[题解] luogu P1985 [USACO07OPEN]翻转棋

Posted 2022-05-07 martixx

题面
今天学搜索，正好水一发以前做的这道毒瘤题

话说这道题做了我一天，别人都是各种优化，不超100行

天真的我硬核刚了220行，全程0优化水过

但其实不用这么长，我有的函数写的有点重复了（

思路：

显然是dfs，一行一行的来

搜到[i, j]时(i > 1)，看[i - 1, j]是否为黑，是的话就翻转[i, j],

也就是说搜完当前行就要保证上一行的棋全都翻成了白色

当搜到最后一行时，

既要保证上一行翻成白色，还要保证自己也都翻成白色，

最后还要特判一下最后两个的翻转.

当时年少轻狂，我想着层次一定要清晰，
于是就SB地分别打了四个函数：

1. 特判第一行,firstLineS
2. 当只有一列的时候,dfs1
3. 当搜到最后一行时或本来只有一行时，dfsn
4. 正常搜索,dfs

这个题有个坑，92分卡了一下午: 搜到的第一个解不能直接输出，它是最优解，但不一定是字典序最小的，所以继续搜完

[collapse title="Code" status="false"]

#include <bits/stdc++.h>

using namespace std;

int n, m, a, minans = 99999;
int Chess[25][25], ans[25][25], minan[25][25];

void c(int i, int j) 

    if(Chess[i][j]%2 == 0) Chess[i][j] = 1;
    else Chess[i][j] = 0;

void print() 

    a = 0;
    for (int i = 1; i <= m; i++)
        for (int j = 1; j <= n; j++)
            if (Chess[i][j] % 2 == 1) return ;
    for (int i = 1; i <= m; i++)
        for (int j = 1; j <= n; j++)
            a += ans[i][j] % 2;
    if(minans > a) 
    
        minans = a;
        for (int i = 1; i <= m; i++)
            for (int j = 1; j <= n; j++)
                minan[i][j] = ans[i][j] % 2;
    

int back1(int p) 

    if ( Chess[m][p] == 1 && p == n)
        return 1;
    else if (p != n)
        return 1;
    return 0;

int back2(int p) 

    if ( Chess[m][p] == 0 && p == n)
        return 0;
    else if (p != n)
        return 0;
    return 1;

void dfsn(int num)     
    if (num == n + 1) 
        print();
        return ;
    
    int line = m;
    if (m == 1)
    
        if (num == 1)
        
            dfsn(num + 1);    
            c(line, num + 1);
            c(line, num);
            ans[line][num]++;
            dfsn(num + 1);
        
        if (Chess[line][num - 1]==0 && back2(num)==0)
            dfsn(num+1);
        else if (Chess[line][num - 1]==1 && back1(num)==1)
        
            c(line, num - 1);
            c(line, num + 1);
            c(line, num);
            ans[line][num]++;
        
            dfsn(num + 1);
        
    
    else if (num == 1)
    
        if (Chess[m - 1][1] == 0)
            dfsn(2);    
    
        else 
        
            c(m - 1 , 1);
            c(m, 2);
            c(m, 1);
            ans[m][1]++;
        
            dfsn(2);
        
    
    
    else if (Chess[line - 1][num]==1 && Chess[line][num - 1]==1 && back1(num)==1)
    
        c(line - 1 , num);
        c(line, num - 1);
        c(line, num + 1);
        c(line, num);
        ans[line][num]++;
        
        dfsn(num + 1);
        /*  
        ans[line][num]--;
        c(line - 1, num);
        c(line, num - 1);
        c(line, num + 1);
        c(line, num);
        */
    
    else if (Chess[line - 1][num] == 0 && Chess[line - 1][num] == 0 && back2(num) == 0)
        dfsn(num + 1);

void dfs(int line, int num)

    if (num == n + 1 && line == m - 1)
    
        dfsn(1);
        return ;
    
    if (num == n + 1)
    
        dfs(line + 1, 1);
        return ;
    
    if (Chess[line - 1][num] == 0)
        dfs(line, num + 1);
    else
    
        c(line - 1, num);
        c(line + 1, num);
        c(line, num - 1);
        c(line, num + 1);
        c(line, num);
        ans[line][num]++;
        dfs(line, num + 1);
 /*
        ans[line][num]--;       
        c(line - 1, num);
        c(line + 1, num);
        c(line, num - 1);
        c(line, num + 1);
        c(line, num);
*/
    

void firstLineS(int k)

    if (k == n + 1) 
    
        if (m > 2)
            dfs(2, 1);
        else if (m == 2)
            dfsn(1);
        return ;
     
    firstLineS(k + 1);
    c(1, k);
    c(1, k - 1);
    c(1, k + 1);
    c(2, k);
    ans[1][k]++;
    firstLineS(k + 1);
    ans[1][k]--;
    c(1, k);
    c(1, k - 1);
    c(1, k + 1);
    c(2, k);

void dfs1(int num)

    if (num == m + 1) 
    
        print();
        return ;
    
    if (num == 1)
    
        dfs1(num + 1);
        ans[num][1]++;
        c(num, 1);
        c(num + 1, 1);
        dfs1(num + 1);
        ans[num][1]--;
        c(num, 1);
        c(num + 1, 1);
    
    if(Chess[num - 1][1] == 0)
        dfs1(num + 1);
    else  
        ans[num][1]++;
        c(num, 1);
        c(num + 1, 1);
        c(num - 1, 1);
        
        dfs1(num + 1); 
        
        ans[num][1]--;
        c(num + 1, 1);
        c(num - 1, 1);
        c(num, 1);
    


int main()   

    cin >> m>> n;
    for (int i = 1; i <= m; i++)
        for (int j = 1; j <= n; j++)
            cin >> Chess[i][j];
    if (m == 1) dfsn(1);
    if (n == 1) dfs1(1);
    firstLineS(1);
    if (minans==99999)
        cout<<"IMPOSSIBLE"<<endl;
    else
        for (int i = 1; i <= m; i++)
           
            for (int j = 1; j <= n; j++)
                cout << minan[i][j]%2<<" ";
            cout << endl;
        
    return 0;

[/collapse]