洛谷P1074 靶形数独(算竞进阶习题)

还是数独。。

比上一个多了个分数矩阵，其实没什么差别，但是数据好像水了许多。。。

#include <bits/stdc++.h>
#define INF 0x3f3f3f3f
using namespace std;
typedef long long ll;
inline int lowbit(int x){ return x & (-x); }
inline int read(){
    int X = 0, w = 0; char ch = 0;
    while(!isdigit(ch)) { w |= ch == '-'; ch = getchar(); }
    while(isdigit(ch)) X = (X << 3) + (X << 1) + (ch ^ 48), ch = getchar();
    return w ? -X : X;
}
inline int gcd(int a, int b){ return a % b ? gcd(b, a % b) : b; }
inline int lcm(int a, int b){ return a / gcd(a, b) * b; }
template<typename T>
inline T max(T x, T y, T z){ return max(max(x, y), z); }
template<typename T>
inline T min(T x, T y, T z){ return min(min(x, y), z); }
template<typename A, typename B, typename C>
inline A fpow(A x, B p, C lyd){
    A ans = 1;
    for(; p; p >>= 1, x = 1LL * x * x % lyd)if(p & 1)ans = 1LL * x * ans % lyd;
    return ans;
}
int a[10][10], row[9], col[9], grid[9], cnt[512], num[512], tot, ans;

const int s[10][10]{
    {6, 6, 6, 6, 6, 6, 6, 6, 6},
    {6, 7, 7, 7, 7, 7, 7, 7, 6},
    {6, 7, 8, 8, 8, 8, 8, 7, 6},
    {6, 7, 8, 9, 9, 9, 8, 7, 6},
    {6, 7, 8, 9, 10, 9, 8, 7, 6},
    {6, 7, 8, 9, 9, 9, 8, 7, 6},
    {6, 7, 8, 8, 8, 8, 8, 7, 6},
    {6, 7, 7, 7, 7, 7, 7, 7, 6},
    {6, 6, 6, 6, 6, 6, 6, 6, 6}
};

int g(int x, int y){ return (x / 3) * 3 +(y / 3); }

void flip(int x, int y, int z){
    row[x] ^= (1 << z);
    col[y] ^= (1 << z);
    grid[g(x, y)] ^= (1 << z);
}

void dfs(int step, int score){
    if(step == 0){
        //cout << score << endl;
        //for(int i = 0; i < 9; i ++){for(int j = 0; j < 9; j ++)printf("%d ", a[i][j]);puts("");}
        ans = max(ans, score);
        return;
    }
    int x = -1, y = -1, val = INF;
    for(int i = 0; i < 9; i ++){
        for(int j = 0; j < 9; j ++){
            if(a[i][j] != 0) continue;
            int tmp = row[i] & col[j] & grid[g(i, j)];
            if(tmp == 0) return;
            if(cnt[tmp] < val) val = cnt[tmp], x = i, y = j;
        }
    }
    int tmp = row[x] & col[y] & grid[g(x, y)];
    for(; tmp; tmp -= lowbit(tmp)){
        int k = num[lowbit(tmp)];
        a[x][y] = k + 1;
        flip(x, y, k);
        dfs(step - 1, score + (s[x][y] * a[x][y]));
        flip(x, y, k);
        a[x][y] = 0;
    }
}

int main(){

    for(int i = 0; i < (1 << 9); i ++){
        for(int j = i; j; j -= lowbit(j)) cnt[i] ++;
    }
    for(int i = 0; i < 9; i ++) num[1 << i] = i;
    for(int i = 0; i < 9; i ++) row[i] = col[i] = grid[i] = (1 << 9) - 1;
    for(int i = 0; i < 9; i ++){
        for(int j = 0; j < 9; j ++) a[i][j] = read();
    }
    int temp = 0;
    for(int i = 0; i < 9; i ++){
        for(int j = 0; j < 9; j ++){
            if(a[i][j] != 0) flip(i, j, a[i][j] - 1), temp += (a[i][j] * s[i][j]);
            else tot ++;
        }
    }
    dfs(tot, temp);
    printf(ans == 0 ? "-1\n" : "%d\n", ans);
    //for(int i = 0; i < 9; i ++){for(int j = 0; j < 9; j ++)printf("%d ", a[i][j]);puts("");}
    return 0;
}