ural 1009. K-based Numbers
2013-04-22 11:00
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1009. K-based Numbers
Time Limit: 1.0 secondMemory 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 N digits.
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 |
#include <iostream> #include <algorithm> #define MAX 20 using namespace std; int dp[MAX]={0}; int main(){ int n,k; cin >> n >> k; dp[1] = k-1; dp[2] =k*(k-1); for(int i = 3; i <= n; i ++ ){ dp[i] = (k-1)*dp[i-1]+(k-1)*dp[i-2]; } cout<< dp <<endl; return 0; }
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