1 #include <iostream>
  2 #include <queue>
  3 #include <stack>
  4 #include <cstdio>
  5 #include <vector>
  6 #include <map>
  7 #include <set>
  8 #include <bitset>
  9 #include <algorithm>
 10 #include <cmath>
 11 #include <cstring>
 12
 
 #include <cstdlib>
 13 #include <string>
 14 #include <sstream>
 15 #include <time.h>
 16 #define x first
 17 #define y second
 18 #define pb push_back
 19 #define mp make_pair
 20 #define lson l,m,rt*2
 21 #define rson m+1,r,rt*2+1
 22 #define mt(A,B) memset(A,B,sizeof(A))
 23
 
 using namespace std;
 24 typedef long long LL;
 25 typedef unsigned long long ull;
 26 //const double PI = acos(-1);
 27 const int N=3e3+10;
 28 const LL mod=1e9+7;
 29 const int inf = 0x3f3f3f3f3f;
 30 const LL INF=0x3f3f3f3f3f3f3f3fLL;
 31 const double eps=1e-8;
 32 LL dp[300][20][2][2];
 33 int num[300];
 34
 
 char s[300];
 35 LL dfs(int pos,int pre,int limit,int flag,int zero)
 36 {
 37      LL res=0;
 38      if(pos<0)
 39      {
 40          if(zero)return 0;
 41          else return 1;
 42      }
 43      if(!limit&&dp[pos][pre][flag][zero]!=-1)return dp[pos][pre][flag][zero];
 44 
 45      int top=limit?num[pos]:9;
 46      if(zero)
 47      {
 48          for(int i=0;i<=top;i++)
 49          {
 50              res=(res+dfs(pos-1,i,limit&&(num[pos]==i),0,i==0))%mod;
 51          }
 52      }
 53      else
 54      {
 55          if(flag)
 56          {
 57              for(int i=pre;i<=top;i++)
 58              {
 59                  res=(res+dfs(pos-1,i,limit&&(num[pos]==i),1,0))%mod;
 60              }
 61          }
 62          else
 63          {
 64              for(int i=min(pre,top);i>=0;i--)
 65              {
 66                  res=(res+dfs(pos-1,i,limit&&(num[pos]==i),0,0))%mod;
 67              }
 68              for(int i=pre+1;i<=top;i++)
 69              {
 70                  res=(res+dfs(pos-1,i,limit&&(num[pos]==i),1,0))%mod;
 71              }
 72          }
 73      }
 74 
 75      if(!limit)dp[pos][pre][flag][zero]=res;
 76      return res;
 77 }
 78 void solve()
 79 {
 80      int n;
 81      mt(dp,-1);
 82      scanf("%s",s);
 83      n=strlen(s);
 84      for(int i=n-1,j=0;i>=0;i--,j++)num[j]=s[i]-‘0‘;
 85      printf("%lld\n",dfs(n-1,0,1,0,1));
 86 }
 87 int main()
 88 {
 89 #ifdef Local
 90     freopen("data.h","r",stdin);
 91     //freopen("out.txt","w",stdout);
 92 #endif
 93     //ios::sync_with_stdio(false);
 94     //cin.tie(0);
 95     //solve();
 96     int T,cas=1;
 97     cin>>T;
 98     while(T--)
 99     {
100         //printf("Case #%d: ",cas++);
101         solve();
102     }
103 #ifdef Local
104     cerr << "time: " << (LL) clock() * 1000 / CLOCKS_PER_SEC << " ms" << endl;
105 #endif
106     return 0;
107 }

HDU 6148 Valley Numer（數位DP）