【NOIP 2009】 靶形数独

【题目链接】

https://www.luogu.org/problemnew/show/P1074

【算法】

搜索 + 剪枝

【代码】

#include<bits/stdc++.h>
using namespace std;
const int INF = 2e9;
 
struct point
{
        int x,y;
} a[];
 
int i,j,ans,n,Mask,t;
int val[][];
int w[],num[];
bool used[];
int row[],col[],grid[];
bool solved;
 
const int s[][] =
{
{,,,,,,,,},
{,,,,,,,,},
{,,,,,,,,},
{,,,,,,,,},
{,,,,,,,,},
{,,,,,,,,},
{,,,,,,,,},
{,,,,,,,,},
{,,,,,,,,}
};
 
inline int lowbit(int x)
{
        return x & (-x);
}
inline void chkmax()
{
        int i,ret = ;
        for (i = ; i < ; i++)
        {
                for (j = ; j < ; j++)
                {
                        ret += val[i][j] * s[i][j];
                }
        }
        ans = max(ans,ret);
}
inline void dfs(int dep)
{
        int i,mn,pos,v,t;
        if (dep > n)
        {
                solved = true;
                chkmax();
                return;
        }    else
        {
                v = ; mn = INF;
                for (i = ; i <= n; i++)
                {
                        if (!used[i])
                        {
                                t = row[a[i].x] & col[a[i].y] & grid[a[i].x/*+a[i].y/];
                                if (!t) continue;
                                if (w[t] < mn)
                                {
                                        mn = w[t];
                                        pos = i;
                                        v = t;
                                }
                        }
                }
                while (v)
                {
                        used[pos] = true;
                        val[a[pos].x][a[pos].y] = num[lowbit(v)] + ;
                        row[a[pos].x] ^= lowbit(v);
                        col[a[pos].y] ^= lowbit(v);
                        grid[a[pos].x/*+a[pos].y/] ^= lowbit(v);
                        dfs(dep+);
                        used[pos] = false;
                        row[a[pos].x] ^= lowbit(v);
                        col[a[pos].y] ^= lowbit(v);
                        grid[a[pos].x/*+a[pos].y/] ^= lowbit(v);
                        val[a[pos].x][a[pos].y] = ;
                        v -= lowbit(v);
                }
        }
}
 
int main()
{
 
        Mask = ( << ) - ;
        for (i = ; i <= Mask; i++)
        {
                w[i] = ;
                t = i;
                while (t)
                {
                        w[i]++;
                        t -= lowbit(t);
                }
        }
        for (i = ; i < ; i++) num[ << i] = i;
        for (i = ; i < ; i++) row[i] = col[i] = grid[i] = Mask;
        for (i = ; i < ; i++)
        {
                for (j = ; j < ; j++)
                {
                        scanf("%d",&val[i][j]);
                        if (!val[i][j])
                        {
                                n++;
                                a[n] = (point){i,j};
                        } else
                        {
                                row[i] ^= ( << (val[i][j] - ));
                                col[j] ^= ( << (val[i][j] - ));
                                grid[i/*+j/] ^= ( << (val[i][j] - ));
                        }
                }
        }
        solved = false;
        dfs();
        if (solved) printf("%d\n",ans);
        else printf("-1\n");
 
        return ;
 
}