Project Euler Problem 18 and 67: Maximum path sum

Problem

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

Solution

Once again, don't use recursive prematurely!

This one requires working from bottom to top.

 private static final int ROW = 15;  
      private static final int[][] M = new int[ROW][ROW];  
      public static void main(String[] args) {  
           readFile();  
           for (int i=ROW-2; i >= 0; i--){  
                for (int j=0; j <= i; j++){  
                     M[i][j] = Math.max(M[i+1][j], M[i+1][j+1]) + M[i][j];  
                }  
           }  
           System.out.println(M[0][0]);       
      }  
      private static void readFile() {  
           File file = new File("Q18.txt");  
           try {  
                Scanner sc = new Scanner(file);  
                int i = 0;  
                while (sc.hasNextLine()) {  
                     int j = 0;  
                     Scanner lineSc = new Scanner(sc.nextLine());  
                     while (lineSc.hasNextInt()){  
                          M[i][j++]=lineSc.nextInt();       
                     }  
                     i++;  
                }  
                sc.close();  
           } catch (FileNotFoundException e) {  
                e.printStackTrace();  
           }  
      }