传送门:https://www.luogu.org/problemnew/show/P5004
分析
动态规划转移方程是这样的\(f[i]=\sum^{i-m-1}_{j=0}f[j]\)。
那么很明显的是要构造举证,而且要维护前缀和,所以需要保留\(m+1\)项。
ac代码
#include <bits/stdc++.h>
#define ll long long
#define ms(a, b) memset(a, b, sizeof(a))
#define inf 0x3f3f3f3f
#define N 25
#define mod ((int)1e9 + 7)
using namespace std;
template <typename T>
inline void read(T &x) {
x = 0; T fl = 1;
char ch = 0;
while (ch < '0' || ch > '9') {
if (ch == '-') fl = -1;
ch = getchar();
}
while (ch >= '0' && ch <= '9') {
x = (x << 1) + (x << 3) + (ch ^ 48);
ch = getchar();
}
x *= fl;
}
ll n;
int m;
struct Matrix {
int a[N][N], x, y;
void init() {
memset(a, 0, sizeof(a));
x = y = 0;
}
Matrix operator *(const Matrix &rhs) const{
Matrix res; res.init();
res.x = x, res.y = rhs.y;
int c = y;
for (int i = 1; i <= x; i ++) {
for (int j = 1; j <= y; j ++) {
for (int k = 1; k <= c; k ++) {
res.a[i][j] = (res.a[i][j] + (ll) a[i][k] * rhs.a[k][j]) % mod;
}
}
}
return res;
}
Matrix power(Matrix a, ll b) {
Matrix res;
res.init();
res.x = res.y = a.x;
for (int i = 1; i <= res.x; i ++) res.a[i][i] = 1;
for (; b; b >>= 1) {
if (b & 1) res = res * a;
a = a * a;
}
return res;
}
}a, b;
int main() {
read(n); read(m);
if (n <= m) {
printf("%lld\n", n + 1);
return 0;
}
a.x = a.y = m + 2, b.x = m + 2, b.y = 1;
for (int i = 2; i <= m + 2; i ++)
b.a[i][1] = 1;
b.a[1][1] = m + 1;
a.a[1][1] = a.a[1][2] = 1;
a.a[2][2] = a.a[2][m + 2] = 1;
for (int i = 3; i <= m + 2; i ++) a.a[i][i - 1] = 1;
a = a.power(a, n - m);
b = a * b;
printf("%d\n", b.a[1][1]);
return 0;
}
原文地址:https://www.cnblogs.com/chhokmah/p/10568032.html
时间: 2024-11-09 09:56:02