2017 百度之星 复赛 Valley Numer（数位dp）

Valley Numer

数位dp，state标志前面若干位是否存在递增序列。

代码：

#include <bits/stdc++.h>
using namespace std;

typedef long long ll ;

const int max_n=105;
const int mod = 1000000007;

ll n;
ll dp[max_n][13][2], a[max_n];
string s;

ll dfs(int pos,int pre,int limit,int state)
{
    if(pos == -1) return 1;
    if(!limit && dp[pos][pre][state] != -1) return dp[pos][pre][state];
    
    ll tmp = 0;
    int up = limit?a[pos]:9;
    
    for(int i = 0; i <= up; i++)
    {
        if(pre==11 && i==0){
        //注意处理前导0的情况，全0的情况下要填入一个不影响结果的数字
            tmp = (tmp + dfs(pos-1, 11, limit&&i==up, 0))%mod;
            continue;
        }
        if(i<pre && state) continue;
        if(i<=pre)
            tmp = (tmp + dfs(pos-1, i, limit&&i==up, state))%mod;
        else
            tmp = (tmp + dfs(pos-1, i, limit&&i==up, 1))%mod;
    }
    if(!limit) dp[pos][pre][state] = tmp;
    return tmp;
}

ll solve()
{
    int pos = 0;
    for(int i = s.length()-1; i>=0; i--)
    {
        a[pos++] = (s[i]-'0');
    }
    return dfs(pos-1,11,1,0);
}

int main()
{
    int T;
	scanf("%d",&T);
    memset(dp, -1, sizeof(dp));
    while(T--)
    {
        cin>>s;
        printf("%I64d\n",solve()-1);
    }
    return 0;
}