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1009. K-based Numbers
Time limit: 0.5 second
Memory limit: 64 MB
Memory limit: 64 MB
Let’s consider K-based numbers, containing exactly N digits. We define a number to be valid if its K-based notation doesn’t contain two successive zeros. For example:
- 1010230 is a valid 7-digit number;
- 1000198 is not a valid number;
- 0001235 is not a 7-digit number, it is a 4-digit number.
Given two numbers N and K, you are to calculate an amount of valid K based numbers, containing Ndigits.
You may assume that 2 ≤ K ≤ 10; N ≥ 2; N + K ≤ 18.
Input
The numbers N and K in decimal notation separated by the line break.
Output
The result in decimal notation.
Sample
| input | output |
|---|---|
2 10 | 90 |
import java.io.BufferedReader;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.StringTokenizer;public class Main {public static void main(String[] args) {new Task().solve();}
}class Task {InputReader in = new InputReader(System.in);PrintWriter out = new PrintWriter(System.out);long[][][] dp = new long[19][2][11] ;int[] bit ;long dfs(int pos , int pre , int k){if(pos == -1){return 1 ;}if(dp[pos][pre][k] != -1){return dp[pos][pre][k] ;}long sum = 0 ;for(int i = 0 ; i < k ; i++){if(pre == 0 && i == 0){continue ;}sum += dfs(pos-1 , i == 0 ? 0 : 1 , k) ;}return dp[pos][pre][k] = sum ;}void solve() {for(int i = 0 ; i < 19 ; i++){for(int j = 0 ; j < 2 ; j++){Arrays.fill(dp[i][j] , -1) ;}}while(in.hasNext()){int n = in.nextInt() ;int k = in.nextInt() ;out.println(dfs(n-1 , 0 , k)) ;out.flush() ;} out.flush();}}class InputReader {public BufferedReader reader;public StringTokenizer tokenizer;public InputReader(InputStream stream) {reader = new BufferedReader(new InputStreamReader(stream), 32768);tokenizer = new StringTokenizer("");}private void eat(String s) {tokenizer = new StringTokenizer(s);}public String nextLine() {try {return reader.readLine();} catch (Exception e) {return null;}}public boolean hasNext() {while (!tokenizer.hasMoreTokens()) {String s = nextLine();if (s == null)return false;eat(s);}return true;}public String next() {hasNext();return tokenizer.nextToken();}public int nextInt() {return Integer.parseInt(next());}public int[] nextInts(int n){int[] nums = new int[n] ;for(int i = 0 ; i < n ; i++){nums[i] = nextInt() ;}return nums ;}public long nextLong() {return Long.parseLong(next());}public double nextDouble() {return Double.parseDouble(next());}public BigInteger nextBigInteger() {return new BigInteger(next());}}
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