- 传送门 -
http://poj.org/problem?id=2762
| Time Limit: 2000MS | | Memory Limit: 65536K |
| Total Submissions: 18189 | | Accepted: 4868 |
Description
In order to make their sons brave, Jiajia and Wind take them to a big cave. The cave has n rooms, and one-way corridors connecting some rooms. Each time, Wind choose two rooms x and y, and ask one of their little sons go from one to the other. The son can either go from x to y, or from y to x. Wind promised that her tasks are all possible, but she actually doesn't know how to decide if a task is possible. To make her life easier, Jiajia decided to choose a cave in which every pair of rooms is a possible task. Given a cave, can you tell Jiajia whether Wind can randomly choose two rooms without worrying about anything?
Input
The first line contains a single integer T, the number of test cases. And followed T cases.
The first line for each case contains two integers n, m(0 < n < 1001,m < 6000), the number of rooms and corridors in the cave. The next m lines each contains two integers u and v, indicating that there is a corridor connecting room u and room v directly.
Output
The output should contain T lines. Write 'Yes' if the cave has the property stated above, or 'No' otherwise.
Sample Input
1
3 3
1 2
2 3
3 1
Sample Output
Yes
Source
POJ Monthly--2006.02.26,zgl & twb
- 题意 -
给一些有向边, 判断图中两点是否联通(从 x 走到 y, 或从 y 走到 x, 满足其中至少一个)
- 思路 -
tarjan缩点后, 我们发现, 一定是一条链才满足条件(两条分岔路上的点无法联通).
暴力判链...慢如狗...
注意整张图为一个强连通分量的情况.
细节见代码.
- 代码 -
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<vector>
using namespace std;
const int N = 1e3 + 5;
const int M = 6e3 + 5;
int IN[N], OUT[N];
int STK[N];
int DFN[N], BL[N], LOW[N];
int NXT[M], TO[M], HD[N];
int cas, n, m, sz, cnt, tot, top;
vector<int> G[N];
void init() {
memset(HD, 0 ,sizeof (HD));
memset(DFN, 0 ,sizeof (DFN));
memset(BL, 0, sizeof (BL));
memset(IN, 0, sizeof (IN));
memset(OUT, 0, sizeof (OUT));
sz = cnt = tot = top = 0;
}
void tarjan(int x) {
DFN[x] = LOW[x] = ++tot;
STK[++top] = x;
for (int i = HD[x]; i; i = NXT[i]) {
int v = TO[i];
if (!DFN[v]) {
tarjan(v);
LOW[x] = min(LOW[x], LOW[v]);
}
else if (!BL[v]) LOW[x] = min(LOW[x], DFN[v]);
}
if (LOW[x] == DFN[x]) {
cnt ++;
int tmp;
G[cnt].clear();
do {
tmp = STK[top--];
BL[tmp] = cnt;
G[cnt].push_back(tmp);
}while (tmp != x);
}
}
int main() {
scanf("%d", &cas);
while (cas--) {
init();
scanf("%d%d", &n, &m);
for (int i = 1; i <= m; ++i) {
int a, b;
scanf("%d%d", &a, &b);
TO[++sz] = b;
NXT[sz] = HD[a];
HD[a] = sz;
}
for (int i = 1; i <= n; ++i)
if (!DFN[i]) tarjan(i);
for (int i = 1; i <= cnt; ++i) {
for (int j = 0; j < G[i].size(); ++j) {
int u = G[i][j];
for (int k = HD[u]; k; k = NXT[k]) {
int v = TO[k];
if (i != BL[v]) {
IN[BL[v]] ++;
OUT[i] ++;
}
}
}
}
int f1 = -1, f2 = -1;
for (int i = 1; i <= cnt; ++i) {
if (IN[i] == 0) f1 ++;
else if (OUT[i] == 0) f2 ++;
else if (IN[i] != 1 || OUT[i] != 1) {
f1 = f2 = -2;
break;
}
}
if ((f1 == 0 && f2 == 0) || cnt == 1) printf("Yes
"); //注意判 cnt==1 的情况
else printf("No
");
}
return 0;
}