Problem 18

Problem Statement :Problem18

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

Approach:

• For solving this we generate all possible paths from the top to the bottom.
• At every point we have 2 directions to search and we explore every possible path through recursion.
• when the path terminates we put the result in  a global list.
• Next after generation of all possible paths we find the maximum from the global list.

Solution:

import java.util.ArrayList;
import java.util.List;

public class problem18 {
 static List<Integer> l = new ArrayList<Integer>();
 static int M[][] = { { 75, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
   { 95, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
   { 17, 47, 82, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
   { 18, 35, 87, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
   { 20, 04, 82, 47, 65, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
   { 19, 01, 23, 75, 03, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
   { 88, 02, 77, 73, 07, 63, 67, 0, 0, 0, 0, 0, 0, 0, 0 },
   { 99, 65, 04, 28, 06, 16, 70, 92, 0, 0, 0, 0, 0, 0, 0 },
   { 41, 41, 26, 56, 83, 40, 80, 70, 33, 0, 0, 0, 0, 0, 0 },
   { 41, 48, 72, 33, 47, 32, 37, 16, 94, 29, 0, 0, 0, 0, 0 },
   { 53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14, 0, 0, 0, 0 },
   { 70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57, 0, 0, 0 },
   { 91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48, 0, 0 },
   { 63, 66, 04, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31, 0 },
   { 4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23 } },
   n = 15;

 public static void getSum(int csum, int x, int y) {
  if (x == n - 1) {
   csum = csum + M[x][y];
   l.add(csum);
   return;
  }
  csum = csum + M[x][y];
  int bsum, rsum, lsum;
  getSum(csum, x + 1, y);
  getSum(csum, x + 1, y + 1);
 }

 public static void main(String args[]) {
  long t1 = System.currentTimeMillis();
  getSum(0, 0, 0);
  int max = l.get(0);
  for (int i = 1; i < l.size(); i++) {
   if (l.get(i) >= max) {
    max = l.get(i);
   }
  }
  System.out.println(max);
  long t2 = System.currentTimeMillis();
  System.out.println("TIME: " + (t2 - t1) + " millisec");
 }
}