青蛙跳台阶python解法

版权声明：非诚勿扰 https://blog.csdn.net/kaikai0803/article/details/84578910

# 解法一：递归思想
# 如果当前跳了一阶，还剩余n-1阶
# 如果当前跳了两阶，还剩余n-2阶
# 分别对n-1阶与n-2阶求次数，再相加
def jumpFloor(number):
	if number in (1, 2):
		return number
	return jumpFloor(number-1)+jumpFloor(number-2)

a = jumpFloor(10)
print(a)


# 解法二：循环实现，避免阶数过大造成时间超限
def jumpFloor(number):
    if number == 1 or number == 2:
        return number
    n, m = 1, 2
    for i in range(number-2):
    	result = m + n
    	n, m = m, result
    return result

a = jumpFloor(10)
print(a)


# 解法三：公式
# 设n级台阶，跳了z次，x次跳一阶，y次跳两阶。
# >>> z = x + y
# >>> n = 2*x + y

# @param {integer} n
# @return {integer}
def climbStairs(n):
    def fact(n):
        result=1
        for i in range(1,n+1):
            result*=i
        return result
    total=0
    # for i in range(n/2+1):	# float不能作为range的参数
    for i in range(n//2+1):
        total+=fact(i+n-2*i)/fact(i)/fact(n-2*i)
    return total

a = climbStairs(10)
print(a)