cf 401D. Roman and Numbers 数位dp,状压
2015-02-04 23:05
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题意:给出两个数n,m,求x的个数,x需满足,x可由n的各位数字重新排列得到;x无前导零;x%m==0;
分析:比较简单的一道数位dp,由于n最多只有17位,可以状态压缩,dp[s][v]表示用掉集合s中的数,余数为v的个数,状态转移方程dp[s+k][(v*10+dig[k])%m]+=dp[s][v];
分析:比较简单的一道数位dp,由于n最多只有17位,可以状态压缩,dp[s][v]表示用掉集合s中的数,余数为v的个数,状态转移方程dp[s+k][(v*10+dig[k])%m]+=dp[s][v];
#include<iostream> #include<string> #include<cstring> #include<cstdio> #include<cmath> #include<iomanip> #include<map> #include<algorithm> #include<queue> #include<set> #define inf 10000000 #define pi acos(-1.0) #define eps 1e-8 #define seed 131 using namespace std; typedef pair<int,int> pii; typedef unsigned long long ULL; typedef long long LL; const int maxn=100005; LL n; int m; LL dp[1<<18][100]; int dig[18]; int d[10]; int main() { scanf("%I64d%d",&n,&m); int k=0; memset(d,0,sizeof(d)); while(n) { dig[k]=n%10; d[dig[k]]++; n/=10; k++; } LL ans=1; for(int i=0;i<10;i++) { while(d[i]>1) { ans*=d[i]; d[i]--; } } memset(dp,0,sizeof(dp)); dp[0][0]=1; for(int i=0;i<(1<<k);i++) { for(int j=0;j<m;j++) { if(dp[i][j]==0) continue; for(int f=0;f<k;f++) { if(i==0&&dig[f]==0) continue; if(!((1<<f)&i)) { dp[i|(1<<f)][(j*10+dig[f])%m]+=dp[i][j]; //dp[i|(1<<f)][(j*10+dig[f])%m]%=m; } } } } cout<<dp[(1<<k)-1][0]/ans; return 0; }
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