2020牛客多校第六场 - H Harmony Pairs

传送门：2020牛客多校第六场 - H Harmony Pairs

思路分析

$dp[pos][sum][lima][limb]$ 表示搜索到第$pos$位，差为$sum$，$a$，$b$有无限制的方案数
$sum$初始值1000防止负数溢出

AC代码

#include <bits/stdc++.h>
#define fi first
#define se second
#define ll long long
#define pb push_back
#define mp make_pair
#define fun function
#define sz(x) (x).size()
#define lowbit(x) (x)&(-x)
#define all(x) (x).begin(),(x).end()
#define mem(a,b) memset(a,b,sizeof(a))
 
namespace FastIO {
#define BUF_SIZE 100000
#define OUT_SIZE 100000
    bool IOerror=0;
    inline char nc() {
        static char buf[BUF_SIZE],*p1=buf+BUF_SIZE,*pend=buf+BUF_SIZE;
        if(p1==pend) {
            p1=buf;
            pend=buf+fread(buf,1,BUF_SIZE,stdin);
            if(pend==p1) {
                IOerror=1;
                return -1;
            }
        }
        return *p1++;
    }
    inline bool blank(char ch) {
        return ch==' '||ch=='\n'||ch=='\r'||ch=='\t';
    }
    template<class T> inline bool read(T &x) {
        bool sign=0;
        char ch=nc();
        x=0;
        for(; blank(ch); ch=nc());
        if(IOerror)return false;
        if(ch=='-')sign=1,ch=nc();
        for(; ch>='0'&&ch<='9'; ch=nc())x=x*10+ch-'0';
        if(sign)x=-x;
        return true;
    }
    template<class T,class... U>bool read(T& h,U&... t) {
        return read(h)&&read(t...);
    }
#undef OUT_SIZE
#undef BUF_SIZE
};
using namespace std;
using namespace FastIO;
 
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
 
const int INF = 0x3f3f3f3f;
const int mod = 1e9+7;
 
ll dp[1111][2222][2][2];
char s[1111];
 
ll dfs(int pos,int sum,int lima,int limb) {
    if(s[pos]=='\0') {
        return (sum>1000);
    }
 
    if(dp[pos][sum][lima][limb] !=-1) return dp[pos][sum][lima][limb];
     
    ll ans=0;
     
    int upb=limb?s[pos]-'0':9;
    for(int i=0; i<=upb; i++) {
        int upa=lima?i:9;
        for(int j=0; j<=upa; j++) {
            ans=(ans + dfs(pos+1,sum+j-i,lima&&j==i,limb&&i==upb))%mod;
        }
    }
    return dp[pos][sum][lima][limb]=ans;
}
 
int main() {
 
#ifdef xiaofan
    freopen("1.in","r",stdin);
    freopen("1.out","w",stdout);
#endif
 
    mem(dp,-1);
    scanf("%s",s+1);
    printf("%lld\n",dfs(1,1000,1,1));
 
 
 
 
    return 0;
}