ural 1009 K-based Numbers



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

2
10

90

Problem Source: USU Championship 1997

Tags: dynamic programming  (

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DP题。。。不过不怎么清楚，先留个坑。。

#include <cstdio>
#include <algorithm>
#include <map>
#include <cstring>
#include <cmath>
#include <iostream>
using namespace std;
#define lson l , m , rt << 1
#define rson m + 1 , r , rt << 1 | 1
#define LL __int64
typedef long long ll;
#define PI 3.1415926
int mat[150][150];
int vis[150];
int b[150];
int n,l,flag;
int main()
{
    ll dp[50];
    int n,k;
    while(cin>>n>>k)
    {
        dp[0]=k-1;
        dp[1]=k*(k-1);
        for(int i=2;i<=n;i++)
            dp[i]=(k-1)*(dp[i-1]+dp[i-2]);
        cout<<dp[n-1]<<endl;
    }
}