7, Appalachian Fibonacci number

Topic one:

We all know that Fibonacci number, and now asked to enter an integer n, you output the n-th Fibonacci number Fibonacci sequence of item (from 0, the first 0 is 0) n <= 39

 

public int Fibonacci(int n) {
             if(n==0) return 0;
          if(n==1) return 1;
          return Fibonacci(n-1)+Fibonacci(n-2);
    }

 

Topic two:

A frog can jump on a Class 1 level, you can also hop on level 2. The frog jumped seeking a total of n grade level how many jumps (the order of different calculation different results).

the n steps: a first step jump, remaining n-1; the first-order Jump 2, n-2 order left

Results f (n) = f (n-1) + f (n-2)

n=1 f(1)=1

n=2 f(2)=2

 public int JumpFloor(int n) {
          if(n==1) return 1;
          if(n==2) return 2;
          return JumpFloor(n-1)+JumpFloor(n-2);
    }

 

Topic three:

A frog can jump on a Class 1 level, you can also hop on level 2 ...... n It can also jump on stage.

The frog jumped seeking a total of n grade level how many jumps.

Similarly:

f(n)=f(n-1)+...+f(0)

f(n-1)=f(n-2)+...+f(0)

f(n)-f(n-1)=f(n-1)

f(n)=2*f(n-1)

public int JumpFloorII(int target) {
        if (target <= 0) {
            return -1;
        } else if (target == 1) {
            return 1;
        } else {
            return 2 * JumpFloorII(target - 1);
        }
    }

 Topic Four:

We can use a small rectangle 2 * 1 sideways or vertically to cover a larger rectangle.

Will the small rectangle of n 2 * 1 coverage without overlap a large rectangle 2 * n, a total of how many ways?

Been to Appalachian Fibonacci number is still recommended (see Notes 1, 2 Appalachian consider Fibonacci number)

public int RectCover(int target) {
        if(target<=0){
            return 0;
        }else if(target<=2){
            return target;
        }else {
            return RectCover(target-1)+RectCover(target-2); 
        }
       
    }