1009. K-based Numbers

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 itsK-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 Ndigits.

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

用二進制位模擬，其中，0表示0,1表示非0的數

#include <iostream>
using namespace std;

bool hasSucZero(int i)
{
	int pre = i & 1, now;
	i = i>>1;
	while (i > 0)
	{
		now = i & 1;
		if (now == 0 && now == pre)
			return 0;
		else
		{
			pre = now;
			i = i>>1;
		}
	}
	return 1;
}

int typeOf(int i, int k)
{
	int ans = 1;
	while (i > 0)
	{
		if ((i&1) == 1)
			ans *= (k - 1);
		i = i>>1;
	}
	return ans;
}

int main()
{
	int i, k, n, ans = 0;
	cin>>n>>k;
	for (i=(1<<(n-1)); i<(1<<n); i++)
		if (hasSucZero(i))
			ans += typeOf(i, k);
	cout<<ans<<endl;
}