hdu4965---Fast matrix calculation (matrix)

Problem Description
One day, Alice and Bob felt bored again, Bob knows Alice was a girl who loves math and are just learning something about mat Rix, so he decided-make a crazy problem for her.

Bob has a six-faced dice which have numbers 0, 1, 2, 3, 4 and 5 on each face. At first, he'll choose a number N (4 <= n <=), and for N times, he keeps throwing the He dice for K times (2 < ; =k <= 6) and writes down their number on the top face to make an n*k matrix A, in which each element was not less than 0 And not greater than 5. Then he does similar thing again with a bit difference:he keeps throwing his dice for N times and each time repeat it for K Times to write down a k*n matrix B, with which each element was not less than 0 and not greater than 5. With the both Matrix A and B formed, Alice's task is to perform the following 4-step calculation.

Step 1:calculate a new n*n matrix C = a*b.
Step 2:calculate M = c^ (n*n).
Step 3:for each element x in M, calculate x% 6. All the remainders form a new matrix M '.
Step 4:calculate The sum of all the elements in M '.

Bob just made this problem for kidding and he sees Alice taking it serious, so he also wonders what's the answer is. And then Bob turn-to-because he is not good at math.

Input
The input contains several test cases. Each test case is starts with the integer n and K, indicating the numbers n and K described above. Then N lines follow, and each of the line have K integers between 0 and 5, representing Matrix A. Then K lines follow, and each line has N integers between 0 and 5, representing Matrix B.

The end of input is indicated by N = K = 0.

Output
For each case, output the sum of the "elements in M '" line.

Sample Input

4 2 5 5 4 4 5 4 0 0 4 2 5 5 1 3 1 5 6 3 1 2 3 0 3 0 2 3 4 4 3 2 2 5 5 0 5 0 3 4 5 1 1 0 5 3 2 3 3 2 2 0 0

Sample Output

14 56

Author
Sysu

Source
Multi-university Training Contest 9

Recommend
We have carefully selected several similar problems for you:5189 5188 5186 5185 5184

Directly according to the practice of test instructions, make a 1000*1000 matrix, light once multiplication time out

Notice that C = a*b
c * C * ....c = A(b*a) (b*a) ..... *b
Where B*a is a k*k matrix, do n^2-1 times of the fast power, so that the time to control down

/************************************************************************* > File Name:hdu4965.cpp > Auth Or:alex > Mail: [email protected] > Created time:2015 March 16 Monday 17:51 56 seconds ******************************** ****************************************/#include <map>#include <set>#include <queue>#include <stack>#include <vector>#include <cmath>#include <cstdio>#include <cstdlib>#include <cstring>#include <iostream>#include <algorithm>using namespace STD;Const DoublePI =ACOs(-1.0);Const intINF =0x3f3f3f3f;Const DoubleEPS =1e-15;typedef Long LongLL;typedefPair <int,int> PLL;inta[1010][Ten];intb[Ten][1010];intd[1010][1010];intans[1010][1010];intKclassmartix{ Public:intmat[Ten][Ten]; Martix () {memset(Mat,0,sizeof(MAT)); } Martixoperator* (ConstMartix &b)Const; martix&operator= (ConstMartix &b);}; Martix Martix::operator* (ConstMartix &b)Const{Martix C; for(inti =0; i < K; ++i) { for(intj =0; J < K; ++J) {C.mat[i][j] =0; for(intK =0; K < K; ++K) {C.mat[i][j] + = ThisMAT[I][K] * B.mat[k][j]; C.MAT[I][J]%=6; }        }    }returnC;} martix& Martix::operator= (ConstMartix &b) { for(inti =0; i < K; ++i) { for(intj =0; J < K; ++J) { ThisMAT[I][J] = B.mat[i][j]; }    }return* This;} Martix Fastpow (Martix A,intN) {Martix ans; for(inti =0; i < K; ++i) {Ans.mat[i][i] =1; } while(n) {if(N &1) {ans = ans * A; } N >>=1;    A = a * A; }returnAns;}intMain () {intN while(~scanf("%d%d", &n, &k)) {if(!n &&!) K) { Break; } for(inti =0; I < n; ++i) { for(intj =0; J < K; ++J) {scanf("%d", &a[i][j]); }        } for(inti =0; i < K; ++i) { for(intj =0; J < N; ++J) {scanf("%d", &b[i][j]); }} Martix C; for(inti =0; i < K; ++i) { for(intj =0; J < K; ++J) { for(intK =0; K < n;                    ++K) {C.mat[i][j] + = b[i][k] * A[k][j]; C.MAT[I][J]%=6; }}} C = Fastpow (c, n * N-1); for(inti =0; I < n; ++i) { for(intj =0; J < K; ++J) {D[i][j] =0; for(intK =0; K < K;                    ++K) {D[i][j] + = a[i][k] * C.mat[k][j]; D[I][J]%=6; }            }        }intres =0; for(inti =0; I < n; ++i) { for(intj =0; J < N; ++J) {Ans[i][j] =0; for(intK =0; K < K;                    ++K) {Ans[i][j] + = d[i][k] * B[k][j]; ANS[I][J]%=6;             } res + = Ans[i][j]; }        }printf("%d\n", res); }return 0;}

hdu4965---Fast matrix calculation (matrix)