[UVA1292 / poj1463] Strategic game

Consider plain search. For each node on the tree, the state is only selected or not selected.

And it is obvious: if the current node is selected, the child node can be selected or not; and if the current node is not selected, the child node must be selected.

It is easy to see that the search trees thus generated will have a lot of overlap. So consider memoized search.

Use an array d[cur][2] to record the search results of the current node selected (d[cur][1]) or not selected (d[cur][0]).

Ultimately, the time complexity is O(n) level.

Code below:

 1 #include <cstdio>
 2 #include <iostream>
 3 #include <vector>
 4 #include <cstring>
 5 using namespace std;
 6 const int MAXN = 1500 + 20;
 7 const int INF = 0x7f7f7f7f;
 8 
 9 inline int read()
10 {
11     int x = 0; char ch = getchar();
12     while(!isdigit(ch)) ch = getchar();
13     while(isdigit(ch)) x = x * 10 + ch - '0', ch = getchar();
14     return x;
15 }
16 
17 int N;
18 vector<int> g[MAXN];
19 int d[MAXN][2];
20 
21 inline void clean()
22 {
23     for(int i = 0; i <= N; i++)
24         g[i].clear();
25     memset(d, 0x7f, sizeof(d));
26 }
27 
28 int dfs(int cur, bool opt, int fa)
29 {
30     if(g[cur].size() == 1 && g[cur][0] == fa)
31         return opt;
32         
33     int ans = 0;
34     if(!opt)
35     {
36         for(int i = 0; i < (int) g[cur].size(); i++)
37         {
38             int v = g[cur][i];
39             if(v != fa)
40             {
41                 if(d[v][true] == INF) d[v][true] = dfs(v, true, cur);
42                 ans += d[v][true];
43             }
44         }
45     }
46     else
47     {
48         for(int i = 0; i < (int) g[cur].size(); i++)
49         {
50             int v = g[cur][i];
51             if(v != fa)
52             {
53                 if(d[v][true] == INF) d[v][true] = dfs(v, true, cur);
54                 if(d[v][false] == INF) d[v][false] = dfs(v, false, cur);
55                 ans += min(d[v][false], d[v][true]);
56             }
57         }
58         ans++;
59     }
60     return ans;
61 }
62 
63 inline void solve()
64 {
65     cout<<min(dfs(0, true, 0), dfs(0, false, 0))<<endl;
66 }
67 
68 int main()
69 {
70     //freopen("1292.txt", "r", stdin);
71     while(cin>>N)
72     {
73         clean();
74         int u, v, c;
75         for(int i = 1; i <= N; i++)
76         {
77             u = read(), c = read();
78             for(int j = 1; j <= c; j++)
79             {
80                 v = read();
81                 g[u].push_back(v);
82                 g[v].push_back(u);
83             }
84         }
85         solve();
86     }
87     return 0;
88 }