URAL1009——DP——K-based Numbers

標籤：

Description

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

input	output
210	90

 大意：和flag那道一樣，如果前面是1的話,目前狀態是由dp[n-1]轉移過來，若果前面是0的話說明前面的前面是1當前的狀態是由dp[n-2]轉移過來的（0是肯定要的），對於每一種情況都有（k-1）種方法，一開始考慮0的狀態想錯了。。WA了幾發

#include<cstdio>#include<cstring>#include<algorithm>using namespace std;int main(){    long long dp[200];    int n,k;    while(~scanf("%d%d",&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] + dp[i-2]);        printf("%lld\n",dp[n]);    }    return 0;}

　　

URAL1009——DP——K-based Numbers