POJ3233 matrix Power Series "matrices fast Power"

Topic Links:

http://poj.org/problem?id=3233

Main topic:

Given a n*n matrix A and an integer k, it is required to calculate s = a + a^2 + a^3 + ... + a^k.

Ideas:

The a^i of each item is calculated by using the Matrix fast power, and then the matrix is added, taking into account that the K value is very large, all using

Two-part solution.

AC Code:

#include <iostream> #include <algorithm> #include <cstdio> #include <cstring>using namespace std;const int MAXN = 110;struct matrax{int M[MAXN][MAXN];} A,per;int n,m;void Init () {for (int i = 0, i < n; ++i) for (int j = 0; J < N; ++j) {scanf            ("%d", &a.m[i][j]);            A.M[I][J]%= m;        PER.M[I][J] = (i = = j);    }}matrax Add (Matrax A,matrax b) {Matrax C; for (int i = 0, i < n; ++i) {for (int j = 0; j < N; ++j) {C.m[i][j] = (A.m[i][j] + b.m[        I][J])% M; }} return C;}    Matrax Multi (Matrax A,matrax b) {Matrax C;            for (int i = 0, i < n; ++i) {for (int j = 0; j < N; ++j) {c.m[i][j] = 0;            for (int k = 0; k < N; ++k) {C.m[i][j] + = a.m[i][k] * B.m[k][j];        } C.m[i][j]%= m; }} return C;}    Matrax Power (int k) {Matrax P,ans = per;    p = A;      while (k) {  if (k&1) {ans = Multi (ans,p);        k--;            } else {k >>= 1;        p = Multi (p,p); }} return ans;    Matrax matraxsum (int k) {if (k = = 1) return A;    Matrax temp,b;    temp = Matraxsum (K/2);        if (k&1) {b = Power (k/2+1);        temp = ADD (Temp,multi (temp,b));    temp = ADD (temp,b);        } else {b = Power (K/2);    temp = ADD (Temp,multi (temp,b)); } return temp;}    int main () {int k;        while (~SCANF ("%d%d%d", &n,&k,&m)) {Init ();        Matrax ans = matraxsum (k); for (int i = 0, i < N; ++i) {for (int j = 0; j < N-1; ++j) {printf ("%d"            , Ans.m[i][j]);        } printf ("%d\n", ans.m[i][n-1]); }} return 0;}

POJ3233 matrix Power Series "matrices fast Power"