200. Number of Islands
1. Description
Given an m x n 2D binary grid grid which represents a map of ‘1’s (land) and ‘0’s (water), return the number of islands.
An island is surrounded by water and is formed by connecting adjacent lands horizontally or vertically. You may assume all four edges of the grid are all surrounded by water.
2. Example
Example 1
Input: grid = [
[“1”,“1”,“1”,“1”,“0”],
[“1”,“1”,“0”,“1”,“0”],
[“1”,“1”,“0”,“0”,“0”],
[“0”,“0”,“0”,“0”,“0”]
]
Output: 1
Example 2
Input: grid = [
[“1”,“1”,“0”,“0”,“0”],
[“1”,“1”,“0”,“0”,“0”],
[“0”,“0”,“1”,“0”,“0”],
[“0”,“0”,“0”,“1”,“1”]
]
Output: 3
3. Constraints
- m == grid.length
- n == grid[i].length
- 1 <= m, n <= 300
- grid[i][j] is ‘0’ or ‘1’.
4. Solutions
Depth-First Search
m = grid.size(), n = grid.front().size()
Time complexity: O(mn)
Space complexity: O(mn)
class Solution {
public:
int numIslands(vector<vector<char>> grid) {
const int m = grid.size(), n = grid.front().size();
int island_count = 0;
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (grid[i][j] == '1') {
++island_count;
link_islands(grid, m, n, i, j);
}
}
}
return island_count;
}
private:
void link_islands(
vector<vector<char>> &grid,
const int m,
const int n,
const int i,
const int j) {
if (0 <= i && i < m && 0 <= j && j < n && grid[i][j] == '1') {
grid[i][j] = '0';
link_islands(grid, m, n, i + 1, j);
link_islands(grid, m, n, i - 1, j);
link_islands(grid, m, n, i, j + 1);
link_islands(grid, m, n, i, j - 1);
}
}
};