关灯1

位运算写法

#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1000;
const int MAXM = 10;
int n, m;
int a[MAXN + 5];
int aa[MAXN + 5];
int cnt(int x)
{
    int res = 0;
    while (x > 0)
    {
        res += 1;
        x -= (x & (-x));
    }
    return res;
}
int main()
{
    cin >> n >> m;
    int mask = (1 << m) - 1;
    for (int i = 0; i < n; i++)
    {
        a[i] = 0;
        for (int j = 0; j < m; j++)
        {
            int x;
            cin >> x;
            a[i] = a[i] * 2 + x;
        }
    }
    int ans = -1;
    for (int first = 0; first <= (1 << m) - 1; first++)
    {
        for (int i = 0; i < n; i++)
            aa[i] = a[i];
        int now = cnt(first);
        aa[0] ^= first;
        aa[0] ^= (first >> 1);
        aa[0] ^= ((first << 1) & mask);
        aa[1] ^= first;
        for (int i = 1; i < n; i++)
        {
            now += cnt(aa[i - 1]);
            aa[i] ^= aa[i - 1];
            aa[i] ^= (aa[i - 1] >> 1);
            aa[i] ^= ((aa[i - 1] << 1) & mask);
            aa[i + 1] ^= (aa[i - 1]);
        }
        if (aa[n - 1] == 0 && (ans == -1 || now < ans))
            ans = now;
    }
    cout << ans << "\n";
    return 0;
}

dfs 枚举第一行的写法

#include <bits/stdc++.h>
using namespace std;
int n, m;
int a[1005][15];
int b[1005][15]; // 记录那些位置操作了
int ans;
// 计算 a[x][y] 在当前按键情况下的亮灯情况
int cal(int x, int y)
{
    int sum = 0;
    sum += a[x][y];
    sum += b[x][y];
    sum += b[x - 1][y];
    sum += b[x + 1][y];
    sum += b[x][y - 1];
    sum += b[x][y + 1];
    return sum % 2;
}
// 当前枚举第一排的第 pos 个位置
void dfs(int pos)
{
    if (pos == m + 1)
    {
        // 第一行的前 m 个都按完了，先清空一下下面 2~n 行的案件情况
        for (int i = 2; i <= n; i++)
            for (int j = 1; j <= m; j++)
                b[i][j] = 0;
        // 枚举第 2~n 行分别怎么按
        for (int i = 2; i <= n; i++)
            // 如果上一行的这个位置是一个 1，那么这一行的这个位置就需要按
            for (int j = 1; j <= m; j++)
                if (cal(i - 1, j) == 1)
                    b[i][j] = 1;
        // 按完了，此时 1~n-1 行全对了，只需要检查最后一行对不对了
        bool flag = true;
        for (int j = 1; j <= m; j++)
            if (cal(n, j) == 1)
                flag = false;
        // 尝试更新答案
        if (flag)
        {
            // 算算按了几个位置
            int cnt = 0;
            for (int i = 1; i <= n; i++)
                for (int j = 1; j <= m; j++)
                    if (b[i][j])
                        cnt++;
            if (ans == -1 || cnt < ans)
                ans = cnt;
        }
        return;
    }
    b[1][pos] = 0;
    dfs(pos + 1); // 不按
    b[1][pos] = 0;
    b[1][pos] = 1;
    dfs(pos + 1); // 按
    b[1][pos] = 0;
}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin >> n >> m;
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= m; j++)
            cin >> a[i][j];
    ans = -1;
    dfs(1);
    cout << ans;

    return 0;
}