CodeForces 567F DP Mausoleum

  1 #include <iostream>
  2 #include <cstdio>
  3 #include <cstring>
  4 #include <algorithm>
  5 #include <vector>
  6 #include <map>
  7 #define MP make_pair
  8 using namespace std;
  9
 10 typedef long long LL;
 11
 12 const int maxn = 80;
 13
 14 int n, k;
 15
 16 vector<int> G[maxn], req[maxn];
 17
 18 LL d[maxn][maxn];
 19
 20 bool check(int L, int R, int l, int r)
 21 {
 22     for(int i = 0; i < G[l].size(); i++)
 23     {
 24         int v = G[l][i], t = req[l][i];
 25         if(t == -2)
 26         {
 27             if(v < L || v > R || v == r) return false;
 28         }
 29         else if(t == -1)
 30         {
 31             if(v < L || v > R) return false;
 32         }
 33         else if(!t)
 34         {
 35             if(v != r) return false;
 36         }
 37         else if(t == 1)
 38         {
 39             if(v >= L && v <= R && v != r) return false;
 40         }
 41         else
 42         {
 43             if(v >= L && v <= R) return false;
 44         }
 45     }
 46
 47     for(int i = 0; i < G[r].size(); i++)
 48     {
 49         int v = G[r][i], t = req[r][i];
 50         if(t == -2)
 51         {
 52             if(v < L || v > R || v == l) return false;
 53         }
 54         else if(t == -1)
 55         {
 56             if(v < L || v > R) return false;
 57         }
 58         else if(!t)
 59         {
 60             if(v != l) return false;
 61         }
 62         else if(t == 1)
 63         {
 64             if(v >= L && v <= R && v != l) return false;
 65         }
 66         else
 67         {
 68             if(v >= L && v <= R) return false;
 69         }
 70     }
 71
 72     return true;
 73 }
 74
 75 LL dp(int L, int R)
 76 {
 77     LL& ans = d[L][R];
 78     if(ans >= 0) return d[L][R];
 79     if(L + 1 == R)
 80     {
 81         if(check(L, R, L, R)) return 1LL;
 82         return 0;
 83     }
 84
 85     ans = 0;
 86
 87     if(check(L, R, L, L + 1))
 88         ans += dp(L + 2, R);
 89     if(check(L, R, L, R))
 90         ans += dp(L + 1, R - 1);
 91     if(check(L, R, R - 1, R))
 92         ans += dp(L, R - 2);
 93
 94     return ans;
 95 }
 96
 97 int main()
 98 {
 99     scanf("%d%d", &n, &k);
100     char eq[10];
101     while(k--)
102     {
103         int u, v;
104         scanf("%d", &u);
105         scanf("%s", eq);
106         scanf("%d", &v);
107
108         int t;
109         if(strcmp(eq, "<") == 0) t = -2;
110         else if(strcmp(eq, "<=") == 0) t = -1;
111         else if(strcmp(eq, "=") == 0) t = 0;
112         else if(strcmp(eq, ">=") == 0) t = 1;
113         else if(strcmp(eq, ">") == 0) t = 2;
114         else exit(1234);
115
116         if(u == v)
117         {
118             if(abs(t) <= 1) continue;
119             else { puts("0"); exit(0); }
120         }
121
122         req[u].push_back(t); req[v].push_back(-t);
123         G[u].push_back(v); G[v].push_back(u);
124     }
125
126     memset(d, -1, sizeof(d));
127
128     printf("%I64d\n", dp(1, n * 2));
129
130     return 0;
131 }

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