[UVA][組合] 124 - Following Orders
Following Orders
| Following Orders |
Background
Order is an important concept in mathematics and in computer science. For example, Zorn's Lemma states: ``a partially ordered set in which every chain has an upper bound contains a maximal element.'' Order is also important in reasoning about the fix-point semantics of programs.
This problem involves neither Zorn's Lemma nor fix-point semantics, but does involve order.
The Problem
Given a list of variable constraints of the form
x < y, you are to write a program that prints all
orderings of the variables that are consistent with the constraints.
For example, given the constraints x < y and x < z there
are two orderings of the variables x, y, and z that are consistent with these
constraints: x y z and x z y.
The Input
The input consists of a sequence of constraint specifications. A
specification consists of two lines: a list of variables on one line
followed by a list of constraints on the next line. A constraint is
given by a pair of variables,
where x y indicates that x < y.
All variables are single character, lower-case letters. There will be at least two variables, and no more than 20 variables in a specification. There will be at least one constraint, and no more than 50 constraints in a specification. There will be at least one, and no more than 300 orderings consistent with the contraints in a specification.
Input is terminated by end-of-file.
The Output
For each constraint specification, all orderings consistent with the constraints should be printed. Orderings are printed in lexicographical (alphabetical) order, one per line.
Output for different constraint specifications is separated by a blank line.
Sample Input
a b f g a b b f v w x y z v y x v z v w v
Sample Output
abfg abgf agbf gabf wxzvy wzxvy xwzvy xzwvy zwxvy zxwvy
#include <stdio.h>
#include <string.h>
#include <iostream>
#include <sstream>
using namespace std;
int can[26], map[26][26], used[26];
char str[26];
void DFS(int idx, int n) {
if(idx == n) {
str[idx] = '\0';
puts(str);
return;
}
int i, j;
for(i = 0; i < 26; i++) {
if(can[i] == 1 && used[i] == 0) {
for(j = 0; j < 26; j++)
if(map[i][j] == 1 && used[j] == 1)
return;
used[i] = 1;
str[idx] = i+'a';
DFS(idx+1, n);
used[i] = 0;
}
}
}
int main() {
stringstream sin;
string line;
char ch1, ch2, first = 0;
while(getline(cin, line)) {
if(first)
puts("");
first = 1;
memset(can, 0, sizeof(can));
memset(map, 0, sizeof(map));
memset(used, 0, sizeof(used));
sin.clear();
sin << line;
while(sin >> ch1) {
can[ch1-'a'] = 1;
}
int n = 0;
for(int i = 0; i < 26; i++)
n += can[i];
getline(cin, line);
sin.clear();
sin << line;
while(sin >> ch1 >> ch2) {
map[ch1-'a'][ch2-'a'] = 1;
}
DFS(0, n);
}
return 0;
}