给你一个由 '1'(陆地)和 '0'(水)组成的的二维网格,请你计算网格中岛屿的数量。
岛屿总是被水包围,并且每座岛屿只能由水平方向和/或竖直方向上相邻的陆地连接形成。
此外,你可以假设该网格的四条边均被水包围。
示例 1:
输入:grid = [
["1","1","1","1","0"],
["1","1","0","1","0"],
["1","1","0","0","0"],
["0","0","0","0","0"]
]
输出:1示例 2:
输入:grid = [
["1","1","0","0","0"],
["1","1","0","0","0"],
["0","0","1","0","0"],
["0","0","0","1","1"]
]
输出:3提示:
m == grid.lengthn == grid[i].length1 <= m, n <= 300grid[i][j]的值为'0'或'1'
解题思路:广度优先遍历
这道题具体思路可以参考递归专题中的笔记,这里不再赘述!
使用 bfs 来解决问题,其实思路都是一样的,以每个元素为起点找寻所有的岛屿,并且记录数量,当遇到 1 的时候,则将记录数量增加,然后进行广度优先遍历,将 1 修改为 0。然后继续遍历二维数组直到岛屿都找到了为止!
这里我们采用的修改方式是直接修改原数组,如果不直接修改原数组也是可以的,就得用一个 used 数组来判断是否走过,都是一样的套路,这里就不演示了!
此外,我们将 {i, j} 邻近的符合要求的节点添加到队列中时,就要将其从 1 改为 0,这样子可以减少许多不必要的重复遍历操作,并且不这么做的话,这道题也是会超时的!
class Solution {
private:
int dx[4] = { 0, 0, 1, -1 };
int dy[4] = { -1, 1, 0, 0 };
public:
int numIslands(vector<vector<char>>& grid) {
// 以每个元素为起点找寻所有的岛屿,并且记录数量
int ret = 0;
for(int i = 0; i < grid.size(); ++i)
{
for(int j = 0; j < grid[i].size(); ++j)
{
if(grid[i][j] == '1')
{
ret++;
bfs(grid, i, j); // 进行广度优先遍历,将'1'修改为'0'
}
}
}
return ret;
}
void bfs(vector<vector<char>>& grid, int i, int j)
{
queue<pair<int, int>> qe;
qe.push({i, j});
grid[i][j] = '0';
while(!qe.empty())
{
auto [x, y] = qe.front();
qe.pop();
for(int k = 0; k < 4; ++k)
{
int newx = x + dx[k], newy = y + dy[k];
if(newx >= 0 && newy >= 0 && newx < grid.size() && newy < grid[newx].size() && grid[newx][newy] == '1')
{
qe.push({newx, newy});
grid[newx][newy] = '0'; // 提前将邻近节点改为'0',可以减少许多不必要的重复
}
}
}
}
};