problem18.go

// Copyright 2015 Peter Mrekaj. All rights reserved.
// Use of this source code is governed by a MIT-style
// license that can be found in the LICENSE.txt file.

package euler

// Problem18 is solution for finding the maximum
// total from top to bottom of the triangle.
func Problem18() int {
	triangle := [][]int{
		{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},
	}

	// Next solution is based on dynamic programming.
	for x := len(triangle) - 1; x > 0; x-- {
		for y := 0; y < len(triangle[x])-1; y++ {
			triangle[x-1][y] += Max(triangle[x][y], triangle[x][y+1])
		}
	}
	return int(triangle[0][0])
}