洛谷 2476 [SCOI2008]着色方案

Posted 2020-10-29 Driver_Lao

50%的数据满足：1 <= k <= 5, 1 <= ci <= 3

100%的数据满足：1 <= k <= 15, 1 <= ci <= 5

【题解】

　　本题中ci很小，因此可以直接5维保存可以涂i块的油漆有多少种颜色。然后利用乘法原理进行DP

　　

 1 #include<cstdio>
 2 #include<algorithm>
 3 #define LL long long
 4 #define rg register
 5 #define N 16
 6 #define Mod (1000000007)
 7 using namespace std;
 8 LL f[N][N][N][N][N][6];
 9 bool v[N][N][N][N][N][6];
10 int n,cnt[6];
11 inline int read(){
12     int k=0,f=1; char c=getchar();
13     while(c<\'0\'||c>\'9\')c==\'-\'&&(f=-1),c=getchar();
14     while(\'0\'<=c&&c<=\'9\')k=k*10+c-\'0\',c=getchar();
15     return k*f;
16 }
17 LL dfs(int a,int b,int c,int d,int e,int last){
18     if(v[a][b][c][d][e][last]) return f[a][b][c][d][e][last];
19     if(a+b+c+d+e==0) return 1;
20     LL tmp=0;
21     if(a) tmp+=(a-(last==2))*dfs(a-1,b,c,d,e,1);
22     if(b) tmp+=(b-(last==3))*dfs(a+1,b-1,c,d,e,2);
23     if(c) tmp+=(c-(last==4))*dfs(a,b+1,c-1,d,e,3);
24     if(d) tmp+=(d-(last==5))*dfs(a,b,c+1,d-1,e,4);
25     if(e) tmp+=e*dfs(a,b,c,d+1,e-1,5);
26     v[a][b][c][d][e][last]=1;
27     return f[a][b][c][d][e][last]=(tmp%Mod);
28 }
29 int main(){
30     n=read();
31     for(rg int i=1;i<=n;i++){
32         int x=read();
33         cnt[x]++;
34     }
35     printf("%lld\\n",dfs(cnt[1],cnt[2],cnt[3],cnt[4],cnt[5],0));
36     return 0;
37 }

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