Dynamic Programming Problem

SumArray.java

/**
 * SumArray.  Given an input list of integers 'A' with length N,
 * calculate a NxN matrix 'B' such that the value of a cell B(i,j) is the 
 * sum of A(i)..A(j) forall i<=j.
 */
public class SumArray {

  public static void main(String[] args) {
    int[] a = new int[]{ 12, 3, 6, 2, 23, 44 };
    int[][] b = makeArray(a);
    System.out.println("--- INPUT ---");
    printRow(a);
    System.out.println("--- OUTPUT ---");
    for(int[] row : b) {
      printRow(row);
    }
  }

  static int[][] makeArray(int[] a) {
    int n = a.length;
    int[][] b = new int[n][n];

    for (int i = 0; i < n; i++) {
      for (int j = i; j < n; j++) {
        if (i == 0) {
          // If this is the first row, calculate the sum based on the
          // current into the input array (a[i]) and the aggregate sum
          // calculated so far (the previous cell in this column)
          b[i][j] = a[j] + (j > 0 ? b[i][j - 1] : 0);
        } else {
          // If this is not the first row, we can find the sum based
          // on the difference between the cell above us (previous
          // column) and the index value of the input array (a[i -
          // 1]).
          b[i][j] = b[i - 1][j] - a[i - 1];
        }
      }
    }
    return b;
  }

  static void printRow(int[] row) {
    for (int i : row) {
      System.out.print(i);
      System.out.print("\t");
    }
    System.out.println();
  }

}

--- INPUT ---
12	3	6	2	23	44	
--- OUTPUT ---
12	15	21	23	46	90	
0	3	9	11	34	78	
0	0	6	8	31	75	
0	0	0	2	25	69	
0	0	0	0	23	67	
0	0	0	0	0	44