HDU 3943 K-th Nya Number

K-th Nya Number

Time Limit: 1000ms

Memory Limit: 65536KB

This problem will be judged on HDU. Original ID: 3943
64-bit integer IO format: %I64d      Java class name: Main

Arcueid likes nya number very much.
A nya number is the number which has exactly X fours and Y sevens(If X=2 and Y=3 , 172441277 and 47770142 are nya numbers.But 14777 is not a nya number ,because it has only 1 four).
Now, Arcueid wants to know the K-th nya number which is greater than P and not greater than Q.

Input

The first line contains a positive integer T (T<=100), indicates there are T test cases.
The second line contains 4 non-negative integers: P,Q,X and Y separated by spaces.
( 0<=X+Y<=20 , 0< P<=Q <2^63)
The third line contains an integer N(1<=N<=100).
Then here comes N queries.
Each of them contains an integer K_i (0<K_i <2^63).

Output

For each test case, display its case number and then print N lines.
For each query, output a line contains an integer number, representing the K_i-th nya number in (P,Q].
If there is no such number,please output "Nya!"(without the quotes).

Sample Input

1
38 400 1 1
10
1
2
3
4
5
6
7
8
9
10

Sample Output

Case #1:
47
74
147
174
247
274
347
374
Nya!
Nya!

Source

2011 Multi-University Training Contest 11 - Host by UESTC

 

解题：数位dp+二分

 1 #include <bits/stdc++.h>
 2 using namespace std;
 3 using LL = long long;
 4 const int maxn = 22;
 5 LL dp[maxn][maxn][maxn];
 6 int bt[maxn],x,y;
 7 LL dfs(int len,int a,int b,bool flag){
 8     if(len == -1) return a == x && y == b;
 9     if(!flag && dp[len][a][b] != -1) return dp[len][a][b];
10     int u = flag?bt[len]:9;
11     LL ans = 0;
12     for(int i = 0; i <= u; ++i){
13         if(i == 4) ans += dfs(len-1,a + 1,b,flag&&i == u);
14         else if(i == 7) ans += dfs(len-1,a,b + 1,flag&&i==u);
15         else ans += dfs(len-1,a,b,flag&&i==u);
16     }
17     if(!flag) dp[len][a][b] = ans;
18     return ans;
19 }
20 LL solve(LL x){
21     int cnt = 0;
22     while(x){
23         bt[cnt++] = x%10;
24         x /= 10;
25     }
26     return dfs(cnt - 1,0,0,true);
27 }
28 int main(){
29     int kase,m,cs = 1;
30     scanf("%d",&kase);
31     while(kase--){
32         LL P,Q,K;
33         scanf("%I64d%I64d%d%d",&P,&Q,&x,&y);
34         memset(dp,-1,sizeof dp);
35         scanf("%d",&m);
36         printf("Case #%d:\n",cs++);
37         LL tmp = solve(P);
38         while(m--){
39             scanf("%I64d",&K);
40             K += tmp;
41             LL low = P + 1,high = Q,ans = -1;
42             while(low <= high){
43                 LL mid = (low + high)>>1;
44                 if(solve(mid) >= K){
45                     ans = mid;
46                     high = mid - 1;
47                 }else low = mid + 1;
48             }
49             if(ans == -1) puts("Nya!");
50             else printf("%I64d\n",ans);
51         }
52     }
53     return 0;
54 }

View Code