• [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。

     1 #include <algorithm>
     2 #include <iostream>
     3 #include <iomanip>
     4 #include <cstring>
     5 #include <climits>
     6 #include <complex>
     7 #include <fstream>
     8 #include <cassert>
     9 #include <cstdio>
    10 #include <bitset>
    11 #include <vector>
    12 #include <deque>
    13 #include <queue>
    14 #include <stack>
    15 #include <ctime>
    16 #include <set>
    17 #include <map>
    18 #include <cmath>
    19 
    20 using namespace std;
    21 
    22 const int maxn = 10;
    23 typedef struct Matrix {
    24     int m[maxn][maxn];
    25     int r;
    26     int c;
    27     Matrix(){
    28         r = c = 0;
    29         memset(m, 0, sizeof(m));
    30     } 
    31 } Matrix;
    32 
    33 Matrix mul(Matrix m1, Matrix m2, int mod) {
    34     Matrix ans = Matrix();
    35     ans.r = m1.r;
    36     ans.c = m2.c;
    37     for(int i = 1; i <= m1.r; i++) {
    38         for(int j = 1; j <= m2.r; j++) {
    39                for(int k = 1; k <= m2.c; k++) {
    40                 if(m2.m[j][k] == 0) continue;
    41                 ans.m[i][k] = ((ans.m[i][k] + m1.m[i][j] * m2.m[j][k] % mod) % mod) % mod;
    42             }
    43         }
    44     }
    45     return ans;
    46 }
    47 
    48 Matrix quickmul(Matrix m, int n, int mod) {
    49     Matrix ans = Matrix();
    50     for(int i = 1; i <= m.r; i++) {
    51         ans.m[i][i]  = 1;
    52     }
    53     ans.r = m.r;
    54     ans.c = m.c;
    55     while(n) {
    56         if(n & 1) {
    57             ans = mul(m, ans, mod);
    58         }
    59         m = mul(m, m, mod);
    60         n >>= 1;
    61     }
    62     return ans;
    63 }
    64 
    65 int a, b, n, m;
    66 
    67 int main() {
    68     // freopen("in", "r", stdin);
    69        m = 7;
    70     while(~scanf("%d %d %d", &a, &b, &n)) {
    71         Matrix p;
    72         while(a < 0) a += m;
    73         while(b < 0) b += m;
    74         p.r = 2, p.c = 1;
    75         p.m[1][1] = 1;
    76         p.m[2][1] = 1;
    77         if(n <= 4) {
    78             printf("%d
    ", p.m[4-n+1][1] % m);
    79             continue;
    80         }
    81         Matrix s;
    82         s.r = s.c = 2;
    83         s.m[1][1] = a, s.m[1][2] = b;
    84         s.m[2][1] = 1, s.m[2][2] = 0;
    85         s = quickmul(s, n-2, m);
    86         int ans = 0;
    87         for(int i = 1; i <= p.r; i++) {
    88             ans = (ans + (p.m[i][1] * s.m[1][i]) % m) % m;
    89         }
    90         printf("%d
    ", ans % m);
    91     }
    92     return 0;
    93 }
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  • 原文地址:https://www.cnblogs.com/kirai/p/5473756.html
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