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Problem solution · C++

Find the Safest Path in a Grid

Find the Safest Path in a Grid: a C++ solution using breadth-first search. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Breadth-first search
Source
walkccc LeetCode Solutions
Length
87 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

Breadth-first search

For Find the Safest Path in a Grid, the implementation explores reachable states in layers, which is the standard shape for unweighted shortest paths and minimum-step transitions.

  1. Model each valid configuration as a state and each legal move as an edge.
  2. Seed the queue with the starting state and mark it immediately.
  3. Expand each state once, recording distance or reachability for unseen neighbours.

Code notes

  • 87 lines of C++ from the credited upstream file 2812.cpp.
  • The implementation visibly relies on sequence storage, work queue.
  • 8 loop blocks detected.

Complexity

Verify that each state and transition is processed only a bounded number of times; that determines the traversal cost.

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 Safest Path in a Grid · C++C++
Use this to learn the idea, then write your own version.
class Solution { public:  int maximumSafenessFactor(vector<vector<int>>& grid) {    const vector<vector<int>> distToThief = getDistToThief(grid);    int l = 0;    int r = grid.size() * 2;     while (l < r) {      const int m = (l + r) / 2;      if (hasValidPath(distToThief, m))        l = m + 1;      else        r = m;    }     return l - 1;  }  private:  static constexpr int kDirs[4][2] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};   bool hasValidPath(const vector<vector<int>>& distToThief, int safeness) {    if (distToThief[0][0] < safeness)      return false;     const int n = distToThief.size();    queue<pair<int, int>> q{{{0, 0}}};    vector<vector<bool>> seen(n, vector<bool>(n));    seen[0][0] = true;     while (!q.empty()) {      const auto [i, j] = q.front();      q.pop();      if (distToThief[i][j] < safeness)        continue;      if (i == n - 1 && j == n - 1)        return true;      for (const auto& [dx, dy] : kDirs) {        const int x = i + dx;        const int y = j + dy;        if (x < 0 || x == n || y < 0 || y == n)          continue;        if (seen[x][y])          continue;        q.emplace(x, y);        seen[x][y] = true;      }    }     return false;  }   vector<vector<int>> getDistToThief(const vector<vector<int>>& grid) {    const int n = grid.size();    vector<vector<int>> distToThief(n, vector<int>(n));    queue<pair<int, int>> q;    vector<vector<bool>> seen(n, vector<bool>(n));     for (int i = 0; i < n; ++i)      for (int j = 0; j < n; ++j)        if (grid[i][j] == 1) {          q.emplace(i, j);          seen[i][j] = true;        }     for (int dist = 0; !q.empty(); ++dist) {      for (int sz = q.size(); sz > 0; --sz) {        const auto [i, j] = q.front();        q.pop();        distToThief[i][j] = dist;        for (const auto& [dx, dy] : kDirs) {          const int x = i + dx;          const int y = j + dy;          if (x < 0 || x == n || y < 0 || y == n)            continue;          if (seen[x][y])            continue;          q.emplace(x, y);          seen[x][y] = true;        }      }    }     return distToThief;  }};

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