ural 1009

1009. K-based Numbers

Time limit: 1.0 second

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 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

ural上面的dp专题的第一题。。
dp[i][0] 表示前i位有多少种，并且第i位不是0, dp[i][1] 表示前i位有多少种， 并且第i位是0；
转移方程：
dp[i][0] = dp[i-1][0] * (k-1) + dp[i-1][1]*(k-1);
dp[i][1] = dp[i-1][0];
并且：
dp[1][0] = k-1;
dp[1][1] = 0;

#include <bits/stdc++.h>
using namespace std;
int n,k;
long long dp[30][3];
int main(){
cin>>n>>k;
dp[1][0] = k-1;
dp[1][1] = 0;
for(int i=2; i<=n; i++){
dp[i][0] = dp[i-1][0] * (k-1) + dp[i-1][1]*(k-1);
dp[i][1] = dp[i-1][0];
}
cout<<dp
[0]+dp
[1]<<endl;
return 0;
}