HDU--5151（区间DP）
2014-12-27 23:34:16
思路：用dp[i][j]表示处理区间[i，j]的方案数，然后枚举区间[i，j]中最后坐下的人是k。
转移方程：dp[i][j] = Sima(dp[i][k - 1] * dp[k + 1][j] * C(j - i , k - i)) (i <= k <= j)
之所以乘以组合数是因为：看成给人安排座位，要在j - i步中安排调除k以外的j - i个人，选k - i步安排左边的人，另外j - k步安排右边的人。
1 #include <cstdio> 2 #include <cstring> 3 #include <cstdlib> 4 #include <cmath> 5 #include <vector> 6 #include <map> 7 #include <set> 8 #include <stack> 9 #include <queue> 10 #include <iostream> 11 #include <algorithm> 12 using namespace std; 13 #define lp (p << 1) 14 #define rp (p << 1|1) 15 #define getmid(l,r) (l + (r - l) / 2) 16 #define MP(a,b) make_pair(a,b) 17 typedef long long ll; 18 typedef unsigned long long ull; 19 const int INF = 1 << 30; 20 const ll mod = 1000000007; 21 22 int N,val[110]; 23 ll dp[110][110],c[210][210]; 24 25 int main(){ 26 for(int i = 0; i <= 200; ++i){ 27 c[i][0] = c[i][i] = 1; 28 for(int j = 1; j < i; ++j){ 29 c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % mod; 30 } 31 } 32 while(scanf("%d",&N) != EOF){ 33 for(int i = 1; i <= N; ++i) 34 scanf("%d",&val[i]); 35 memset(dp,0,sizeof(dp)); 36 for(int i = 1; i <= N; ++i) 37 dp[i][i] = dp[i][i - 1] = dp[i + 1][i] = 1; 38 for(int len = 1; len <= N; ++len){ 39 for(int i = 1; i + len <= N; ++i){ 40 int j = i + len; 41 for(int k = i; k <= j; ++k) if(k == i || k == j || (val[k - 1] == val[k + 1])){ 42 dp[i][j] = (dp[i][j] + ((dp[i][k - 1] * dp[k + 1][j]) % mod * c[j - i][k - i]) % mod) % mod; 43 } 44 } 45 } 46 printf("%I64d\n",dp[1][N]); 47 } 48 return 0; 49 }
