Question

934. Shortest Bridge

中文文档

Description

You are given an n x n binary matrix grid where 1 represents land and 0 represents water.

An island is a 4-directionally connected group of 1's not connected to any other 1's. There are exactly two islands in grid.

You may change 0's to 1's to connect the two islands to form one island.

Return _the smallest number of _0_'s you must flip to connect the two islands_.

 

Example 1:

Input: grid = [[0,1],[1,0]]
Output: 1

Example 2:

Input: grid = [[0,1,0],[0,0,0],[0,0,1]]
Output: 2

Example 3:

Input: grid = [[1,1,1,1,1],[1,0,0,0,1],[1,0,1,0,1],[1,0,0,0,1],[1,1,1,1,1]]
Output: 1

 

Constraints:

• n == grid.length == grid[i].length
• 2 <= n <= 100
• grid[i][j] is either 0 or 1.
• There are exactly two islands in grid.

Solutions

Solution 1

class Solution:
  def shortestBridge(self, grid: List[List[int]]) -> int:
    def dfs(i, j):
      q.append((i, j))
      grid[i][j] = 2
      for a, b in pairwise(dirs):
        x, y = i + a, j + b
        if 0 <= x < n and 0 <= y < n and grid[x][y] == 1:
          dfs(x, y)

    n = len(grid)
    dirs = (-1, 0, 1, 0, -1)
    q = deque()
    i, j = next((i, j) for i in range(n) for j in range(n) if grid[i][j])
    dfs(i, j)
    ans = 0
    while 1:
      for _ in range(len(q)):
        i, j = q.popleft()
        for a, b in pairwise(dirs):
          x, y = i + a, j + b
          if 0 <= x < n and 0 <= y < n:
            if grid[x][y] == 1:
              return ans
            if grid[x][y] == 0:
              grid[x][y] = 2
              q.append((x, y))
      ans += 1

class Solution {
  private int[] dirs = {-1, 0, 1, 0, -1};
  private Deque<int[]> q = new ArrayDeque<>();
  private int[][] grid;
  private int n;

  public int shortestBridge(int[][] grid) {
    this.grid = grid;
    n = grid.length;
    for (int i = 0, x = 1; i < n && x == 1; ++i) {
      for (int j = 0; j < n; ++j) {
        if (grid[i][j] == 1) {
          dfs(i, j);
          x = 0;
          break;
        }
      }
    }
    int ans = 0;
    while (true) {
      for (int i = q.size(); i > 0; --i) {
        var p = q.pollFirst();
        for (int k = 0; k < 4; ++k) {
          int x = p[0] + dirs[k], y = p[1] + dirs[k + 1];
          if (x >= 0 && x < n && y >= 0 && y < n) {
            if (grid[x][y] == 1) {
              return ans;
            }
            if (grid[x][y] == 0) {
              grid[x][y] = 2;
              q.offer(new int[] {x, y});
            }
          }
        }
      }
      ++ans;
    }
  }

  private void dfs(int i, int j) {
    grid[i][j] = 2;
    q.offer(new int[] {i, j});
    for (int k = 0; k < 4; ++k) {
      int x = i + dirs[k], y = j + dirs[k + 1];
      if (x >= 0 && x < n && y >= 0 && y < n && grid[x][y] == 1) {
        dfs(x, y);
      }
    }
  }
}

class Solution {
public:
  const static inline vector<int> dirs = {-1, 0, 1, 0, -1};

  int shortestBridge(vector<vector<int>>& grid) {
    int n = grid.size();
    queue<pair<int, int>> q;
    function<void(int, int)> dfs = [&](int i, int j) {
      grid[i][j] = 2;
      q.emplace(i, j);
      for (int k = 0; k < 4; ++k) {
        int x = i + dirs[k], y = j + dirs[k + 1];
        if (x >= 0 && x < n && y >= 0 && y < n && grid[x][y] == 1) {
          dfs(x, y);
        }
      }
    };
    for (int i = 0, x = 1; i < n && x; ++i) {
      for (int j = 0; j < n; ++j) {
        if (grid[i][j]) {
          dfs(i, j);
          x = 0;
          break;
        }
      }
    }
    int ans = 0;
    while (1) {
      for (int h = q.size(); h; --h) {
        auto [i, j] = q.front();
        q.pop();
        for (int k = 0; k < 4; ++k) {
          int x = i + dirs[k], y = j + dirs[k + 1];
          if (x >= 0 && x < n && y >= 0 && y < n) {
            if (grid[x][y] == 1) return ans;
            if (grid[x][y] == 0) {
              grid[x][y] = 2;
              q.emplace(x, y);
            }
          }
        }
      }
      ++ans;
    }
  }
};

func shortestBridge(grid [][]int) (ans int) {
  n := len(grid)
  dirs := []int{-1, 0, 1, 0, -1}
  type pair struct{ i, j int }
  q := []pair{}
  var dfs func(int, int)
  dfs = func(i, j int) {
    grid[i][j] = 2
    q = append(q, pair{i, j})
    for k := 0; k < 4; k++ {
      x, y := i+dirs[k], j+dirs[k+1]
      if x >= 0 && x < n && y >= 0 && y < n && grid[x][y] == 1 {
        dfs(x, y)
      }
    }
  }
  for i, x := 0, 1; i < n && x == 1; i++ {
    for j := 0; j < n; j++ {
      if grid[i][j] == 1 {
        dfs(i, j)
        x = 0
        break
      }
    }
  }
  for {
    for i := len(q); i > 0; i-- {
      p := q[0]
      q = q[1:]
      for k := 0; k < 4; k++ {
        x, y := p.i+dirs[k], p.j+dirs[k+1]
        if x >= 0 && x < n && y >= 0 && y < n {
          if grid[x][y] == 1 {
            return
          }
          if grid[x][y] == 0 {
            grid[x][y] = 2
            q = append(q, pair{x, y})
          }
        }
      }
    }
    ans++
  }
}