让我们想象一下对f(4)进行评估(您考虑的示例)。这是怎么回事。堆栈从看起来像
I need to compute f(4)
然后f(4)的计算返回到f(3),堆栈看起来像
I need to compute f(4), so I need to compute f(3)
然后我们继续下降,最终到达
I need to compute f(4), so I need to compute f(3), so I need to compute f(2), so I need to compute f(1), so I need to compute f(0)
然后,我们可以将f(0)计算为1,最后一次调用返回。倒数第二个调用(用于计算f(1)的那个),然后要计算f(0)的第二个副本,堆栈将转到:
I need to compute f(4), so I need to compute f(3), so I need to compute f(2), so I need to compute f(1), and although I've already computed the first f(0)=1, I still need to compute the second occurrence of f(0), so I need to compute f(0) (again)
然后返回,因此f(1)的计算可以返回,我们得到
I need to compute f(4), so I need to compute f(3), so I need to compute f(2), and although I've already computed the first f(1)=2, I still need to compute the second occurrence of f(0)
从那里堆栈变成:
I need to compute f(4), so I need to compute f(3), so I need to compute f(2), and although I've already computed the first f(1)=2, I still need to compute the second occurrence of f(0), so... I need to compute f(1)
它将继续像以前一样计算f(1)。
关键是,即使(最终)将执行2 ^ n次运算,堆栈也只能达到n的深度。因此,时间复杂度为O(2 ^ n),但空间复杂度仅为O(n)。



