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HDU 5015 233 Matrix 矩阵快速幂
可以构造如下矩阵
A:
1 0 0 0 0 0 0 0 0 0 0 0
1 10 0 0 0 0 0 0 0 0 0 0
1 10 1 0 0 0 0 0 0 0 0 0
1 10 1 1 0 0 0 0 0 0 0 0
1 10 1 1 1 0 0 0 0 0 0 0
1 10 1 1 1 1 0 0 0 0 0 0
1 10 1 1 1 1 1 0 0 0 0 0
1 10 1 1 1 1 1 1 0 0 0 0
1 10 1 1 1 1 1 1 1 0 0 0
1 10 1 1 1 1 1 1 1 1 0 0
1 10 1 1 1 1 1 1 1 1 1 0
1 10 1 1 1 1 1 1 1 1 1 1
A0:
3
233
a0+233
a0+a1+233
a0+a1+a2+233
....
这样就有第m列为A^(m-1)*A0
#include <cstdio>#include <cstring>#include <algorithm>#include <queue>#include <stack>#include <map>#include <set>#include <climits>#include <iostream>#include <string>using namespace std; #define MP make_pair#define PB push_backtypedef long long LL;typedef unsigned long long ULL;typedef vector<int> VI;typedef pair<int, int> PII;typedef pair<double, double> PDD;const int INF = INT_MAX / 3;const double eps = 1e-8;const LL LINF = 1e17;const double DINF = 1e60;const LL mod = 1e7 + 7;const int maxn = 15;struct Matrix { int n, m; LL data[maxn][maxn]; Matrix(int n = 0, int m = 0): n(n), m(m) { memset(data, 0, sizeof(data)); } void print() { for(int i = 1; i <= n; i++) { for(int j = 1; j <= m; j++) { cout << data[i][j] << " "; } cout << endl; } }};Matrix operator * (Matrix a, Matrix b) { Matrix ret(a.n, b.m); for(int i = 1; i <= a.n; i++) { for(int j = 1; j <= b.m; j++) { for(int k = 1; k <= a.m; k++) { ret.data[i][j] += a.data[i][k] * b.data[k][j]; ret.data[i][j] %= mod; } } } return ret;}Matrix pow(Matrix mat, LL p) { Matrix ret(mat.n, mat.m); if(p == 0) { for(int i = 1; i <= mat.n; i++) ret.data[i][i] = 1; return ret; } if(p == 1) return mat; ret = pow(mat * mat, p / 2); if(p & 1) ret = ret * mat; return ret;}int main() { Matrix A(12, 12); A.data[1][1] = 1; for(int i = 2; i <= 12; i++) { A.data[i][1] = 1; A.data[i][2] = 10; } for(int i = 3; i <= 12; i++) { for(int j = 1, k = 3; j < i - 1; j++, k++) { A.data[i][k] = 1; } } A.print(); LL n, m; while(cin >> n >> m) { LL a[11] = {0}; for(int i = 1; i <= n; i++) cin >> a[i]; Matrix A0(12, 1); A0.data[1][1] = 3; A0.data[2][1] = 233; for(int i = 3, j = 1; i <= 12; i++, j++) { A0.data[i][1] = a[j] + A0.data[i - 1][1]; } Matrix ans = pow(A, m - 1) * A0; cout << ans.data[n + 2][1] << endl; } return 0;}
HDU 5015 233 Matrix 矩阵快速幂
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