HDU [P5015] 233 Matrix

矩阵快速幂

按列递推

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <cstring>
#define ll long long
using namespace std;
const int MOD = 10000007;
int n, m;
struct Matrix {
	ll num[15][15];
	void clear() {
		memset(num, 0, sizeof(num));
	}
	void unit() {
		clear();
		for(int i = 0; i <= n + 1; i++) num[i][i] = 1;
	}
	Matrix operator * (const Matrix & b) {
		Matrix ans;
		ans.clear();
		for(int i = 0; i <= n + 1; i++) {
			for(int j = 0; j <= n + 1; j++) {
				ll tmp = 0ll;
				for(int k = 0; k <= n + 1; k++) {
					tmp += num[i][k] * b.num[k][j];
				}
				ans.num[i][j] = tmp % MOD;
			}
		}
		return ans;
	}
	Matrix operator ^ (ll k) {
		Matrix ans, tt = (*this);
		ans.unit();
		while(k) {
			if(k & 1ll) ans = ans * tt;
			tt = tt * tt;
			k >>= 1;
		}
		return ans;
	}
	void print() {
		for(int i = 0; i <= n + 1; i ++) {
			for(int j = 0; j <= n + 1; j++) {
				printf("%lld ", num[i][j]);
			}
			printf("
");
		}
	}
};
int main() {
	while(~scanf("%d %d", &n, &m)) {
		Matrix a, b;
		a.clear(); b.clear();
		for(int i = 0; i <= n + 1; i++) {
			if(i <= n) a.num[i][0] = 10; 
			a.num[i][n + 1] = 1;
		}
		for(int i = 1; i <= n; i++) {
			for(int j = 1; j <= i; j++) {
				a.num[i][j] = 1;
			}
		}
		b.num[0][0] = 23; b.num[n + 1][0] = 3;
		for(int i = 1; i <= n; i++) scanf("%lld", &b.num[i][0]);
		b = (a ^ m) * b;
		cout << b.num[n][0] << endl;
	}
	return 0;
}