1_Fibonacci.py

# 大家都知道斐波那契数列，现在要求输入一个整数n，请你输出斐波那契数列的第n项（从0开始，第0项为0）  n<=39
class Solution:

    # 递归实现
    def Fibonacci(self, n):
        if n == 0:
            return 0;
        if n == 1:
            return 1;
        if n > 0:
            return self.Fibonacci(n - 1) + self.Fibonacci(n - 2);
        else:
            return None

    # 非递归实现
    # 当 n = 2的时候， h = f(1) + f(0) = 1 + 0 = 1
    # 当 n = 3的时候， h = f(2) + f(1) = 1 + 1 = 2
    # 当 n = 4的时候， h = f(3) + f(2) = 3 + 1 = 4
    def Fibonacci2(self, n):
        if n == 0:
            return 0;
        if n == 1:
            return 1;

        ret = 0
        a = 1
        b = 0
        for i in range(0, n - 1):
            ret = a + b
            b = a
            a = ret
        return ret

    # 记忆化搜索，保留中间结果
    map = {}
    def Fibonacci3(self, n):
        if n == 0:
            return 0
        if n == 1:
            return 1
        if self.map.get(n) == None:
            self.map[n] = self.Fibonacci3(n - 1) + self.Fibonacci3(n - 2)
        return self.map[n]

    # 动态规划
    map2 = {}
    def Fibonacci4(self, n):
        self.map2[0] = 0
        self.map2[1] = 1
        for i in range(2, n+1):
            self.map2[i] = self.map2.get(i-1) + self.map2.get(i - 2)
        return self.map2.get(n)

if __name__ == '__main__':
    print(Solution().Fibonacci4(10))