POJ 2282 Counting Problem

Posted 2020-09-27

http://poj.org/problem?id=2282

题意:问[a,b]内 数字[0~9]分别出现多少次? a,b<=1e9.

数位DP dp[len][sta]:当前长度为len 数字y的初始状态为sta时,数字y共出现了多少次?

枚举当前位 如果为i!=num ,len-1位y的初始状态为sta

如果i==num ,len-1位y的初始状态为sta+1
当前位<0 则返回y的出现次数

#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
typedef long long ll;
const ll mod=1e9+7;
const int N=3e2+20;
ll a[N],num;
ll dp[N][N];
int dfs(int pos,int sta,bool lead,bool limit)
{
    if(pos==-1)
        return sta;
    if(!lead&&!limit&&dp[pos][sta]!=-1)
        return dp[pos][sta];
    int up=limit?a[pos]:9;
    int res=0;
    for(int i=0;i<=up;i++)
    {
        if(lead&&i==0)    
            res+=dfs(pos-1,sta,true,limit&&i==a[pos]);
        else
            res+=dfs(pos-1,sta+(i==num),false,limit&&i==a[pos]);
    }
    if(!lead&&!limit)
        dp[pos][sta]=res;
    return res;
}
int solve(int x)
{
    int pos=0;
    while(x)
    {
        a[pos++]=x%10;
        x/=10;
    }
    return dfs(pos-1,0,true,true);
}
int main()
{
    int a,b;
    memset(dp,-1,sizeof(dp));
    while(cin>>a>>b&&(a+b))
    {
        if(a>b)
            swap(a,b);
        num=0;
        cout<<solve(b)-solve(a-1);
        for(num=1;num<=9;num++)
            cout<<‘ ‘<<solve(b)-solve(a-1);    
        cout<<endl;
    }
    return 0;
}