Milking Grid poj2185

使用KMP算法解决二维网格最小重复单元问题

最新推荐文章于 2022-10-25 15:57:00 发布

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最新推荐文章于 2022-10-25 15:57:00 发布

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原文链接：http://www.cnblogs.com/Tinamei/p/4803094.html

本文详细介绍了如何运用KMP算法解决二维网格中寻找最小重复单元的问题，通过实例展示了从行和列的角度进行匹配，最终计算出整个网格的最小单位面积。

Milking Grid

POJ - 2185

提交状态

已开启划词翻译

问题描述

Every morning when they are milked, the Farmer John's cows form a rectangular grid that is R (1 <= R <= 10,000) rows by C (1 <= C <= 75) columns. As we all know, Farmer John is quite the expert on cow behavior, and is currently writing a book about feeding behavior in cows. He notices that if each cow is labeled with an uppercase letter indicating its breed, the two-dimensional pattern formed by his cows during milking sometimes seems to be made from smaller repeating rectangular patterns.

Help FJ find the rectangular unit of smallest area that can be repetitively tiled to make up the entire milking grid. Note that the dimensions of the small rectangular unit do not necessarily need to divide evenly the dimensions of the entire milking grid, as indicated in the sample input below.

输入

* Line 1: Two space-separated integers: R and C

* Lines 2..R+1: The grid that the cows form, with an uppercase letter denoting each cow's breed. Each of the R input lines has C characters with no space or other intervening character.

输出

* Line 1: The area of the smallest unit from which the grid is formed

样例输入

2 5
ABABA
ABABA

样例输出

提示

The entire milking grid can be constructed from repetitions of the pattern 'AB'.

来源

USACO 2003 Fall

kmp延伸……你是猪么

做两次KMP

行和列分别是len-next[len];

最后两个结果相乘就可以了

本题只是把线性变成平面，kmp对字符的操作变成字符串……

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<cstring>
 4 
 5 using namespace std;
 6 
 7 #define maxn 1000008
 8 
 9 char s[maxn][80];
10 int r, c, next[maxn];
11 
12 bool same1(int i, int j)   // 判断第i行和第j行是否相等
13 {
14     for(int k = 0; k < c; k++)
15         if(s[i][k] != s[j][k])
16             return false;
17     return true;
18 }
19 
20 bool same2(int i, int j)  // 判断第i列和第j列是否相等。
21 {
22     for(int k = 0; k < r; k++)
23         if(s[k][i] != s[k][j])
24             return false;
25     return true;
26 }
27 
28 int main()
29 {
30     while(~scanf("%d%d", &r, &c))
31     {
32         for(int i = 0; i < r; i++)
33             scanf("%s", s[i]);
34         int j, k;
35         memset(next, 0, sizeof(next));
36         j = 0;
37         k = next[0] = -1;
38         while(j < r)
39         {
40             while(-1 != k && !same1(j, k))
41                 k = next[k];
42             next[++j] = ++k;
43         }
44         int ans1 = r - next[r];     //  r-next[r]就是需要的最短的长度可以覆盖这个平面
45         memset(next, 0, sizeof(next));
46         j = 0;
47         k = next[0] = -1;
48         while(j < c)
49         {
50             while(-1 != k && !same2(j, k))
51                 k = next[k];
52             next[++j] = ++k;
53         }
54         int ans2 = c - next[c];  //列的 
55 
56         printf("%d\n", ans1*ans2);
57     }
58     return 0;
59 }