xtu summer individual 6 D - Checkposts

Checkposts

Time Limit: 2000ms

Memory Limit: 262144KB

This problem will be judged on  CodeForces. Original ID: 427C
64-bit integer IO format: %I64d      Java class name: (Any)

 

 

Your city has  n junctions. There are m one-way roads between the junctions. As a mayor of the city, you have to ensure the security of all the junctions.

 

To ensure the security, you have to build some police checkposts. Checkposts can only be built in a junction. A checkpost at junction i can protect junction j if either i = j or the police patrol car can go to j from i and then come back to i.

Building checkposts costs some money. As some areas of the city are more expensive than others, building checkpost at some junctions might cost more money than other junctions.

You have to determine the minimum possible money needed to ensure the security of all the junctions. Also you have to find the number of ways to ensure the security in minimum price and in addition in minimum number of checkposts. Two ways are different if any of the junctions contains a checkpost in one of them and do not contain in the other.

Input

In the first line, you will be given an integer n, number of junctions (1 ≤ n ≤ 105). In the next line, n space-separated integers will be given. The ith integer is the cost of building checkpost at the ith junction (costs will be non-negative and will not exceed 109).

The next line will contain an integer m (0 ≤ m ≤ 3·105). And each of the next m lines contains two integers ui and vi (1 ≤ ui, vi ≤ n; u ≠ v). A pair ui, vi means, that there is a one-way road which goes from ui to vi. There will not be more than one road between two nodes in the same direction.

 

Output

Print two integers separated by spaces. The first one is the minimum possible money needed to ensure the security of all the junctions. And the second one is the number of ways you can ensure the security modulo 1000000007 (109 + 7).

 

Sample Input

Input

3
1 2 3
3
1 2
2 3
3 2

Output

3 1

Input

5
2 8 0 6 0
6
1 4
1 3
2 4
3 4
4 5
5 1

Output

8 2

Input

10
1 3 2 2 1 3 1 4 10 10
12
1 2
2 3
3 1
3 4
4 5
5 6
5 7
6 4
7 3
8 9
9 10
10 9

Output

15 6

Input

2
7 91
2
1 2
2 1

Output

7 1

Source

Codeforces Round #244 (Div. 2)

 

 

解题：强连通，看有多少个强联通块。每个强联通块里面就个最小的值，然后记录下这个块里，这样小的值有多少个！然后把所有块的最小值的数目乘起来，就是方案数，各块的最小值加起来，就是最小的那个什么什么。。。。注意要用长整型变量，注意要取模。

 

 1 #include <iostream>

 2 #include <cstdio>

 3 #include <cstring>

 4 #include <cmath>

 5 #include <algorithm>

 6 #include <climits>

 7 #include <vector>

 8 #include <queue>

 9 #include <cstdlib>

10 #include <string>

11 #include <set>

12 #include <stack>

13 #define LL long long

14 #define INF 0x3f3f3f3f

15 using namespace std;

16 const int maxn = 100010;

17 const LL mod = 1000000007;

18 vector<int>g[maxn];

19 stack<int>s;

20 int w[maxn],dfn[maxn],low[maxn],n,m,id,scc;

21 bool instack[maxn];

22 LL cnt[maxn],sum,ways;

23 void tarjan(int u){

24     dfn[u] = low[u] = ++id;

25     instack[u] = true;

26     s.push(u);

27     int v;

28     for(v = 0; v < g[u].size(); v++){

29         if(!dfn[g[u][v]]){

30             tarjan(g[u][v]);

31             low[u] = min(low[u],low[g[u][v]]);

32         }else if(instack[g[u][v]] && low[u] > dfn[g[u][v]])

33             low[u] = dfn[g[u][v]];

34     }

35     if(dfn[u] == low[u]){

36         int theMin = INF;

37         do{

38             v = s.top();

39             s.pop();

40             if(w[v] < theMin){

41                 theMin = w[v];

42                 cnt[scc] = 1;

43             }else if(w[v] == theMin){

44                 cnt[scc]++;

45             }

46             instack[v] = false;

47         }while(v != u);

48         scc++;

49         sum += theMin;

50     }

51 }

52 int main() {

53     int i,j,u,v;

54     while(~scanf("%d",&n)){

55         for(i = 1; i <= n; i++)

56             scanf("%d",w+i);

57         for(i = 0; i <= n; i++){

58             g[i].clear();

59             instack[i] = false;

60             low[i] = dfn[i] = 0;

61             cnt[i] = 0;

62         }

63         scanf("%d",&m);

64         for(i = 0; i < m; i++){

65             scanf("%d %d",&u,&v);

66             g[u].push_back(v);

67         }

68         while(!s.empty()) s.pop();

69         sum = scc = id = 0;

70         for(i = 1; i <= n; i++)

71             if(!dfn[i]) tarjan(i);

72         for(ways = 1,i = 0; i < scc; i++){

73             ways = ((ways%mod)*(cnt[i]%mod))%mod;

74         }

75         printf("%I64d %I64d\n",sum,ways);

76     }

77     return 0;

78 }

View Code