[51NOD1126]求递推序列的第n项(矩阵快速幂)

时间:2023-03-09 01:50:05
[51NOD1126]求递推序列的第n项(矩阵快速幂)

题目链接:http://www.51nod.com/onlineJudge/questionCode.html#!problemId=1126

存在参数a,b为负数的情况。这时候要这么处理:

根据mod值(7)加至刚好大于0。

否则有些样例是过不去的。

 #include <algorithm>
#include <iostream>
#include <iomanip>
#include <cstring>
#include <climits>
#include <complex>
#include <fstream>
#include <cassert>
#include <cstdio>
#include <bitset>
#include <vector>
#include <deque>
#include <queue>
#include <stack>
#include <ctime>
#include <set>
#include <map>
#include <cmath> using namespace std; const int maxn = ;
typedef struct Matrix {
int m[maxn][maxn];
int r;
int c;
Matrix(){
r = c = ;
memset(m, , sizeof(m));
}
} Matrix; Matrix mul(Matrix m1, Matrix m2, int mod) {
Matrix ans = Matrix();
ans.r = m1.r;
ans.c = m2.c;
for(int i = ; i <= m1.r; i++) {
for(int j = ; j <= m2.r; j++) {
for(int k = ; k <= m2.c; k++) {
if(m2.m[j][k] == ) continue;
ans.m[i][k] = ((ans.m[i][k] + m1.m[i][j] * m2.m[j][k] % mod) % mod) % mod;
}
}
}
return ans;
} Matrix quickmul(Matrix m, int n, int mod) {
Matrix ans = Matrix();
for(int i = ; i <= m.r; i++) {
ans.m[i][i] = ;
}
ans.r = m.r;
ans.c = m.c;
while(n) {
if(n & ) {
ans = mul(m, ans, mod);
}
m = mul(m, m, mod);
n >>= ;
}
return ans;
} int a, b, n, m; int main() {
// freopen("in", "r", stdin);
m = ;
while(~scanf("%d %d %d", &a, &b, &n)) {
Matrix p;
while(a < ) a += m;
while(b < ) b += m;
p.r = , p.c = ;
p.m[][] = ;
p.m[][] = ;
if(n <= ) {
printf("%d\n", p.m[-n+][] % m);
continue;
}
Matrix s;
s.r = s.c = ;
s.m[][] = a, s.m[][] = b;
s.m[][] = , s.m[][] = ;
s = quickmul(s, n-, m);
int ans = ;
for(int i = ; i <= p.r; i++) {
ans = (ans + (p.m[i][] * s.m[][i]) % m) % m;
}
printf("%d\n", ans % m);
}
return ;
}