矩阵合集

极大全1矩阵

悬线法：悬线的定义，就是一条竖线，这条竖线要满足上端点在整个矩形上边界或者是一个障碍点。然后以这条悬线进行左右移动，直到移至障碍点或者是矩阵边界，进而确定这条悬线所在的极大矩阵。

一些定义：

up[i][j]为矩阵上的点(i,j)向上的悬线长度

lft[i][j]为矩阵上的点(i,j)向左扩展而不会碰到障碍点的长度

rgt[i][j]为矩阵上的点(i,j)向右扩展而不会碰到障碍点的长度

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
#include<cmath>
#include<stack>
#include<cstdlib>
#include<queue>
#include<set>
#include<string.h>
#include<vector>
#include<deque>
#include<map>
using namespace std;
#define INF 0x3f3f3f3f3f3f3f3f
#define inf 0x3f3f3f3f
#define eps 1e-4
#define bug printf("*********
")
#define debug(x) cout<<#x"=["<<x<<"]" <<endl
typedef long long LL;
typedef long long ll;
const int maxn = 2e3 + 5;
const int mod = 998244853;

char s[maxn][maxn];
int up[maxn][maxn],lft[maxn][maxn],rgt[maxn][maxn];

int main() {
    int n, m;
    scanf("%d %d", &n, &m);
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= m; j++) {
            scanf(" %c", s[i] + j);
            lft[i][j] = rgt[i][j] = j;
             up[i][j] = 1;
        }
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= m; j++)
            if (s[i][j] == '1' && s[i][j - 1] == '1')
                lft[i][j] = lft[i][j - 1];
        for (int j = m; j >= 1; j--)
            if (s[i][j] == '1' && s[i][j + 1] == '1')
                rgt[i][j] = rgt[i][j + 1];
    }
    int ans = 0;
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= m; j++) {
            if (i > 1 && s[i][j] == '1' && s[i - 1][j] == '1') {
                lft[i][j] = max(lft[i][j], lft[i - 1][j]);
                rgt[i][j] = min(rgt[i][j], rgt[i - 1][j]);
                up[i][j] = up[i - 1][j] + 1;
            }
            ans = max(ans, (rgt[i][j] - lft[i][j] + 1) * up[i][j]);
        }
    }
    printf("%d
",ans);
}