求N的阶乘,对于阶乘,一般的递归运算的函数可以为
![](http://www.cppblog.com/Images/OutliningIndicators/ExpandedBlockStart.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/InBlock.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/InBlock.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/InBlock.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/InBlock.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/ExpandedBlockEnd.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/None.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/ExpandedBlockStart.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/InBlock.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/InBlock.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/InBlock.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/InBlock.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/ExpandedSubBlockEnd.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/InBlock.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/InBlock.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/ExpandedBlockEnd.gif)
![](http://www.cppblog.com/images/cppblog_com/wangfeng2500/fib.jpg)
它的递归函数都会写
![](http://www.cppblog.com/Images/OutliningIndicators/None.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/None.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/ExpandedBlockStart.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/InBlock.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/InBlock.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/InBlock.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/InBlock.gif)
![](http://www.cppblog.com/Images/OutliningIndicators/ExpandedBlockEnd.gif)
但是它的递归函数实在效率太低,重复计算的值相当的多,所以我们需要改进,使用循环
long
fibonacci( int n )
{
long next_older_result = 0;
long previous_result = 1;
long result = 1;
if( 1 == n)
return 0;
else if( 2 == n)
return 1;
int i = 2;
while(i < n){
i++;
next_older_result = previous_result;
previous_result = result;
result = previous_result + next_older_result;
}
return result;
}
如果你仔细观察一下,你会发现以上两个的递归调用都是函数所执行的最后一项任务。这个函数是尾部递归fibonacci( int n )
{
long next_older_result = 0;
long previous_result = 1;
long result = 1;
if( 1 == n)
return 0;
else if( 2 == n)
return 1;
int i = 2;
while(i < n){
i++;
next_older_result = previous_result;
previous_result = result;
result = previous_result + next_older_result;
}
return result;
}
尾部递归很容易也成非递归的形式。