Generate 10-digit number using a phone keypad

Question

Given a phone keypad as shown below:

1 2 3
4 5 6
7 8 9
  0

How many different 10-digit numbers can be formed starting from 1? The constrain

Answer 1

//Both the iterative and recursive with memorize shows count as 1424 for 10 digit numbers starting with 1. 
int[][] b = {{4,6},{6,8},{7,9},{4,8},{0,3,9},{},{1,7,0},{2,6},{1,3},{2,4}};
public int countIterative(int digit, int length) {
    int[][] matrix = new int[length][10];
    for(int dig =0; dig <=9; dig++){
          matrix[0][dig] = 1;
    }
    for(int len = 1; len < length; len++){
        for(int dig =0; dig <=9; dig++){
          int sum = 0;
          for(int i : b[dig]){
            sum += matrix[len-1][i];
          }
          matrix[len][dig] = sum;
        }
    }
    return matrix[length-1][digit];
}

public int count(int index, int length, int[][] matrix ){
    int sum = 0;
    if(matrix[length-1][index] > 0){
        System.out.println("getting value from memoize:"+index + "length:"+ length);
        return matrix[length-1][index];
    }
    if( length == 1){
        return 1;
    }
    for(int i: b[index] )  {
         sum += count(i, length-1,matrix);
    }
    matrix[length-1][index] = sum;
    return sum;
}