FZU 1692 Key problem (Construction matrix + rapid matrix power)

FZU 1692 Key problem (Construction matrix + rapid matrix power)

 

[Question]: 1. The question refers to a circle of n people. Each person initially has an ai apple and is now playing m games, after each game, I personally can add R * A (I + N-1) % n + L * A (I + 1) % n Apples (wrong question ), q: The number of apples for each person after the m-round game

[Idea ]:

 

According to the question, we can list the number of apples for each person after a round.

A0 = a0 + R * an-1 + L * a1

A1 = a1 + R * a0 + L * a2

.............................

An-1 = an-1 + R * an-2 + L * a0

3. Based on the second idea, we can construct the following matrix:

1 L 0... R a0'

R 1 L... * a1'

......

... R 1 L an-2 an-2'

L... R 1 an-1 an-1'

4. Then, based on 3, we can use the Matrix to quickly obtain the final answer, but the n of the question is 100 at the maximum, and m is 10 ^ 9 at the maximum, the time complexity of each case is O (Logm * n ^ 3). When n is at most 100, it will

5. We found that in the initial matrix, the matrix is a cyclical homogeneous structure, that is, each row of the matrix can be pushed from the previous row, so we only need to use O (n ^ 2) the first line of time is obtained, and then the remaining n-1 rows are obtained by recursion. The total time complexity is O (Logm * n ^ 2)

Code:

 

/*Problem id. FZU 1692RunID: 631373UserID: ACM_herongweiSubmit time: 2015-09-04 11:58:16Language: C++Length: 1806 Bytes.Result: Accepted*/#include 
 
  #include 
  
   #include 
   
    #include using namespace std;typedef long long LL;const int N=105;int arr[N];int n,m,L,R,MOD;struct mut{    LL mat[N][N];    mut()    {        memset(mat,0,sizeof(mat));    }    void init()    {        for(int i=0; i
    
     >=1;    }    return unit;}void solve(){    int ans=0;    mut unit,a;    scanf(%d %d %d %d %d,&n,&m,&R,&L,&MOD);    for(int i=0; i