POJ 3150 Cellular Automaton(矩阵快速幂)
来源:互联网 发布:冲压模具书籍 知乎 编辑:程序博客网 时间:2024/06/09 19:07
Cellular Automaton
Time Limit: 12000MS Memory Limit: 65536K
Total Submissions: 3504 Accepted: 1421
Case Time Limit: 2000MS
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
这道题目的矩阵好找,但是由于n比较大,用n*n的矩阵再加上快速幂,是O(n^3*log k) 回超时。观察矩阵,发现矩阵是一个循环矩阵,无论矩阵取多少次方,矩阵的每一行相当于第一行向后推了一步,所以说是循环矩阵,这样我们只要计算矩阵的第一行就可以知道矩阵的其他行,所以只开一维数组效率就是O(n^2log k)
#include <iostream>#include <string.h>#include <stdlib.h>#include <algorithm>#include <math.h>#include <stdio.h>using namespace std;typedef long long int LL;int n,m,d,k;struct Node{ LL a[505];};Node multiply(Node a,Node b){ Node c; memset(c.a,0,sizeof(c.a)); for(int i=0;i<n;i++) { int cnt=(n-i)%n; for(int j=0;j<n;j++) { (c.a[i]+=(a.a[j]*b.a[cnt++])%m)%=m; if(cnt==n) cnt=0; } } return c;}Node get(Node a,int x){ Node c; memset(c.a,0,sizeof(c.a)); c.a[0]=1; for(x;x;x>>=1) { if(x&1) c=multiply(c,a); a=multiply(a,a); } return c;}int main(){ scanf("%d%d%d%d",&n,&m,&d,&k); Node a;Node b; memset(a.a,0,sizeof(a.a)); memset(b.a,0,sizeof(b.a)); for(int i=0;i<n;i++) scanf("%lld",&b.a[i]); a.a[0]=1; for(int i=1;i<=d;i++) a.a[i]=a.a[n-i]=1; a=get(a,k); a=multiply(b,a); for(int i=0;i<n;i++) if(i==n-1) printf("%lld\n",a.a[i]); else printf("%lld ",a.a[i]); return 0;}
- POJ 3150 Cellular Automaton(矩阵快速幂)
- poj 3150Cellular Automaton(矩阵快速幂)
- poj 3150 Cellular Automaton(矩阵快速幂)
- POJ 3150 Cellular Automaton(矩阵快速幂)
- POJ 3150 Cellular Automaton(矩阵快速幂)
- POJ 3150 Cellular Automaton --矩阵快速幂及优化
- [POJ 3150] Cellular Automaton (矩阵快速幂 + 矩阵乘法优化)
- POJ 3150 Cellular Automaton(矩阵快速幂+特殊矩阵的性质)
- poj3150 Cellular Automaton(矩阵快速幂)
- 【poj 3150】Cellular Automaton 矩阵
- Poj 3150 Cellular Automaton(矩阵快速幂, 循环矩阵快速幂)
- UVA - 1386 Cellular Automaton (矩阵快速幂)
- UvaLive 3704 Cellular Automaton (矩阵快速幂)
- UVA Live 3704 Cellular Automaton (循环矩阵+快速幂)
- LA 3704 Cellular Automaton / 矩阵快速幂
- LA 3704 Cellular Automaton (矩阵快速幂)
- [FFT] [矩阵快速幂] [POJ3150] Cellular Automaton
- POJ 3150 Cellular Automaton 矩阵dp
- javascript基础十(知识点类js中的跨域)
- 用sqlserver手动写个split(字符分割)
- 如何看待APP应用中的“意见反馈”功能
- 51Nod 1050 循环数组最大子段和(DP—最大子段和变形)
- 系统调用 open close ioct1
- POJ 3150 Cellular Automaton(矩阵快速幂)
- dream & game!
- Javascript-Arrays
- LeetCode94 Binary Tree Inorder Traversal(迭代实现) Java
- C++作业4
- Node.js#0基础
- Android 程序进入后台 恢复到前台
- ZOJ 2965 Accurately Say "CocaCola"!
- ext Ext.data.MemoryProxy做代理加载dom