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Problem solution · C++

Find the Minimum Area to Cover All Ones II

Find the Minimum Area to Cover All Ones II: a C++ solution using sliding window or two pointers. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Sliding window or two pointers
Source
walkccc LeetCode Solutions
Length
73 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Sliding window or two pointers

For Find the Minimum Area to Cover All Ones II, the implementation maintains a moving interval and updates only the information that enters or leaves the window.

  1. Choose the invariant that makes a window valid or useful.
  2. Advance the right boundary and add the new element.
  3. Move the left boundary only as needed while maintaining the invariant and updating the answer.

Code notes

  • 73 lines of C++ from the credited upstream file 3197.cpp.
  • The implementation visibly relies on sequence storage.
  • 14 loop blocks detected.

Complexity

Confirm that neither pointer moves backwards; if so, the scan is usually linear apart from the window’s data-structure operations.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeFind the Minimum Area to Cover All Ones II · C++C++
Use this to learn the idea, then write your own version.
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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