POJ 1094 Sorting It All Out(欧拉排序)

Sorting It All Out

Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 27374 Accepted: 9483

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.

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.

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 6A<BA<CB<CC<DB<DA<B3 2A<BB<A26 1A<Z0 0

Sample Output

Sorted sequence determined after 4 relations: ABCD.Inconsistency found after 2 relations.Sorted sequence cannot be determined.

赤裸裸的欧拉排序问题，不过有个小陷阱就是说判断出是连通图而且有欧拉序还不行，还必须当前输出的值有一条有向边指向上一个输出的值，这样才能确定所有字母的大小问题，比较水，不多说了，直接上代码

#include<iostream>#include<cstdio>#include<cmath>#include<cstdlib>#include<cstring>using namespace std;int first[27], next[900][2], letters[27], vis[27];int n, m, k;bool dfs(int i){    vis[i] = -1;    bool judge = false;    for(int u = first[i]; u != -1; u = next[u][0])    {        if(vis[next[u][1]] == 0)            judge = dfs(next[u][1]);        if(judge || vis[next[u][1]] == -1)            return true;    }    vis[i] = 1;    return false;}//找错误bool findw(){    memset(vis, 0, sizeof(vis));    bool judge = false;    for(int i = 0; i < n; i++)    {        if(!vis[i])            judge = dfs(i);        if(judge)            return true;    }    return false;}bool dfs2(int i){    bool judge = true;    for(int u = first[i]; u != -1 && judge; u = next[u][0])        if(vis[next[u][1]] == 0)            judge = dfs2(next[u][1]);    if(!judge)        return false;    for(int u = first[i]; u != -1 && judge; u = next[u][0])        if(next[u][1] == letters[k+1])            judge = false;    if(judge && k != n-1)        return false;    vis[i] = 1;    letters[k--] = i;    return true;}//找排序bool finds(){    memset(letters, -1, sizeof(letters));    memset(vis, 0, sizeof(vis));    k = n-1;    bool judge = true;    for(int i = 0; i < n && judge; i++)    {        if(!vis[i] && first[i] != -1)            judge = dfs2(i);    }    if(!judge)        return false;    for(int i = 0; i < n; i++)        if(letters[i] == -1)            return false;//    cout << "bool finds()  return true" << endl;    return true;}int main(){//    freopen("1094.in", "r", stdin);    char str[5];    while(scanf("%d%d", &n, &m) && n)    {        memset(first, -1, sizeof(first));        bool inc, det;        inc = det = false;        int x = 0;        for(int i = 1; i <= m; i++)        {            scanf("%s", str);            if(inc || det)                continue;//            cout << "--------------" << endl;            next[i][0] = first[str[0] - 'A'];            next[i][1] = str[2] - 'A';            first[str[0] - 'A'] = i;            if(inc = findw())//找错误                x = i;            else if(det = finds())//找排序                x = i;        }        if(inc)            printf("Inconsistency found after %d relations.\n", x);        else if(det)        {            printf("Sorted sequence determined after %d relations: ", x);            for(int i = 0; i < n; i++)                printf("%c", letters[i] + 'A');            printf(".\n");        }        else            printf("Sorted sequence cannot be determined.\n");    }    return 0;}