n = 3 n=3 n=3 时，状压dp，用二进制表示每一列的情况， d p [ i ] [ j ] dp[i][j] dp[i][j] 表示第 i i i 列变成状态 j j j 的最小操作数，转移方程 d p [ i ] [ j ] = min ( d p [ i ] [ j ] , d p [ i − 1 ] [ k ] + c h a n g e ( i , j ) ) dp[i][j]=\min(dp[i][j],\ dp[i-1][k]+change(i, j)) dp[i][j]=min(dp[i][j], dp[i−1][k]+change(i,j)) （如果 k k k 和 j j j 状态合法）
cpp复制代码
#include <bits/stdc++.h>
using namespace std;
#define int long long
using i64 = long long;
typedef pair<int, int> PII;
typedef pair<int, char> PIC;
typedef pair<double, double> PDD;
typedef pair<int, PII> PIII;
typedef pair<int, pair<int, bool>> PIIB;
const int N = 1e6 + 10;
const int maxn = 1e6 + 10;
const int mod = 1e9 + 7;
const int mod1 = 954169327;
const int mod2 = 906097321;
const int INF = 0x3f3f3f3f3f3f3f3f;
void solve()
{
int n, m;
cin >> n >> m;
vector<vector<char>> g(n + 1, vector<char>(m + 1));
for (int i = 1; i <= n; i ++ )
for (int j = 1; j <= m; j ++ )
cin >> g[i][j];
if (n >= 4) cout << -1 << '\n';
else if (n == 1) cout << 0 << '\n';
else if (n == 2)
{
vector<int> cnt(m + 1);
for (int i = 1; i <= m; i ++ )
{
int tmp = 0;
for (int j = 1; j <= n; j ++ )
{
if (g[j][i] == '1') tmp ++ ;
}
cnt[i] = tmp;
}
vector<int> ans(3);
for (int k = 0; k < 3; k ++ )
{
ans[k] += abs(cnt[1] - k);
int lst = k;
for (int i = 2; i <= m; i ++ )
{
if (lst & 1)
{
if (cnt[i] & 1) ans[k] ++ ;
lst = 0;
}
else
{
if (cnt[i] % 2 == 0) ans[k] ++ ;
lst = 1;
}
}
}
cout << min({ans[0], ans[1], ans[2]}) << '\n';
}
else if (n == 3)
{
// 将每一列转化成二进制
vector<int> mp(m + 1);
for (int i = 1; i <= m; i ++ )
{
int tmp = 0;
for (int j = 1; j <= n; j ++ )
{
if (g[j][i] == '1') tmp += (1ll << (j - 1));
}
mp[i] = tmp;
}
// 转化步数
auto change = [&](int a, int b)
{
int state = (a ^ b);
int ans = 0;
for (int i = 0; i < 3; i ++ )
{
if ((state >> i) & 1) ans ++ ;
}
return ans;
};
// 判断相邻状态合法性
auto check = [&](int a, int b)
{
int a1 = ((a >> 0) & 1), a2 = ((a >> 1) & 1), a3 = ((a >> 2) & 1);
int b1 = ((b >> 0) & 1), b2 = ((b >> 1) & 1), b3 = ((b >> 2) & 1);
if ((a1 + a2 + b1 + b2) % 2 == 0) return false;
if ((a2 + a3 + b2 + b3) % 2 == 0) return false;
return true;
};
// 初始化
vector<vector<int>> dp(m + 1, vector<int>(8, INF));
for (int i = 0; i < 8; i ++ ) dp[1][i] = change(mp[1], i);
for (int i = 2; i <= m; i ++ )
{
for (int j = 0; j < 8; j ++ ) // i-1列的状态
{
for (int k = 0; k < 8; k ++ ) // i列的状态
{
if (!check(j, k)) continue; // jk作为相邻状态不合法
dp[i][k] = min(dp[i][k], dp[i - 1][j] + change(mp[i], k));
}
}
}
int ans = INF;
for (int i = 0; i < 8; i ++ ) ans = min(ans, dp[m][i]);
if (ans == INF) cout << -1 << '\n';
else cout << ans << '\n';
}
}
signed main()
{
ios::sync_with_stdio(false);
cin.tie(0), cout.tie(0);
int t = 1;
// cin >> t;
while (t--)
{
solve();
}
}