The case of the M-fork Tree First order and post sequence

Title Description:

We is all familiar with pre-order, In-order and post-order traversals of binary trees. A common problem in data structure classes are to find the pre-order traversal of a binary tree when given the In-order and Post-order traversals. Alternatively, you can find the Post-order traversal when given the In-order and pre-order. However cannot determine the in-order traversal of a tree when given its pre-order and Post-order Traversa Ls. Consider the four binary trees below:

All of these trees has the same pre-order and Post-order traversals. This phenomenon isn't restricted to binary trees, but holds for general m-ary trees as well.

Input:

        input would consist of mul Tiple problem instances. Each instance would consist of a line of the form
m s1 s2
        indicating tha t the trees is m-ary trees, S1 is the pre-order traversal and S2 is the Post-order traversal. All traversal strings would consist of lowercase alphabetic characters. For all input instances, 1 <= m <= and the length of S1 and S2 would be between 1 and inclusive. If the length of S1 is K (which is the same as the length of S2, of course), the first k letters of the alphabet would be u Sed in the strings. An input line of 0 would terminate the input.

Output:

For each problem instance, you should output one line containing the number of possible trees which would result in the PR E-order and Post-order traversals for the instance. All output values would be within the range of a 32-bit signed integer. For each problem instance, you be guaranteed that there was at least one tree with the given pre-order and Post-order Trav Ersals.

Sample input:

2 ABC cba2 ABC bca10 ABC bca13 abejkcfghid JKEBFGHICDA

Sample output:

4145207352860

Classic Code:

#include <stdio.h> #include <string.h> char pre[30], post[30]; int m; int find( char * p, char x) {      int i=0;      while (p[i]!=x) i++;      return i; } typedef long long ll; ll C( int a, int b) {      ll u = 1;      ll d = 1;      while (b) {      u *= a--;      d *= b--;      }      return u/d; } ll test( char * p, char * q, int n) {      if (n==0) return 1;      ll f = 1;      int c = 0;      int i;      while (n) {      c++;      i = find(q,*p);      f *= test(p+1,q,i);      p += i+1;      q += i+1;      n -= i+1;      }      return f * C(m,c); } int main() {      while ( scanf ( "%d%s%s" ,&m,pre,post)==3) {      printf ( "%lld\n" ,test(pre+1,post, strlen (pre)-1));      }        return 0; }Explanation of Baidu Library: Http://wenku.baidu.com/link?url=ZddYeW-pYEgst83coqElNsI-aHY_ Jwyuhwskbhkrxpnwxycmcn0ltdqq7k-igdzkr48wdgg4chriks1h5cwunhzpqbjbl3a4n_oluffbe4i

The case of the M-fork Tree First order and post sequence