计数变化的时间复杂性

Question

我有类似的问题需要链接：coin change algorithm in scala using recursion

代码是递归的，看起来像：

def countChange(money: Int, coins: List[Int]): Int = {
    def count(capacity: Int, changes: List[Int]): Int = {
            if(capacity == 0) 1
            else if(capacity < 0) 0
            else if(changes.isEmpty && capacity >=1 )0
            else count(capacity, changes.tail) + count(capacity - changes.head, changes)
    }
count(money, coins)
}

我的问题是如何分析此算法的时间复杂度？谢谢！

Answer 1

这是树递归的形式，随着输入呈指数增长。 SICP has very nice explanation about this