K-based Numbers
Time Limit:1000MS Memory Limit:65536KB 64bit IO Format:%I64d & %I64u
Submit Status
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
2
10
90
/*************************************************************************
> File Name: i.cpp
> Author:yuan
> Mail:
> Created Time: 2014年11月09日 星期日 21时52分04秒
************************************************************************/
#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<cmath>
using namespace std;
long long ans[2][20];
int n,k;
int main()
{
cin>>n>>k;
memset(ans,0,sizeof(ans));
ans[0][1]=0;ans[1][1]=k-1;/*分别指定了长度为1,末尾数字为0的个数为0,不为的个数为k-1*/
for(int i=2;i<=n;i++)
{
ans[0][i]=ans[1][i-1];/*不能出现连续的0,则长度为n末尾为0的个数等于长度为n-1末尾不为0的个数*/
ans[1][i]=(k-1)*(ans[0][i-1]+ans[1][i-1]);/*长度为n，末尾数字不为0的个数：末尾数字可以是1—k-1中的任意一个
倒数第二位可以为0,也可以不为0*/
}
cout<<ans[0][n]+ans[1][n]<<endl;
return 0;
}