Rectangular footprint offer 10. prove safety

10. The rectangular footprint

topic

We can use 2 small rectangle 1 of sideways or vertically to cover a larger rectangle. Will the use of n 2 small rectangle 1 coverage without overlap a large rectangle 2 * n, a total of how many ways?

For n = 3 for example, 2 * 3 tile is covered There are three methods:

Thinking

Or Fibonacci number, 2 * 2 matrix, there are two filling methods, three methods is a method that is 3 * 2, n-2 * a n-1 and n-2 and the

Code

  public static int JumpFloor(int target) {
    if (target <= 0) {
      return 0;
    }
    if(target==1)
    {
      return 1;
    }
    if (target==2)
    {
      return 2;
    }
    int f[] = new int[target + 1];
    f[1] = 1;
    f[2] = 2;
    for (int i = 3; i <= target; i++) {
      f[i] = f[i - 1] + f[i - 2];
    }
    return f[target];
  }