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3197. Find the Minimum Area to Cover All Ones II 👍

  • Time: $O(mn)$
  • Space: $O(1)$
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class Solution {
 public:
  int minimumSum(vector<vector<int>>& grid) {
    const int m = grid.size();
    const int n = grid[0].size();
    int ans = m * n;

    for (int i = 0; i < m; ++i) {
      const int top = minimumArea(grid, 0, i, 0, n - 1);
      for (int j = 0; j < n; ++j)
        ans = min(ans,
                  top + /*left*/ minimumArea(grid, i + 1, m - 1, 0, j) +
                      /*right*/ minimumArea(grid, i + 1, m - 1, j + 1, n - 1));
    }

    for (int i = 0; i < m; ++i) {
      const int bottom = minimumArea(grid, i, m - 1, 0, n - 1);
      for (int j = 0; j < n; ++j)
        ans = min(ans, bottom + /*left*/ minimumArea(grid, 0, i - 1, 0, j) +
                           /*right*/ minimumArea(grid, 0, i - 1, j + 1, n - 1));
    }

    for (int j = 0; j < n; ++j) {
      const int left = minimumArea(grid, 0, m - 1, 0, j);
      for (int i = 0; i < m; ++i)
        ans = min(ans,
                  left + /*top*/ minimumArea(grid, 0, i, j + 1, n - 1) +
                      /*bottom*/ minimumArea(grid, i + 1, m - 1, j + 1, n - 1));
    }

    for (int j = 0; j < n; ++j) {
      const int right = minimumArea(grid, 0, m - 1, j, n - 1);
      for (int i = 0; i < m; ++i)
        ans =
            min(ans, right + /*top*/ minimumArea(grid, 0, i, 0, j - 1) +
                         /*bottom*/ minimumArea(grid, i + 1, m - 1, 0, j - 1));
    }

    for (int i1 = 0; i1 < m; ++i1)
      for (int i2 = i1 + 1; i2 < m; ++i2)
        ans =
            min(ans, /*top*/ minimumArea(grid, 0, i1, 0, n - 1) +
                         /*middle*/ minimumArea(grid, i1 + 1, i2, 0, n - 1) +
                         /*bottom*/ minimumArea(grid, i2 + 1, m - 1, 0, n - 1));

    for (int j1 = 0; j1 < n; ++j1)
      for (int j2 = j1 + 1; j2 < n; ++j2)
        ans =
            min(ans, /*left*/ minimumArea(grid, 0, m - 1, 0, j1) +
                         /*middle*/ minimumArea(grid, 0, m - 1, j1 + 1, j2) +
                         /*right*/ minimumArea(grid, 0, m - 1, j2 + 1, n - 1));

    return ans;
  }

 private:
  int minimumArea(vector<vector<int>>& grid, int si, int ei, int sj, int ej) {
    int x1 = INT_MAX;
    int y1 = INT_MAX;
    int x2 = 0;
    int y2 = 0;
    for (int i = si; i <= ei; ++i)
      for (int j = sj; j <= ej; ++j)
        if (grid[i][j] == 1) {
          x1 = min(x1, i);
          y1 = min(y1, j);
          x2 = max(x2, i);
          y2 = max(y2, j);
        }
    return x1 == INT_MAX ? 0 : (x2 - x1 + 1) * (y2 - y1 + 1);
  }
};

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class Solution {
  public int minimumSum(int[][] grid) {
    final int m = grid.length;
    final int n = grid[0].length;
    int ans = m * n;

    for (int i = 0; i < m; ++i) {
      final int top = minimumArea(grid, 0, i, 0, n - 1);
      for (int j = 0; j < n; ++j)
        ans = Math.min(ans, top + /*left*/ minimumArea(grid, i + 1, m - 1, 0, j) +
                                /*right*/ minimumArea(grid, i + 1, m - 1, j + 1, n - 1));
    }

    for (int i = 0; i < m; ++i) {
      final int bottom = minimumArea(grid, i, m - 1, 0, n - 1);
      for (int j = 0; j < n; ++j)
        ans = Math.min(ans, bottom + /*left*/ minimumArea(grid, 0, i - 1, 0, j) +
                                /*right*/ minimumArea(grid, 0, i - 1, j + 1, n - 1));
    }

    for (int j = 0; j < n; ++j) {
      final int left = minimumArea(grid, 0, m - 1, 0, j);
      for (int i = 0; i < m; ++i)
        ans = Math.min(ans, left + /*top*/ minimumArea(grid, 0, i, j + 1, n - 1) +
                                /*bottom*/ minimumArea(grid, i + 1, m - 1, j + 1, n - 1));
    }

    for (int j = 0; j < n; ++j) {
      final int right = minimumArea(grid, 0, m - 1, j, n - 1);
      for (int i = 0; i < m; ++i)
        ans = Math.min(ans, right + /*top*/ minimumArea(grid, 0, i, 0, j - 1) +
                                /*bottom*/ minimumArea(grid, i + 1, m - 1, 0, j - 1));
    }

    for (int i1 = 0; i1 < m; ++i1)
      for (int i2 = i1 + 1; i2 < m; ++i2)
        ans = Math.min(ans, /*top*/ minimumArea(grid, 0, i1, 0, n - 1) +
                                /*middle*/ minimumArea(grid, i1 + 1, i2, 0, n - 1) +
                                /*bottom*/ minimumArea(grid, i2 + 1, m - 1, 0, n - 1));

    for (int j1 = 0; j1 < n; ++j1)
      for (int j2 = j1 + 1; j2 < n; ++j2)
        ans = Math.min(ans, /*left*/ minimumArea(grid, 0, m - 1, 0, j1) +
                                /*middle*/ minimumArea(grid, 0, m - 1, j1 + 1, j2) +
                                /*right*/ minimumArea(grid, 0, m - 1, j2 + 1, n - 1));

    return ans;
  }

  private int minimumArea(int[][] grid, int si, int ei, int sj, int ej) {
    int x1 = Integer.MAX_VALUE;
    int y1 = Integer.MAX_VALUE;
    int x2 = 0;
    int y2 = 0;
    for (int i = si; i <= ei; ++i)
      for (int j = sj; j <= ej; ++j)
        if (grid[i][j] == 1) {
          x1 = Math.min(x1, i);
          y1 = Math.min(y1, j);
          x2 = Math.max(x2, i);
          y2 = Math.max(y2, j);
        }
    return x1 == Integer.MAX_VALUE ? 0 : (x2 - x1 + 1) * (y2 - y1 + 1);
  }
}

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class Solution:
  def minimumSum(self, grid: list[list[int]]) -> int:
    m = len(grid)
    n = len(grid[0])
    ans = m * n

    for i in range(m):
      top = self._minimumArea(grid, 0, i, 0, n - 1)
      for j in range(n):
        ans = min(ans, top +
                  self._minimumArea(grid, i + 1, m - 1, 0, j) +
                  self._minimumArea(grid, i + 1, m - 1, j + 1, n - 1))

    for i in range(m):
      bottom = self._minimumArea(grid, i, m - 1, 0, n - 1)
      for j in range(n):
        ans = min(ans, bottom +
                  self._minimumArea(grid, 0, i - 1, 0, j) +
                  self._minimumArea(grid, 0, i - 1, j + 1, n - 1))

    for j in range(n):
      left = self._minimumArea(grid, 0, m - 1, 0, j)
      for i in range(m):
        ans = min(ans, left +
                  self._minimumArea(grid, 0, i, j + 1, n - 1) +
                  self._minimumArea(grid, i + 1, m - 1, j + 1, n - 1))

    for j in range(n):
      right = self._minimumArea(grid, 0, m - 1, j, n - 1)
      for i in range(m):
        ans = min(ans, right +
                  self._minimumArea(grid, 0, i, 0, j - 1) +
                  self._minimumArea(grid, i + 1, m - 1, 0, j - 1))

    for i1 in range(m):
      for i2 in range(i1 + 1, m):
        ans = min(ans, self._minimumArea(grid, 0, i1, 0, n - 1) +
                  self._minimumArea(grid, i1 + 1, i2, 0, n - 1) +
                  self._minimumArea(grid, i2 + 1, m - 1, 0, n - 1))

    for j1 in range(n):
      for j2 in range(j1 + 1, n):
        ans = min(ans, self._minimumArea(grid, 0, m - 1, 0, j1) +
                  self._minimumArea(grid, 0, m - 1, j1 + 1, j2) +
                  self._minimumArea(grid, 0, m - 1, j2 + 1, n - 1))

    return ans

  def _minimumArea(
      self,
      grid: list[list[int]],
      si: int,
      ei: int,
      sj: int,
      ej: int,
  ) -> int:
    x1 = math.inf
    y1 = math.inf
    x2 = 0
    y2 = 0
    for i in range(si, ei + 1):
      for j in range(sj, ej + 1):
        if grid[i][j] == 1:
          x1 = min(x1, i)
          y1 = min(y1, j)
          x2 = max(x2, i)
          y2 = max(y2, j)
    return 0 if x1 == math.inf else (x2 - x1 + 1) * (y2 - y1 + 1)