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Hdu1588Gauss Fibonacci矩阵
题意:求 g(i)=k*i+b; f(g(i)) for 0<=i<n。
#include <cstdio>#include <algorithm>#include <iostream>#include <string.h>typedef long long LL;LL M;using namespace std;struct Matrix{ LL m[4][4];};Matrix Mul(Matrix a, Matrix b){ Matrix ans; for (LL i = 0; i < 2; i++) for (LL j = 0; j < 2; j++){ ans.m[i][j] = 0; for (LL k = 0; k < 2; k++) ans.m[i][j] += a.m[i][k] * b.m[k][j]; ans.m[i][j] %= M; } return ans;}Matrix add(Matrix a, Matrix b){ for (LL i = 0; i < 2; i++) for (LL j = 0; j < 2; j++) a.m[i][j] += b.m[i][j], a.m[i][j] %= M; return a;}Matrix quick(Matrix a, LL b){ Matrix ans; for (LL i = 0; i < 2; i++) for (LL j = 0; j < 2; j++) ans.m[i][j] = (i == j); while (b){ if (b & 1) ans = Mul(ans, a); a = Mul(a, a); b >>= 1; } return ans;}Matrix solve(Matrix a, LL len){ if (len == 1){ Matrix ans; for (int i = 0; i<2; i++) for (int j = 0; j<2; j++) ans.m[i][j] = (i == j); return ans; } Matrix ans = solve(a, len >> 1); Matrix t = quick(a, (len >> 1)); t = Mul(t, ans); ans = add(ans, t); if (len & 1) return add(ans, quick(a, len - 1)); return ans;}void gao(LL n, LL k, LL b){ Matrix ans; ans.m[0][0] = 1; ans.m[0][1] = 1; ans.m[1][0] = 1; ans.m[1][1] = 0; Matrix t = quick(ans, k); Matrix gg = solve(t, n); gg = Mul(gg, quick(ans, b)); cout << gg.m[0][1] % M << endl;}int main(){ LL n, k, b; while (cin >> k >> b >> n >> M){ gao(n, k, b); } return 0;}
Hdu1588Gauss Fibonacci矩阵
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