LightOj 1168 (Wishing Snake)

#lightoj #cp #problem_solving #scc #graph_theory

Idea

SCC

  • Create DAG from SCC and just check if every node is reachable form
    the starting node (i.e node 0) by a single dfs
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201

/**Which of the favors of your Lord will you deny ?**/

#include<bits/stdc++.h>
using namespace std;

#define LL long long
#define PII pair<int,int>
#define MP make_pair
#define F first
#define S second

int scc_num;

vector<int>graph[100010];
vector<int>rev_graph[100010];
vector<int>new_graph[100010];

//vector<int>Map(1010,-1);
//vector<int>SCCMap(1010,0);

int Map[1010];
int SCCMap[1010];

stack<int>stk;

bool visited[1010];

bool flag=true;

void forward_dfs(int node)
{
    visited[node]=true;

    for(int next:graph[node])
    {
        if(visited[next]==false)
            forward_dfs(next);
    }

    stk.push(node);
}

void rev_dfs(int node)
{
    visited[node]=true;
    SCCMap[node]=scc_num;

    for(int next:rev_graph[node])
    {
        if(visited[next]==false)
            rev_dfs(next);
    }
}

void dfs_check(int node)
{
    if(new_graph[node].size()>1)
    {
        flag=false;
        return;
    }

    visited[node]=true;
    for(int next:new_graph[node])
    {
        if(visited[next]==false)
            dfs_check(next);
    }

}

void init()
{
    for(int i=0; i<1010; i++)
    {
        graph[i].clear();
        rev_graph[i].clear();
        new_graph[i].clear();
    }

    fill(visited,visited+1010,false);

//    Map.clear();
//    Map(1010,-1);
//    SCCMap.clear();

    memset(Map,-1,sizeof Map);

    while(!stk.empty())
        stk.pop();

}

int main()
{
    //freopen("LightOj1168.txt","w",stdout);

    int tc;
    scanf("%d",&tc);

    for(int i=1; i<=tc; i++)
    {
        init();

        int n,serial=0;
        scanf("%d",&n);

        Map[0]=serial++;

        for(int j=1; j<=n; j++)
        {
            int wish;
            scanf("%d",&wish);

            for(int k=1; k<=wish; k++)
            {
                int a,b;
                scanf("%d %d",&a,&b);

                if(Map[a]==-1)
                    Map[a]=serial++;
                if(Map[b]==-1)
                    Map[b]=serial++;

                int u=Map[a];
                int v=Map[b];

                //cout<<u<<" --> "<<v<<endl;

                graph[u].push_back(v);
                rev_graph[v].push_back(u);

            }
        }

        //cout<<"Serial "<<serial<<endl;

        for(int k=0; k<serial; k++)
        {
            if(visited[k]==false)
                forward_dfs(k);
        }

        fill(visited,visited+1010,false);

        scc_num=0;

        while(!stk.empty())
        {
            int now=stk.top();
            stk.pop();

            if(visited[now]==false)
            {
                rev_dfs(now);
                scc_num++;
            }
        }

        ///building the new graph (DAG) keeping every sccs as a node

        for(int now=0; now<serial; now++)
        {
            for(int next:graph[now])
            {
                if(SCCMap[now]!=SCCMap[next])
                    new_graph[SCCMap[now]].push_back(SCCMap[next]);
            }
        }

        fill(visited,visited+1010,false);

        //cout<<"SCC  "<<scc_num<<endl;

        flag=true;

        dfs_check(SCCMap[0]); ///  Initially the snake is at checkpoint 0.

        if(flag)
        {
            for(int now=0; now<scc_num; now++)
            {
                if(visited[now]==false)
                {
                    flag=false;
                    break;
                }
            }
        }

        if(flag)
            printf("Case %d: YES\n",i);
        else
            printf("Case %d: NO\n",i);

    }

    return 0;
}