Recursion题目求解

最近在自学CS61A(python)，做homework3的时候遇到一道题，想了半天也解决不了，希望大家帮忙想个算法。。。谢谢！
题目的关键是不能有任何assignment语句，也就是要用recursion，可我想不出做法。
题目如下：

Write a function that takes a positive integer n and returns the number of ten-pairs it contains. A ten-pair is a pairs of digits within n that sum to 10. Do not use any assignment statements.

The number 7,823,952 has 3 ten-pairs. The first and fourth digits sum to 7+3=10, the second and third digits sum to 8+2=10, and the second and last digit sum to 8+2=10:

def ten_pairs(n):    """Return the number of ten-pairs within positive integer n.   
>>> ten_pairs(7823952)   
3   
>>> ten_pairs(55055)   
6   
>>> ten_pairs(9641469)   
6   
"""

递归参数中设置一项保存当前和来进行判断呢，就是类似dfs(int i, int sum)这样

pyemma 发表于 2014-7-6 12:35
递归参数中设置一项保存当前和来进行判断呢，就是类似dfs(int i, int sum)这样

这个我倒是想到了，但是我现在纠结于base case 和 recursive case怎么写。。。

我想了一些方法，但是感觉都不行。。

pyemma 发表于 2014-7-6 12:35
递归参数中设置一项保存当前和来进行判断呢，就是类似dfs(int i, int sum)这样

这个我倒是想到了，但是我现在纠结于base case 和 recursive case怎么写。。。

我想了一些方法，但是感觉都不行。。

my random thoughts...:

the recursion will start from the left most digit and go right (e.g. '7' for 7823952)
for each digit D, it will check it's sum with each of its right side digits(for 7, it checks 7+8, 7+2.....7+2)

regradless of how it is implemented, you should keep tracking three things in the recursion call:
1) the position of digit D
2) the position of right side digit that is summing with D in this recursion (Let's call it X)
3) total number of ten-pairs

the base case would be:
if digit X is the right most bit(e.g. '2' in 7823952), we right-shift digit D to its right neighbour
if digit D is the least significant bit, it means all digit pairs are compared, we can exit the call and return the total number of ten-pairs.

grassgigi 发表于 2014-7-6 14:05
my random thoughts...:

the recursion will start from the left most digit and go right (e.g. '7' f ...

Thank you first for your help!

So how do you keep track of the position of digit D and X? Sequences like string and list are not taught prior to this homework, which means that this problem may be solved without using sequence selection.

Can you elaborate on that?