ural1009(动态规划）

A - K-based NumbersURAL - 1009

 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. The numbers N and K in decimal notation separated by the line break.

2 10

90

思路:一位时有k-1种，两位时有k*(k-1)种，从第三位开始每一位都是(k-1)种乘上(dp[i-1]+dp[i-2])故递推式很容易就推出来了。

#include<iostream>
#include<string.h>
#include<algorithm>
#include<stdio.h>
using namespace std;

long long dp[21];
int n,k,i;
int main()
{
while(~scanf("%d%d",&n,&k))
{
dp[1]=k-1; dp[2]=(k-1)*k;
for (i=3;i<=n;i++)
dp[i]=(k-1)*(dp[i-1]+dp[i-2]);
printf("%lld\n",dp
);
}
return 0;
}