EulerEighteen.java

// Error in Euler solution (they used a bottom up instead of a 
// top down, found this by hand evaluation bottom up using same
// algorithm backwards. 
// Top down solution: 1064
// 75->95->47->87->82->75->73->28->83->47->43->73->91->67->98
// Bottom up solution: 1074 (CORRECT SOLUTION - EULER PHRASED PROBLEM AS TOP DOWN AND WANTS OPTIMAL SOLUTION)
// Example of dynamic programming (bottom up) and the greedy algorithm (top down).

public class EulerEighteen
{
	public static void main(String[] args)
	{
		int sum = 75;
		int i = 0, j = 0;
		boolean cont = true;
		final int[][] list = {
                {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, 9,70,98,73,93,38,53,60,04,23}};
		
		while (cont == true)
		{
			sum += Math.max(list[i+1][j], list[i+1][j+1]);
			if (list[i+1][j+1] > list[i+1][j])
				j++;
			i++;
			if (i == 14)
				cont = false;
		}
		System.out.println(sum);
	}
}