HDU暑假多校第四场J-Let Sudoku Rotate

一、题意

Sudoku is a logic-based, combinatorial number-placement puzzle, which is popular around the world.
In this problem, let us focus on puzzles with 16×16 grids, which consist of 4×4 regions. The objective is to fill the whole grid with hexadecimal digits, i.e. 0123456789ABCDEF, so that each column, each row, and each region contains all hexadecimal digits. The figure below shows a solved sudoku.

考虑一个完成后的数独游戏局面，将16*16的局面分割成4*4的小方块，随机旋转小方块得到一个新的局面，现在给出新的局面，问你最少旋转几次可以得到一个完成的局面。

二、解题思路。

首先考虑暴力搜索，4^16次方次旋转——来自每个小方块4次旋转，一共16个小方块。

但是考虑数独游戏的特征，每走一步都可以判断当前的选择是否合法——因此可以进行剪枝——判断下当前所在方块、所在形状的合法性——已经取到的行、列是否合法。

处于某种我证明不了的原因认为，这种方式将会把剪枝操作剪到足够小，以至于31ms就可以搞定1000组输入。

#include<bits/stdc++.h>
using namespace std;

#define ll long long
const int MAXN=;

char mapp[MAXN][MAXN];

int ans=;

int tran(char c)
{
    if(c>=''&&c<='')return c-'';
    else return c-'A'+;
}

bool check_left(int a,int b)
{
    // int x = a*4;
    int endd = (b+)*;
    if(b == )return true;
    for(int i=;i<;++i)
    {
        int x = a* +i;
        int ch[];
        memset(ch,,sizeof(ch));
        for(int j=;j<endd;++j)
        {
            ch[tran(mapp[x][j])]++;
            if(ch[tran(mapp[x][j])] == )return false;
        }
    }return true;
}

bool check_up(int a,int b)
{
    int endd = (a+)*;
    if(a == )return true;
    for(int j=;j<;++j)
    {
        int y = b*+j;
        int ch[];
        memset(ch,,sizeof(ch));
        for(int i=;i<endd;i++)
        {
            ch[tran(mapp[i][y])]++;
            if(ch[tran(mapp[i][y])] == )return false;

        }
    }return true;
}

bool check(int a,int b)
{
    return check_left(a,b)&&check_up(a,b);
}

bool check(int l)
{
    for(int i=;i<;++i)
    {
        int x = l*+i;
        int ch[];
        memset(ch,,sizeof(ch));
        for(int j=;j<;++j)
        {
            ch[tran(mapp[x][j])]++;
            if(ch[tran(mapp[x][j])]==)return false;
        }
    }
    return true;
}

void change(int a,int b)
{
    int x = a*;
    int y = b*;

    int tmp = mapp[x][y];
    mapp[x][y] = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = tmp;

    tmp = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = tmp;

    tmp = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = tmp;

    tmp = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = tmp;

}

void change1(int a,int b)
{
    int x = a*;
    int y = b*;

    int tmp = mapp[x][y];
    mapp[x][y] = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = tmp;

    tmp = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = tmp;

    tmp = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = tmp;

    tmp = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = mapp[x+][y+];
    mapp[x+][y+] = tmp;

}
bool search(int a,int b,int summ)
{

        // cout<<"search : "<<a<<" "<<b<<" step: "<<summ<<endl;

    if(b==)
    {
        if(check(a)){
            ans += summ;
            return true;
        }
        return false;
    }

    if(search(a,b+,summ))return true;
    for(int i=;i<;++i)
    {
        change1(a,b);
        if(search(a,b+,summ++i))return true;
    }
    change1(a,b);
    return false;
}

bool dfs(int now,int summ)
{
    int a = now/;
    int b = now%;
    if(now == )
    {
        ans = min(ans,summ);
        return true;
    }
    if(check(a,b)&&dfs(now+,summ));
    for(int i=;i<;++i)
    {
        change1(a,b);
        if(!check(a,b))continue;
        dfs(now+,summ+i+);
    }
    change1(a,b);
    return false;
}

void show()
{
    for(int i=;i<;++i)
    {
        for(int j=;j<;++j)
        {
            cout<<mapp[i][j];
        }cout<<endl;
    }
}

void init()
{
    ans = INT_MAX;
    for(int i=;i<;++i)gets(mapp[i]);
    dfs(,);
    cout<<ans<<"\n";
}

int main()
{

    int t;
    // cin>>t;
    scanf("%d\n",&t);
    while(t--)init();

    return ;
}