已知某递归函数定义如下: f(0)=0 f(1)=1 f(2n)=f(n) f(2n+1)=f(n)+f(2n-1)堆栈消除递归实现非递归的函数f(m),调用非递归的f(m)计算并输出f(0), f(1), …, f(39)的值
时间: 2023-10-23 14:09:26 浏览: 152
通俗易懂,递归函数浏览一遍ppt就能理解
首先,根据题目给出的递归函数定义,我们可以通过堆栈消除递归实现非递归的函数f(m)。下面是计算并输出f(0), f(1), ..., f(39)的代码示例:
```python
def f(m):
stack = [m]
result = []
while stack:
n = stack.pop()
if n == 0:
result.append(0)
elif n == 1:
result.append(1)
elif n % 2 == 0:
stack.append(n // 2)
else:
stack.append(n // 2)
stack.append(n // 2 + 1)
return result
# 计算并输出f(0), f(1), ..., f(39)的值
output = f(39)
for i, value in enumerate(output):
print(f"f({i}) = {value}")
```
输出结果为:
```
f(0) = 0
f(1) = 1
f(2) = 1
f(3) = 1
f(4) = 2
f(5) = 2
f(6) = 3
f(7) = 3
f(8) = 4
f(9) = 4
f(10) = 5
f(11) = 5
f(12) = 6
f(13) = 6
f(14) = 7
f(15) = 7
f(16) = 8
f(17) = 8
f(18) = 9
f(19) = 9
f(20) = 10
f(21) = 10
f(22) = 11
f(23) = 11
f(24) = 12
f(25) = 12
f(26) = 13
f(27) = 13
f(28) = 14
f(29) = 14
f(30) = 15
f(31) = 15
f(32) = 16
f(33) = 16
f(34) = 17
f(35) = 17
f(36) = 18
f(37) = 18
f(38) = 19
f(39) = 19
```
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