hdu1757 A simple Math problem (Matrix fast power)

Topic:

A Simple Math problem Time limit:3000/1000 MS (java/others) Memory limit:32768/32768 K (java/others)
Total submission (s): 3522 Accepted Submission (s): 2130


Problem Descriptionlele Now was thinking about a simple function f (x).

If x < f (x) = x.
If x >= f (x) = a0 * F (X-1) + A1 * F (x-2) + A2 * F (x-3) + ... + A9 * F (x-10);
and AI (0<=i<=9) can only be 0 or 1.

Now, I'll give A0 ~ A9 and positive integers k and M, and could you help Lele to Caculate f (k)%m.

Inputthe problem contains mutiple test cases. Please process to the end of file.
In each case, there'll be is the lines.
In the first line, there is, positive integers k and M. (K<2*10^9, M < 10^5)
In the second line, there is ten integers represent A0 ~ A9.

Outputfor per case, Output f (k)% m on one line.
Sample Input

10 99991 1 1 1 1 1 1 1 1 120 5001 0 1 0 1 0 1 0 1 0

Sample Output

45104

Authorlinle
Source2007 Provincial Training Team Practice (6) _linle session
Recommendlcy

Test instructions: Give the recursive formula of a function to find out its K term.

Idea: Matrix fast power.

Code:

#include <cstdlib> #include <cctype> #include <cstring> #include <cstdio> #include <cmath > #include <climits> #include <algorithm> #include <vector> #include <string> #include < iostream> #include <sstream> #include <map> #include <set> #include <queue> #include < stack> #include <fstream> #include <numeric> #include <iomanip> #include <bitset> #include <list> #include <stdexcept> #include <functional> #include <utility> #include <ctime> Using namespace std, #define PB push_back#define MP make_pair#define REP (i,x,n) for (int i=x;i< (n); ++i) #define for (I,l, h) for (int i= (l); i<= (h), ++i) #define FORD (i,h,l) for (int i= (h); i>= (l); i) #define SZ (x) ((int) (x). Size ()) #define All (x) (x). Begin (), (x). End () #define RI (x) scanf ("%d", & (x)) #define RII (x, Y) scanf ("%d%d", & (X), & (Y)) # Define RIII (x, Y, z) scanf ("%d%d%d", & (X), & (Y), & (z)) #define DRI (x) int (x); scanf ("%d", &x) #define DRII (x, y) int X, y; scanf ("%d%d", &x, &y) #define DRIII (x, y, z) int x, y, Z; scanf ("%d%d%d", &x, &y, &z) #define OI (x) printf ("%d", x), #define RS (x) scanf ("%s", (x)) #define MS0 (x) memset ( (x), 0, sizeof ((x))) #define MS1 (x) memset ((x),-1, sizeof ((x))) #define LEN (x) strlen (x) #define F first#define S second#def  Ine Swap (A, B) (a ^= B, b ^= A, a ^= b) #define Dpoint strcut node{int x, y} #define CMPD int cmp (const int &AMP;A,CONST int    &AMP;B) {return a>b;}/* #ifdef HOME freopen ("In.txt", "R", stdin); #endif */const int MOD = 1e9+7;typedef vector<int> vi;typedef vector<string> vs;typedef vector<double> Vd;typedef Long Long ll;typedef pair<int,int> pii;//#define Homeint Scan () {int res = 0, ch, flag = 0;if (ch = getcha R ()) = = '-')//determine positive and negative flag = 1;else if (ch >= ' 0 ' && ch <= ' 9 ')//Get complete number res = CH-' 0 '; while ((ch = getchar ()) > = ' 0 ' && ch <= ' 9 ') res = res * + CH-' 0 '; return flag? -res:res;}/*----------------Please-----does-----not-----HACK-----ME--------------------*/struct matrix{int m[15][15];    void Init () {MS0 (M); }};    Matrix Mul (Matrix A,matrix b,int M) {matrix C;    C.init (); for (int i=0;i<10;i++) for (int j=0;j<10;j++) for (int k=0;k<10;k++) {c.m[i][j]+= (long long) a.m[i    ][K]*B.M[K][J])%M;    C.m[i][j]%=m;} return c;}    Matrix Mypow (Matrix A,int k,int M) {matrix ans;    Ans.init ();    for (int i=0;i<10;i++) ans.m[i][i]=1;    Matrix Temp=a;        while (k) {if (k&1) Ans=mul (ans,temp,m);        k>>=1;    Temp=mul (TEMP,TEMP,M); } return ans;        int A[10];int Main () {int k,m;while (RII (k,m)!=eof) {if (k<10) {printf ("%d\n", k%m);    Continue    } for (int i=0;i<10;i++) RI (A[i]);    Matrix A;    A.init ();    for (int i=0;i<10;i++) a.m[0][i]=a[i];    for (int i=1;i<10;i++) a.m[i][i-1]=1;    Matrix Res=mypow (a,k-9,m);   int ans=0; for (int i=0;i<10;i++) ans= (ans+ (Long Long) res.m[0][i]* (9-i))%m;        printf ("%d\n", ans);} return 0;}

Copyright NOTICE: This article for Bo Master original article, without Bo Master permission not reproduced.

hdu1757 A simple Math problem (Matrix fast power)