package com.algs;
public class Fib
{
/**
* Recursive
*/
public static int fib(int n)
{
if (0 == n)
{
return 0;
}
else if (1 == n)
{
return 1;
}
else
{
return fib(n - 1) + fib(n - 2);
}
}
/**
* tail recursive
*
* @param args
*/
public static int fib2(int n)
{
return fib2Helper(1, 0, n);
}
private static int fib2Helper(int a, int b, int n)
{
if (n == 0)
{
return b;
}
return fib2Helper(a + b, a, n - 1);
}
/**
* while
*
* @param args
*/
public static int fib3(int n)
{
if (0 == n)
{
return 0;
}
else if (1 == n)
{
return 1;
}
int a = 1, b = 0;
while (n-- > 0)
{
int temp = a;
a = a + b;
b = temp;
}
return b;
}
/**
* 自底向上包含"动态规划"思想的解法
*
* @param n
* @return 第n个斐波那契数
*/
public static long downToTopReslove(int n)
{
if (n == 0)
{
return 0;
}
else if (n == 1)
{
return 1;
}
else
{
long[] fibonacciArray = new long[n + 1]; // fibonacciArray[i]表示第i个斐波那契数
fibonacciArray[0] = 0;
fibonacciArray[1] = 1;
for (int i = 2; i <= n; i++)
{
// 注意由于fibonacciArray[0]表示第0个元素，这里是i <= n，而不是i < n
fibonacciArray[i] = fibonacciArray[i - 1] + fibonacciArray[i - 2];
}
return fibonacciArray[fibonacciArray.length - 1];
}
}
public static void main(String[] args)
{
System.out.println(downToTopReslove(100));
}
}