Timus 1009. K-based Numbers

/*
dp[i][0] i位数字的数首位为0 
dp[i][1] i位数字的数首位为1 

*/ 
#include<stdio.h>
int main()
{
    int n,k;
    int dp[20][2];
    while(~scanf("%d%d",&n,&k))
    {
        dp[1][0]=1; //只有一个数字的数首位为0那就只有0一个数 
        dp[1][1]=k-1;//只有一个数字的数首位不为0 ，对于k进制就只有k-1个数，除掉0嘛 
        for(int i=2;i<=16;i++)
        {
            dp[i][0]=dp[i-1][1];//i位数的数且首位为0，等于i-1位数的数首位为1的数，
            dp[i][1]=dp[i-1][0]*(k-1)+dp[i-1][1]*(k-1);//i位数的数且首位为1（即非0），等于i-1位首位为0数的数乘以首位可以放k-1个数（非0）和首位为 非0乘以k-1 
        }
        printf("%d\n",dp[n][1]);
    }
}

 

1009. K-based Numbers

Time Limit: 1.0 second
Memory Limit: 16 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

input	output
2 10	90