[Vijos1067]Warcraft III 守望者的烦恼（DP + 矩阵优化）

传送门

可知

f[i] = f[i - 1] + f[i - 2] + ... + f[i - k]

直接矩阵优化就好了

#include <cstdio>
#include <cstring>
#define p 7777777
#define LL long long

int n, k;

struct Matrix
{
	int n, m;
	LL a[11][11];
	Matrix()
	{
		n = m = 0;
		memset(a, 0, sizeof(a));
	}
};

inline Matrix operator * (Matrix x, Matrix y)
{
	int i, j, k;
	Matrix ans;
	ans.n = x.n;
	ans.m = y.m;
	for(i = 1; i <= x.n; i++)
		for(j = 1; j <= y.m; j++)
			for(k = 1; k <= y.n; k++)
				ans.a[i][j] = (ans.a[i][j] + x.a[i][k] * y.a[k][j]) % p;
	return ans;
}

inline Matrix operator ^ (Matrix x, int y)
{
	int i;
	Matrix ans;
	ans.n = ans.m = k;
	for(i = 1; i <= k; i++) ans.a[i][i] = 1;
	for(; y; y >>= 1)
	{
		if(y & 1) ans = ans * x;
		x = x * x;
	}
	return ans;
}

int main()
{
	int i;
	Matrix ans, sum;
	scanf("%d %d", &k, &n);
	ans.m = ans.a[1][1] = 1;
	sum.n = sum.m = ans.n = k;
	for(i = 1; i <= k; i++) sum.a[1][i] = 1;
	for(i = 2; i <= k; i++) sum.a[i][i - 1] = 1;
	sum = sum ^ n;
	ans = sum * ans;
	printf("%lld\n", ans.a[1][1]);
	return 0;
}