Hdu 6093 --- Rikka with Number (count), hdu6093 --- rikka

Hdu 6093 --- Rikka with Number (count), hdu6093 --- rikka

Question Link

 

Problem DescriptionAs we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them:

In radix d, a number K = (A1A2... am) d (Ai ε [0, d), A1 =0) is good if and only A1 −am is a permutation of numbers from 0 to d −1.

A number K is good if and only if there exists at least one d ≥ 2 and K is good under radix d.

Now, Yuta wants to calculate the number of good numbers in interval [L, R]

It is too difficult for Rikka. Can you help her?

 

InputThe first line contains a number t (1 ≤ t ≤ 20), the number of the testcases.

For each testcase, the first line contains two decimal numbers L, R (1 ≤ L ≤r ≤ 105000 ).

 

OutputFor each testcase, print a single line with a single number -- the answer modulo 998244353.

 

Sample Input25 20123456 123456789 Sample Output3114480 question: If a number x is expressed in the "d" notation, It is 0 ~ An arrangement of D-1 (cannot start with 0). Therefore, this number is called an "excellent number". If any number exists, the hexadecimal number must be 0 ~ In an arrangement of D-1, it is "excellent number". How many excellent numbers are there between L and R? Idea: Base-based computing, boundary searching, there must be a boundary between dl and dr. dl + 1 ~ All arrays in the dr-1 hexadecimal format are in the L ~ Between R. Official question:

 

The Code is as follows:

import java.math.BigInteger;import java.util.Scanner;public class Main {    static int MAXN = 1600;    static BigInteger[] dx = new BigInteger[MAXN];    static long MOD = 998244353;    static long [] fac = new long [MAXN];    static void Init(){        dx[0] = BigInteger.ZERO;        dx[1] = BigInteger.ZERO;        for(int i=2; i<MAXN; i++){            dx[i] = BigInteger.ZERO;            for(int j=i-1; j>=0; j--){                dx[i] = dx[i].multiply(BigInteger.valueOf(i)).add(BigInteger.valueOf(j));            }        }        fac[0] = fac[1] = 1;        for(int i=2; i<MAXN; i++) fac[i]=fac[i-1]*i%MOD;    }    static int Low(BigInteger x){        int low=0, high=MAXN-1;        while(low < high){            int mid = (low+high)/2;            if(dx[mid].compareTo(x)>=0)high = mid;            else low = mid+1;        }        return high;    }    public static void main(String[] args){        Init();        Scanner in = new Scanner(System.in);        int T = in.nextInt();        for(int cas=1; cas<=T; cas++){            int [] vis = new int [MAXN];            for(int i=0; i<MAXN; i++) vis[i] = 0;            BigInteger L, R;            L = in.nextBigInteger();            R = in.nextBigInteger();            int dl = 0, dr = 0;            dl = Low(L)+1;            dr = Low(R)-1;            long ans = fac[dr]-fac[dl-1];            ans = (ans%MOD+MOD)%MOD;            if(dl > dr) ans = 0;             dl--; dr++;                        long ans2=0;            BigInteger tmp = (BigInteger.valueOf(dl)).pow(dl-1);            for(int i=dl; i>=1; i--){                int top = L.divide(tmp).intValue();                if(i==dl && top==0) { ans2 = (ans2+fac[dl]-fac[dl-1])%MOD; break; }                int cnt=0;                for(int o=top+1;o<dl;o++) if(vis[o]==0) cnt++;                ans2 = (ans2+(cnt)*fac[i-1]%MOD)%MOD;                if(vis[top] == 1) break;                L = L.mod(tmp);                if(i==1 && vis[top]==0) ans2=ans2+1;                vis[top] = 1;                tmp = tmp.divide(BigInteger.valueOf(dl));            }                        long ans1 = 0;            for(int i=0; i<MAXN; i++) vis[i] = 0;            tmp = (BigInteger.valueOf(dr)).pow(dr-1);            for(int i=dr; i>=1; i--)            {                int top = R.divide(tmp).intValue();                if(i==dr && top==0) {ans1 = (ans1+fac[dr]-fac[dr-1]%MOD); break;}                int cnt=0;                for(int o=top+1;o<dr;o++) if(vis[o]==0) cnt++;                ans1 = (ans1+(cnt)*fac[i-1]%MOD)%MOD;                if(vis[top] == 1) break;                R = R.mod(tmp);                vis[top] = 1;                tmp = tmp.divide(BigInteger.valueOf(dr));            }//            System.out.println("ans1 -> "+ans1);//            System.out.println("ans2 -> "+ans2);//            System.out.println("ans  -> "+ans);//            System.out.println("DL -> "+dl);//            System.out.println("DR -> "+dr);            ans = ans+ans2 + fac[dr]-fac[dr-1]-ans1;            if(dl==dr) ans=ans2-ans1;            ans = (ans%MOD+MOD)%MOD;            System.out.println(ans);        }    }}