传送门
比较套路的题,首先也有个明显的状态 f [ p o s ] [ n u m ] [ s u m ] f[pos][num][sum] f[pos][num][sum]表示到了 p o s pos pos位,当前数为 n u m num num,各位数字之和为 s u m sum sum。由于 a , b ≤ 1 e 18 a,b\le1e18 a,b≤1e18,所以显然是不行的。看到整除就可以考虑是否可以通过将第二维取模来优化状态呢?我们发现第三维最多只有 9 ∗ 18 9*18 9∗18个数,所以我们枚举第三维的约数,让后将 n u m num num模上约数即可,这样状态只有 20 ∗ 9 ∗ 18 ∗ 9 ∗ 18 20*9*18*9*18 20∗9∗18∗9∗18个了,再乘上枚举约数 9 ∗ 18 9*18 9∗18,复杂度约为 85030560 85030560 85030560,显然可以过掉。
// Problem: P4127 [AHOI2009]同类分布 // Contest: Luogu // URL: https://www.luogu.com.cn/problem/P4127 // Memory Limit: 125 MB // Time Limit: 3000 ms // // Powered by CP Editor (https://cpeditor.org) //#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math") //#pragma GCC target("sse,sse2,sse3,ssse3,sse4.1,sse4.2,avx,avx2,popcnt,tune=native") //#pragma GCC optimize(2) #include<cstdio> #include<iostream> #include<string> #include<cstring> #include<map> #include<cmath> #include<cctype> #include<vector> #include<set> #include<queue> #include<algorithm> #include<sstream> #include<ctime> #include<cstdlib> #include<random> #include<cassert> #define X first #define Y second #define L (u<<1) #define R (u<<1|1) #define pb push_back #define mk make_pair #define Mid ((tr[u].l+tr[u].r)>>1) #define Len(u) (tr[u].r-tr[u].l+1) #define random(a,b) ((a)+rand()%((b)-(a)+1)) #define db puts("---") using namespace std; //void rd_cre() { freopen("d://dp//data.txt","w",stdout); srand(time(NULL)); } //void rd_ac() { freopen("d://dp//data.txt","r",stdin); freopen("d://dp//AC.txt","w",stdout); } //void rd_wa() { freopen("d://dp//data.txt","r",stdin); freopen("d://dp//WA.txt","w",stdout); } typedef long long LL; typedef unsigned long long ULL; typedef pair<int,int> PII; const int N=1000010,mod=1e9+7,INF=0x3f3f3f3f; const double eps=1e-6; LL a,b; int A[20],tot; int limit; LL f[20][9*18+10][9*18+10]; LL dp(int pos,int num,int sum,int flag) { if(sum>limit) return 0; if(pos==0) return num==0&&sum==limit; if(f[pos][num][sum]!=-1&&flag) return f[pos][num][sum]; int x=flag? 9:A[pos]; LL ans=0; for(int i=0;i<=x;i++) { ans+=dp(pos-1,(num*10+i)%limit,sum+i,flag||i<x); } if(flag) f[pos][num][sum]=ans; return ans; } LL solve(LL x) { tot=0; while(x) A[++tot]=x%10,x/=10; return dp(tot,0,0,0); } int main() { // ios::sync_with_stdio(false); // cin.tie(0); //cout<<20*9*18*9*18*9*18<<endl; cin>>a>>b; LL ans=0; for(int i=1;i<=9*18;i++) { limit=i; memset(f,-1,sizeof(f)); ans+=solve(b)-solve(a-1); } cout<<ans<<endl; return 0; } /* */