Fibonacci number
Two ideas
- Iteration
class Solution {
int start1=1,start2=1,t=0;
public int numWays(int n)
{
for(int i=1,i<=n;i++)
{
t=start1+start2;
start1=start2
start2=t;
}
}
}
- Recursion
public int fib(int n)
{
if(n==0)
return 0;
else if(n==1||n==2)
return 1;
else
return fib(n-1)+fib(n-2);
}
Frog jump stairs
Man of few words said on the map analysis:
frog jump from level 0 when layer 0, 0
frog jump from level 0 when the first layer is 1, because only the first layer from 0 jump step to reach the first layer
when it frog to reach the n-layer, there are two ways:
-
From the n-1 layer jump step
-
From the n-2 layer jump-step
According to the permutations and combinations of knowledge, this process for a classification process:
i.e., f (n) = f (n -1) + f (n-2), where f (n) represents from layer 0 to large n-th layer moves
you can see the solution process is actually a Fibonacci number
