Fast power can effectively reduce the amount of calculation by simplifying equation;

8 5 ^ e.g., without in any way simplification, it is 8 * 8 * 8 * 8 * 8;

Fast power index idea is to decompose, thereby reducing the number of calculations, the reference index is a secondary system on separation;

For 5, can be made into two strings 101, so 5 + 0 = 2 ^ 2 ^ 2;

Therefore, 8 ^ 1 ^ 5 = 8 * 8 ^ 4, thereby effectively calculated from twice to five times of the calculation;

int quickpow ( int A, int b) { int RES = . 1 ; // for storing results; int ANS = A; // used to store a binary b-th power; the while (! b = 0 ) { IF (b% 2 == . 1 ) RES * = ANS; ANS * = ANS; B / = 2 ; } return RES; }

It is worth noting that a ans * = ans, since each cycle of the original square is a ^ 2, it is equivalent to a ^ 2 * a ^ 2;

Matrices same thinking power and fast, and it is thought the use of decomposition, the decomposition product of the matrix, is that multiplication is matrix multiplication be substituted;

vector<vector<int>> multi(vector<vector<int>>m1, vector<vector<int>>m2) { vector<vector<int>> m3; m3.resize(n); for (int i = 0; i < n; i++) { m3[i].resize(n); } for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { for (int k = 0; k < n; k++) { m3[i][j] += m1[i][k] * m2[k][j]; } } } return m3; } vector<vector<int>> quckmatrix(vector<vector<int>> m) { vector<vector<int>> ans=m; vector<vector<int>> res; res.resize(n); for (int i = 0; i < n; i++) { RES [I] .resize (n-); } for (int I = 0; I <n-; I ++) { // matrix RES [I] [I] =. 1; } the while (k> 0) { // for k binary operation; IF (K == 2%. 1) { RES = Multi (RES, ANS); } K / = 2; ANS = Multi (ANS, ANS); } return RES; }