# Luogu1_4 cqoi2014 harmony matrix exclusive or Gaussian Element

Source: Internet
Author: User
Tags bitset

Portal

\$ N, m \$ is given. Create a non-full \$0 \$ matrix of \$ n \ times M \$. All the grids meet the following conditions: it is an even sum of the weights of the top, bottom, and left grids. \$ N, m \ Leq 40 \$

You can list the differences or equations of \$ n \ times M \$ and \$ n \ times M \$ equations based on the conditions in the question. (The equations mean that all positions are \$1 \$ or \$0 \$, the answers in the rightmost column need to be generated in the sense of \$ mod \, 2 \$ through equations of different or mutual elimination ).

In theory, when the number of the same element and the number of equations is the same, each element has a unique solution. However, in the case of a solution, some of the equations are linearly related, which means they are eliminated to the end, some rows are changed to \$0 \$ (if not clearly, you can create a \$3 \ times 3 \$ and \$4 \ times 4 \$ table like \$ vegetable chicken \$ me ). We can set all \$0 \$ yuan (also called free yuan) in a row to \$1 \$, because they have no relationship with the final solution of the equation, then, we can launch the above step by step.

Because the complexity is \$1600 ^ 3 \$, the normal Gaussian elimination speed is very slow, so you can use fairy \$ STL \, bitset \$ to optimize

` 1 #include<bits/stdc++.h> 2 using namespace std; 3  4 inline int read(){ 5     int a = 0; 6     bool f = 0; 7     char c = getchar(); 8     while(c != EOF && !isdigit(c)){ 9         if(c == ‘-‘)10             f = 1;11         c = getchar();12     }13     while(c != EOF && isdigit(c)){14         a = (a << 3) + (a << 1) + (c ^ ‘0‘);15         c = getchar();16     }17     return f ? -a : a;18 }19 20 const int dir[5][2] = {0,1,0,-1,1,0,-1,0,0,0};21 bitset < 1600 > gauss[1600] , ans;22 23 int main(){24 #ifdef LG25     freopen("3164.in" , "r" , stdin);26     freopen("3164.out" , "w" , stdout);27 #endif28     int M , N;29     cin >> M >> N;30     for(int i = 0 ; i < M ; i++)31         for(int j = 0 ; j < N ; j++)32             for(int k = 0 ; k < 5 ; k++)33                 if(i + dir[k][0] >= 0 && i + dir[k][0] < M && j + dir[k][1] >= 0 && j + dir[k][1] < N)34                     gauss[i * N + j][(i + dir[k][0]) * N + j + dir[k][1]] = 1;35     int now = 0;36     for(int i = 0 ; i < M * N ; i++){37         int j = now;38         while(j < M * N && !gauss[j][i])39             j++;40         if(j == M * N)41             continue;42         if(j != now)43             swap(gauss[now] , gauss[j]);44         while(++j < M * N)45             if(gauss[j][i])46                 gauss[j] ^= gauss[now];47         now++;48     }49     for(int i = M * N - 1 ; i >= 0 ; i--){50         if(!gauss[i][i])51             ans[i] = 1;52         if(ans[i])53             for(int j = i - 1 ; j >= 0 ; j--)54                 if(gauss[j][i])55                     ans[j] = ans[j] ^ 1;56     }57     for(int i = 0 ; i < M ; i++){58         for(int j = 0 ; j < N ; j++){59             putchar(ans[i * N + j] + 48);60             putchar(‘ ‘);61         }62         putchar(‘\n‘);63     }64     return 0;65 }`

Luogu1_4 cqoi2014 harmony matrix exclusive or Gaussian Element

Related Keywords:
Related Article

The content source of this page is from Internet, which doesn't represent Alibaba Cloud's opinion; products and services mentioned on that page don't have any relationship with Alibaba Cloud. If the content of the page makes you feel confusing, please write us an email, we will handle the problem within 5 days after receiving your email.

If you find any instances of plagiarism from the community, please send an email to: info-contact@alibabacloud.com and provide relevant evidence. A staff member will contact you within 5 working days.

## A Free Trial That Lets You Build Big!

Start building with 50+ products and up to 12 months usage for Elastic Compute Service

• #### Sales Support

1 on 1 presale consultation

• #### After-Sales Support

24/7 Technical Support 6 Free Tickets per Quarter Faster Response

• Alibaba Cloud offers highly flexible support services tailored to meet your exact needs.