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[UVA] 1251 - Repeated Substitution with Sed

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Do you know ``sed,`` a tool provided with Unix? Its most popular use is to substitute every occurrence of a string $ alpha$ contained in the input string (actually each input line) with another string $ beta$. More precisely, it proceeds as follows.

  1. Within the input string, every non-overlapping (but possibly adjacent) occurrences of $ alpha$ are marked. If there is more than one possibility for non-overlapping matching, the leftmost one is chosen.
  2. Each of the marked occurrences is substituted with $ beta$ to obtain the output string; other parts of the input string remain intact.

For example, when $ alpha$ is ``aa`` and $ beta$ is ``bca``, an input string ``aaxaaa`` will produce ``bcaxbcaa``, but not ``aaxbcaa`` nor ``bcaxabca``. Further application of the same substitution to the string ``bcaxbcaa`` will result in ``bcaxbcbca``, but this is another substitution, which is counted as the second one.

In this problem, a set of substitution pairs ( $ alpha_{{i}}^{}$, $ beta_{{i}}^{}$) (i = 1, 2,..., n), an initial string $ gamma$, and a final string $ delta$ are given, and you must investigate how to produce $ delta$ from $ gamma$ with a minimum number of substitutions. A single substitution ($ alpha_{{i}}^{}$,$ beta_{{i}}^{}$) here means simultaneously substituting all the non-overlapping occurrences of $ alpha_{{i}}^{}$, in the sense described above, with $ beta_{{i}}^{}$.

You may use a specific substitution ($ alpha_{{i}}^{}$,$ beta_{{i}}^{}$) multiple times, including zero times.

Input 

The input consists of multiple datasets, each in the following format.


n
$ alpha_{{1}}^{}$ $ beta_{{1}}^{}$
$ alpha_{{2}}^{}$ $ beta_{{2}}^{}$

&vellip#vdots; $ alpha_{{n}}^{}$ $ beta_{{n}}^{}$
$ gamma$
$ delta$


n is a positive integer indicating the number of pairs. $ alpha_{{i}}^{}$ and $ beta_{{i}}^{}$ are separated by a single space. You may assume that 1$ le$|$ alpha_{{i}}^{}$| < |$ beta_{{i}}^{}$|$ le$10 for any i (| s| means the length of the string s), $ alpha_{{i}}^{}$ $ neq$ $ alpha_{{j}}^{}$ for any i $ neq$ j, n$ le$10 and 1$ le$|$ gamma$| < |$ delta$|$ le$10. All the strings consist solely of lowercase letters. The end of the input is indicated by a line containing a single zero.

Output 

For each dataset, output the minimum number of substitutions to obtain $ delta$ from $ gamma$. If $ delta$ cannot be produced from $ gamma$ with the given set of substitutions, output `-1'.

Sample Input 

2 
a bb 
b aa 
a 
bbbbbbbb 
1 
a aa 
a 
aaaaa 
3 
ab aab 
abc aadc 
ad dee 
abc 
deeeeeeeec 
10 
a abc 
b bai 
c acf 
d bed 
e abh 
f fag 
g abe 
h bag 
i aaj 
j bbb 
a 
abacfaabe 
0

Sample Output 

3 
-1 
7 
4


給定一個字串,每次使用一條規則,將字串進行轉換,問最少幾次可以達到目標字串。

替換的時候,先將第一個出現位置的地方給替換,再從上次沒替換到位置開始找尋下一個替換的位置。

利用 bfs 去找到最少步數。

#include <stdio.h>
#include <map>
#include <iostream>
#include <queue>
#include <algorithm>
#include <string.h>
using namespace std;
char a[20][20], b[20][20];
char st[20], ed[20], buf[30];

int main() {
int n;
int i, j, k;
while(scanf("%d", &n) == 1 && n) {
map<string, int> R;
for(i = 0; i < n; i++)
scanf("%s %s", &a[i], &b[i]);
scanf("%s %s", &st, &ed);
if(!strcmp(st, ed)) {
puts("0");
continue;
}
int edlen = strlen(ed);
int p, q;
queue<string> Q;
Q.push(st);
R[st] = 0;
string tn;
while(!Q.empty()) {
tn = Q.front(), Q.pop();
int step = R[tn];
for(i = 0; i < n; i++) {
//replace all a[i]->b[i]
int buflen = 0;
for(j = 0; j < tn.length(); j++) {
for(p = 0, q = j; a[i][p] && q < tn.length(); p++, q++)
if(a[i][p] != tn[q])
break;
if(a[i][p] == '\0') {
for(p = 0; b[i][p]; p++)
buf[buflen++] = b[i][p];
j = q-1;
} else
buf[buflen++] = tn[j];
if(buflen > edlen) break;
}
if(buflen > edlen) continue;
buf[buflen] = '\0';
if(R.find(buf) != R.end())
continue;
R[buf] = step+1;
Q.push(buf);
}
if(R.find(ed) != R.end())
break;
}
if(R.find(ed) == R.end())
puts("-1");
else
printf("%d\n", R[ed]);
}
return 0;
}
 

台長: Morris
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