hdu 6148 数位dp

题意：中文题，求小于等于n的"山谷"数的个数

思路:数位dp，注意此题中状态转移与前导0有关即可。

代码：

#include<bits/stdc++.h>
using namespace std;
#define MEM(a,b) memset(a,b,sizeof(a))
#define bug puts("bug");
#define PB push_back
#define MP make_pair
#define X first
#define Y second
typedef unsigned long long ll;
typedef pair<int,int> pii;
const int maxn=1e5+10;
const int mod=1e9+7;
using namespace std;
ll f[200][20][2];
int len,a[105];
string str;
ll dfs(int p,int nu,int isup,int lim,int lead){
    if(p==str.size())return 1;
    if(!lead&&!lim&&f[p][nu][isup]!=-1)return f[p][nu][isup];
    ll ans=0;
    int up=lim?a[p]:9;
    for(int i=0;i<=up;i++){
        if(isup==0){
            if(i<=nu)ans=(ans+dfs(p+1,(lead&&i==0)?9:i,0,lim&&i==a[p],lead&&i==0))%mod;
            else ans=(ans+dfs(p+1,i,1,lim&&i==a[p],lead&&i==0))%mod;
        }
        else if(isup==1&&i>=nu)ans=(ans+dfs(p+1,i,1,lim&&i==a[p],lead&&i==0))%mod;
    }
    if(!lim&&!lead) return f[p][nu][isup]=ans%mod;
    return ans%mod;
}
int main(){
    int t;
    scanf("%d",&t);
    while(t--){
        cin>>str;
        for(int i=0;i<str.size();i++)a[i]=str[i]-'0';
        memset(f,-1,sizeof(f));
        ll ret=(dfs(0,9,0,1,1)-1LL+mod)%mod;
        cout<<ret<<endl;

    }
    return 0;
}