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 }