QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#49544#4543. SumireYeruihuaAC ✓272ms3776kbC++2.4kb2022-09-21 22:00:292022-09-21 22:00:30

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2022-09-21 22:00:30]
  • 评测
  • 测评结果:AC
  • 用时:272ms
  • 内存:3776kb
  • [2022-09-21 22:00:29]
  • 提交

answer

#include <bits/stdc++.h>
#define IO ios::sync_with_stdio(false), cin.tie(0), cout.tie(0)
#define N 100005
using namespace std;
typedef long long ll;
const int mod = 1e9 + 7;
ll k, b, d, l, r;
ll dp[65][65][2][2]; //前i位,有j位是d,当前位是否有最高位限制,是否有前导0 的方案数
ll digit[65];

ll qpow(ll a,ll b){
    if(a==0)
        return 0;//0^0=0
    ll ans = 1;
    b %= mod;
    while(b){
        if(b&1)
            ans = ans * a % mod;
        b >>= 1;
        a = a * a % mod;
    }
    return ans;
}

ll dfs(int pos,int cnt,int lim,int lead){
    if(!pos)
        return qpow(cnt, k);
    if(dp[pos][cnt][lim][lead] != -1){
        return dp[pos][cnt][lim][lead];
    }
    int up = lim ? digit[pos] : (b - 1);
    ll res = 0;
    if(d==up){
        res += dfs(pos - 1, cnt + 1, lim, 0); //填d
        if(lead){
            res += dfs(pos - 1, cnt, 0, 1);    //填0
            res += (up - 1) * dfs(pos - 1, cnt, 0, 0) % mod;  //不填up和0
        }
        else
            res += up * dfs(pos - 1, cnt, 0, 0) % mod; //不填d
    }
    else if(d==0){
        res += dfs(pos - 1, cnt, lim, 0);//填up
        res += (up - 1) * dfs(pos - 1, cnt, 0, 0) % mod;//填up和d
        if(lead){
            res += dfs(pos - 1, cnt, 0, 1);//0
        }
        else
            res += dfs(pos - 1, cnt + 1, 0, 0);//d
    }
    else if(up>d){
        res += dfs(pos - 1, cnt + 1, 0, 0) + dfs(pos - 1, cnt, lim, 0);//d,up
        if(lead){
            res += dfs(pos - 1, cnt, 0, 1);//0
            res += (up - 2) * dfs(pos - 1, cnt, 0, 0) % mod; //  ! up,d,0
        }
        else
            res += (up - 1) * dfs(pos - 1, cnt, 0, 0) % mod; //  ! up,d
    }
    else{
        res += dfs(pos - 1, cnt, lim, 0);// up
        if(lead){
            res += dfs(pos - 1, cnt, 0, 1);// 0
            res += (up - 1) * dfs(pos - 1, cnt, 0, 0) % mod; //! 0,up
        }
        else
            res += up * dfs(pos - 1, cnt, 0, 0) % mod; // !up
    }
    return dp[pos][cnt][lim][lead] = (res % mod);
}


ll cal(ll x){
    memset(dp, -1, sizeof(dp));
    int pos = 0;
    while(x){
        digit[++pos] = x % b;
        x /= b;
    }
    return dfs(pos, 0, 1, 1);
}

int main(){
    IO;
    int T;
    cin >> T;
    while(T--){
        cin >> k >> b >> d >> l >> r;
        cout << (cal(r) - cal(l - 1) + mod) % mod << endl;
    }
    return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 272ms
memory: 3776kb

input:

10000
3 207891369 69789899 964252340141144201 993463302889356041
3 747663427 196567324 607861784354966835 737019014793415965
7 4 1 75021281026163040 281275352760223247
159801714 6 4 57793681483331990 719907284728404544
760336565 3 2 640278753805042190 790056554571568287
3 3 0 370833904610234656 7289...

output:

348402080
920411258
659717287
394377489
330035010
995308641
312874977
375991223
465046227
263340736
704957449
599053093
345964631
546866401
355527840
906886371
165223493
924963116
97531004
174290409
257548623
852781447
29936714
204554940
926403980
440327688
351876140
824109444
816114821
745424255
69...

result:

ok 10000 lines