Description
A cellular automaton is a collection of cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules that describe the new state of a cell based on the states of neighboring cells. The order of the cellular automaton is the number of cells it contains. Cells of the automaton of order n are numbered from 1 to n.
The order of the cell is the number of different values it may contain. Usually, values of a cell of order m are considered to be integer numbers from 0 to m ? 1.
One of the most fundamental properties of a cellular automaton is the type of grid on which it is computed. In this problem we examine the special kind of cellular automaton — circular cellular automaton of order n with cells of order m. We will denote such kind of cellular automaton as n,m-automaton.
A distance between cells i and j in n,m-automaton is defined as min(|i ? j|, n ? |i ? j|). A d-environment of a cell is the set of cells at a distance not greater than d.
On each d-step values of all cells are simultaneously replaced by new values. The new value of cell i after d-step is computed as a sum of values of cells belonging to the d-enviroment of the cell i modulo m.
The following picture shows 1-step of the 5,3-automaton.
The problem is to calculate the state of the n,m-automaton after k d-steps.
Input
The first line of the input file contains four integer numbers n, m, d, and k (1 ≤ n ≤ 500, 1 ≤ m ≤ 1 000 000, 0 ≤ d < n?2 , 1 ≤ k ≤ 10 000 000). The second line contains n integer numbers from 0 to m ? 1 — initial values of the automaton’s cells.
Output
Output the values of the n,m-automaton’s cells after k d-steps.
Sample Input
sample input #1
5 3 1 1
1 2 2 1 2
sample input #2
5 3 1 10
1 2 2 1 2
Sample Output
sample output #1
2 2 2 2 1
sample output #2
2 0 0 2 2
Source
Northeastern Europe 2006
容易推出轉移矩陣,但是規模太大,還不行
觀察發現這個矩陣的每一行都是循環的,下一行的就是上一行向右循環移動一位,所以我們可以把矩陣乘法降到n^2,只用一維數組來保存,這樣再結合矩陣快速冪就可以ac了
/*************************************************************************
> File Name: POJ3150.cpp
> Author: ALex
> Mail: [email protected]
> Created Time: 2015年03月17日 星期二 20時42分20秒
************************************************************************/
#include