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Problem solution · C++

Shortest Distance from All Buildings

Shortest Distance from All Buildings: 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
67 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 Shortest Distance from All Buildings, 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

  • 67 lines of C++ from the credited upstream file 317.cpp.
  • The implementation visibly relies on sequence storage, work queue.
  • 7 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 codeShortest Distance from All Buildings · C++C++
Use this to learn the idea, then write your own version.
class Solution { public:  int shortestDistance(vector<vector<int>>& grid) {    constexpr int kDirs[4][2] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};    const int m = grid.size();    const int n = grid[0].size();    const int nBuildings = getBuildingsCount(grid);    int ans = INT_MAX;    // dist[i][j] := the total distance of grid[i][j] (0) to reach all the    // buildings (1)    vector<vector<int>> dist(m, vector<int>(n));    // reachCount[i][j] := the number of buildings (1) grid[i][j] (0) can reach    vector<vector<int>> reachCount(m, vector<int>(n));     auto bfs = [&](int row, int col) -> bool {      queue<pair<int, int>> q{{{row, col}}};      vector<vector<bool>> seen(m, vector<bool>(n));      seen[row][col] = true;      int seenBuildings = 1;       for (int step = 1; !q.empty(); ++step)        for (int sz = q.size(); sz > 0; --sz) {          const auto [i, j] = q.front();          q.pop();          for (const auto& [dx, dy] : kDirs) {            const int x = i + dx;            const int y = j + dy;            if (x < 0 || x == m || y < 0 || y == n)              continue;            if (seen[x][y])              continue;            seen[x][y] = true;            if (!grid[x][y]) {              dist[x][y] += step;              ++reachCount[x][y];              q.emplace(x, y);            } else if (grid[x][y] == 1) {              ++seenBuildings;            }          }        }       return seenBuildings == nBuildings;    };     for (int i = 0; i < m; ++i)      for (int j = 0; j < n; ++j)        if (grid[i][j] == 1)  // BFS from this building.          if (!bfs(i, j))            return -1;     for (int i = 0; i < m; ++i)      for (int j = 0; j < n; ++j)        if (reachCount[i][j] == nBuildings)          ans = min(ans, dist[i][j]);     return ans == INT_MAX ? -1 : ans;  }  private:  int getBuildingsCount(vector<vector<int>>& grid) {    return accumulate(        grid.begin(), grid.end(), 0,        [](int acc, vector<int>& row) { return acc + ranges::count(row, 1); });  }};

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