Sorting It All Out
| Time Limit: 1000MS | Memory Limit: 10000K | |
| Total Submissions: 22332 | Accepted: 7705 |
Description
An ascending sorted sequence of distinct values is one in which some form of a less-than operator is used to order the elements from smallest to largest. For example, the sorted sequence A, B, C, D implies that A < B, B < C and
C < D. in this problem, we will give you a set of relations of the form A < B and ask you to determine whether a sorted order has been specified or not.
C < D. in this problem, we will give you a set of relations of the form A < B and ask you to determine whether a sorted order has been specified or not.
Input
Input consists of multiple problem instances. Each instance starts with a line containing two positive integers n and m. the first value indicated the number of objects to sort, where 2 <= n <= 26. The objects to be sorted will
be the first n characters of the uppercase alphabet. The second value m indicates the number of relations of the form A < B which will be given in this problem instance. Next will be m lines, each containing one such relation consisting of three characters:
an uppercase letter, the character "<" and a second uppercase letter. No letter will be outside the range of the first n letters of the alphabet. Values of n = m = 0 indicate end of input.
be the first n characters of the uppercase alphabet. The second value m indicates the number of relations of the form A < B which will be given in this problem instance. Next will be m lines, each containing one such relation consisting of three characters:
an uppercase letter, the character "<" and a second uppercase letter. No letter will be outside the range of the first n letters of the alphabet. Values of n = m = 0 indicate end of input.
Output
For each problem instance, output consists of one line. This line should be one of the following three:
Sorted sequence determined after xxx relations: yyy...y.
Sorted sequence cannot be determined.
Inconsistency found after xxx relations.
where xxx is the number of relations processed at the time either a sorted sequence is determined or an inconsistency is found, whichever comes first, and yyy...y is the sorted, ascending sequence.
Sample Input
4 6 A<B A<C B<C C<D B<D A<B 3 2 A<B B<A 26 1 A<Z 0 0
Sample Output
Sorted sequence determined after 4 relations: ABCD. Inconsistency found after 2 relations. Sorted sequence cannot be determined.
// 首先。有拓扑排序检查是不是有环的存在，要是没有环的话，用flody传递闭包
再判断序列是不是唯一的。
而判断序列是不是唯一的方法是：
n个结点的出度分别是0,1,2,3,4...n-1，是的话就说明是唯一的
代码：
#include<cstdio>
#include<iostream>
#include<queue>
#include<cmath>
#include<cstring>
#include<string>
#include<algorithm>
#include<stack>
using namespace std;
typedef long long LL;
#define clr(x) memset(x,0,sizeof(x));
#define sf scanf
#define pf printf
int map[35][35];
int path[35];
bool vis[35];
int cnt[35];
int N,M;
const int INF=1<<29;
void flody(){//传递闭包
for(int k2=0;k2<N;k2++)
for(int i1=0;i1<N;i1++)
for(int j3=0;j3<N;j3++){
if(map[k2][i1]&&map[i1][j3])
map[k2][j3]=1;
}
}
void updata(int u){
for(int i=0;i<N;i++){
if(map[u][i]) --cnt[i];
}
cnt[u]--;
}
bool topSort(){
clr(cnt);
for(int i=0;i<N;i++)
for(int j=0;j<N;j++){
if(map[i][j]) ++cnt[j];
}
for(int i=0;i<N;i++){
int u=-1;
for(int j=0;j<N;j++){
if(!cnt[j]){
u=j;
break;
}
}
if(u==-1) return true;
path[i]=u;
updata(u);
}
return false;
}
bool judge(){
clr(vis);
for(int i=0;i<N;i++){
int out=0;
for(int j=0;j<N;j++){
if(map[i][j]) out++;
}
if(vis[out]) return false;
vis[out]=true;
}
return true;
}
int main(){
while(sf("%d%d",&N,&M)!=EOF&&N+M){
bool flag=false;
char str[5];
clr(map);
for(int i=1;i<=M;i++){
sf("%s",&str);
if(flag) continue;
int x=str[0]-'A';
int y=str[2]-'A';
if(map[x][y]) continue;
map[x][y]=1;
if(topSort()){
pf("Inconsistency found after %d relations.\n",i);
flag=true;
continue;
}
flody();
if(judge()){
pf("Sorted sequence determined after %d relations: ",i);
for(int j=0;j<N;j++) pf("%c",path[j]+'A');
pf(".\n");flag=true;
}
}
if(!flag)
pf("Sorted sequence cannot be determined.\n");
}
return 0;
}