题目:http://poj.org/problem?id=1094
题意:给定n个字母,和m个它们之间的偏序关系,判断是否可以排成一个全序序列,在第几条关系后能得出全序序列,或者得出有矛盾。否则最后输出无法判断
思路:拓扑排序,如果有环肯定无法排成全序序列。进行拓扑排序时,每次只能有一个点入度为0,否则无法判断。
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#include <map>
#include <cmath>
#include <string>
#include <sstream>
#include <cctype>
#include <queue>
using namespace std;
typedef long long ll;
const int N = 30;
vector<int> G[N];
int n, m, k;
int degree[N], tmp[N], res[N];
bool used[N];
int toposort()
{
queue<int> que;
memcpy(tmp, degree, sizeof degree);
for(int i = 0; i < n; i++)
if(tmp[i] == 0)
que.push(i);
k = 0;
bool f = false;
while(! que.empty())
{
int v = que.front(); que.pop();
res[k++] = v;
if(! que.empty()) f = true; //入度为0的点不止一个,无法排出全序序列
for(int i = 0; i < G[v].size(); i++)
{
if(--tmp[G[v][i]] == 0)
que.push(G[v][i]);
}
}
if(k != n) return -1;
if(f) return 0;
else return 1;
}
int main()
{
char a, b;
while(scanf("%d%d", &n, &m), n || m)
{
memset(degree, 0, sizeof degree);
bool found = false;
for(int i = 0; i < m; i++)
{
scanf(" %c<%c", &a, &b);
if(found) continue;
int x = a - 'A', y = b - 'A';
degree[y]++;
G[x].push_back(y);
int r = toposort();
if(r == 1)
{
printf("Sorted sequence determined after %d relations: ", i + 1);
for(int i = 0; i < k; i++)
printf("%c", res[i] + 'A');
printf(".\n");
found = true;
}
else if(r == -1)
{
printf("Inconsistency found after %d relations.\n", i + 1);
found = true;
}
}
if(!found) printf("Sorted sequence cannot be determined.\n");
for(int i = 0; i < 26; i++)
G[i].clear();
}
return 0;
}