same dimensions as the original big triangle.
	 * For each cell of the big triangle, we consider the sub-triangle whose top is at this cell,
	 * calculate the maximum path sum when starting from this cell, and store the result
	 * in the corresponding cell of the blank triangle.
	 * 
	 * If we start at a particular cell, what is the maximum path total? If the cell is at the
	 * bottom of the big triangle, then it is simply the cell's value. Otherwise the answer is
	 * the cell's value plus either {the maximum path total of the cell down and to the left}
	 * or {the maximum path total of the cell down and to the right}, whichever is greater.
	 * By computing the blank triangle's values from bottom up, the dependent values are always
	 * computed before they are utilized. This technique is known as dynamic programming.
	 */
	
	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},
	};
	
}