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URAL1009——DP——K-based Numbers

时间:2015-05-06 21:06:40      阅读:131      评论:0      收藏:0      [点我收藏+]

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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

inputoutput
2
10
90
 大意:和flag那道一样,如果前面是1的话,当前状态是由dp[n-1]转移过来,若果前面是0的话说明前面的前面是1当前的状态是由dp[n-2]转移过来的(0是肯定要的),对于每一种情况都有(k-1)种方法,一开始考虑0的状态想错了。。WA了几发
#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

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原文地址:http://www.cnblogs.com/zero-begin/p/4482981.html

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