Given a 2D grid consists of 0s (land) and 1s (water). An island is a maximal 4-directionally connected group of 0s and a closed island is an island totally (all left, top, right, bottom) surrounded by 1s.
Return the number of closed islands.
Example 1:
Input: grid = [[1,1,1,1,1,1,1,0],[1,0,0,0,0,1,1,0],[1,0,1,0,1,1,1,0],[1,0,0,0,0,1,0,1],[1,1,1,1,1,1,1,0]] Output: 2 Explanation: Islands in gray are closed because they are completely surrounded by water (group of 1s).
Example 2:
Input: grid = [[0,0,1,0,0],[0,1,0,1,0],[0,1,1,1,0]] Output: 1
Example 3:
Input: grid = [[1,1,1,1,1,1,1],
[1,0,0,0,0,0,1],
[1,0,1,1,1,0,1],
[1,0,1,0,1,0,1],
[1,0,1,1,1,0,1],
[1,0,0,0,0,0,1],
[1,1,1,1,1,1,1]]
Output: 2
Constraints:
1 <= grid.length, grid[0].length <= 1000 <= grid[i][j] <=1
Union find.
class Solution:
def closedIsland(self, grid: List[List[int]]) -> int:
def dfs(i: int, j: int) -> int:
res = int(0 < i < m - 1 and 0 < j < n - 1)
grid[i][j] = 1
for a, b in pairwise(dirs):
x, y = i + a, j + b
if 0 <= x < m and 0 <= y < n and grid[x][y] == 0:
res &= dfs(x, y)
return res
m, n = len(grid), len(grid[0])
dirs = (-1, 0, 1, 0, -1)
return sum(grid[i][j] == 0 and dfs(i, j) for i in range(m) for j in range(n))class UnionFind:
def __init__(self, n: int):
self.p = list(range(n))
self.size = [1] * n
def find(self, x: int) -> int:
if self.p[x] != x:
self.p[x] = self.find(self.p[x])
return self.p[x]
def union(self, a: int, b: int):
pa, pb = self.find(a), self.find(b)
if pa != pb:
if self.size[pa] > self.size[pb]:
self.p[pb] = pa
self.size[pa] += self.size[pb]
else:
self.p[pa] = pb
self.size[pb] += self.size[pa]
class Solution:
def closedIsland(self, grid: List[List[int]]) -> int:
m, n = len(grid), len(grid[0])
uf = UnionFind(m * n + 1)
for i in range(m):
for j in range(n):
if i == 0 or i == m - 1 or j == 0 or j == n - 1:
uf.union(i * n + j, m * n)
if grid[i][j] == 0:
if i < m - 1 and grid[i + 1][j] == 0:
uf.union(i * n + j, (i + 1) * n + j)
if j < n - 1 and grid[i][j + 1] == 0:
uf.union(i * n + j, i * n + j + 1)
ans = 0
for i in range(m):
for j in range(n):
ans += grid[i][j] == 0 and uf.find(i * n + j) == i * n + j
return ansclass Solution {
private int m;
private int n;
private int[][] grid;
public int closedIsland(int[][] grid) {
m = grid.length;
n = grid[0].length;
this.grid = grid;
int ans = 0;
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (grid[i][j] == 0) {
ans += dfs(i, j);
}
}
}
return ans;
}
private int dfs(int i, int j) {
int res = i > 0 && i < m - 1 && j > 0 && j < n - 1 ? 1 : 0;
grid[i][j] = 1;
int[] dirs = {-1, 0, 1, 0, -1};
for (int k = 0; k < 4; ++k) {
int x = i + dirs[k], y = j + dirs[k + 1];
if (x >= 0 && x < m && y >= 0 && y < n && grid[x][y] == 0) {
res &= dfs(x, y);
}
}
return res;
}
}class UnionFind {
private int[] p;
private int[] size;
public UnionFind(int n) {
p = new int[n];
size = new int[n];
for (int i = 0; i < n; ++i) {
p[i] = i;
size[i] = 1;
}
}
public int find(int x) {
if (p[x] != x) {
p[x] = find(p[x]);
}
return p[x];
}
public void union(int a, int b) {
int pa = find(a), pb = find(b);
if (pa != pb) {
if (size[pa] > size[pb]) {
p[pb] = pa;
size[pa] += size[pb];
} else {
p[pa] = pb;
size[pb] += size[pa];
}
}
}
}
class Solution {
public int closedIsland(int[][] grid) {
int m = grid.length, n = grid[0].length;
UnionFind uf = new UnionFind(m * n + 1);
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (i == 0 || i == m - 1 || j == 0 || j == n - 1) {
uf.union(i * n + j, m * n);
}
if (grid[i][j] == 0) {
if (i + 1 < m && grid[i + 1][j] == 0) {
uf.union(i * n + j, (i + 1) * n + j);
}
if (j + 1 < n && grid[i][j + 1] == 0) {
uf.union(i * n + j, i * n + j + 1);
}
}
}
}
int ans = 0;
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (grid[i][j] == 0 && uf.find(i * n + j) == i * n + j) {
++ans;
}
}
}
return ans;
}
}class Solution {
public:
int closedIsland(vector<vector<int>>& grid) {
int m = grid.size(), n = grid[0].size();
int ans = 0;
int dirs[5] = {-1, 0, 1, 0, -1};
function<int(int, int)> dfs = [&](int i, int j) -> int {
int res = i > 0 && i < m - 1 && j > 0 && j < n - 1 ? 1 : 0;
grid[i][j] = 1;
for (int k = 0; k < 4; ++k) {
int x = i + dirs[k], y = j + dirs[k + 1];
if (x >= 0 && x < m && y >= 0 && y < n && grid[x][y] == 0) {
res &= dfs(x, y);
}
}
return res;
};
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
ans += grid[i][j] == 0 && dfs(i, j);
}
}
return ans;
}
};class UnionFind {
public:
UnionFind(int n) {
p = vector<int>(n);
size = vector<int>(n, 1);
iota(p.begin(), p.end(), 0);
}
void unite(int a, int b) {
int pa = find(a), pb = find(b);
if (pa != pb) {
if (size[pa] > size[pb]) {
p[pb] = pa;
size[pa] += size[pb];
} else {
p[pa] = pb;
size[pb] += size[pa];
}
}
}
int find(int x) {
if (p[x] != x) {
p[x] = find(p[x]);
}
return p[x];
}
private:
vector<int> p, size;
};
class Solution {
public:
int closedIsland(vector<vector<int>>& grid) {
int m = grid.size(), n = grid[0].size();
UnionFind uf(m * n + 1);
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (i == 0 || i == m - 1 || j == 0 || j == n - 1) {
uf.unite(i * n + j, m * n);
}
if (grid[i][j] == 0) {
if (i + 1 < m && grid[i + 1][j] == 0) {
uf.unite(i * n + j, (i + 1) * n + j);
}
if (j + 1 < n && grid[i][j + 1] == 0) {
uf.unite(i * n + j, i * n + j + 1);
}
}
}
}
int ans = 0;
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
ans += grid[i][j] == 0 && uf.find(i * n + j) == i * n + j;
}
}
return ans;
}
};func closedIsland(grid [][]int) (ans int) {
m, n := len(grid), len(grid[0])
dirs := [5]int{-1, 0, 1, 0, -1}
var dfs func(i, j int) int
dfs = func(i, j int) int {
res := 1
if i == 0 || i == m-1 || j == 0 || j == n-1 {
res = 0
}
grid[i][j] = 1
for k := 0; k < 4; k++ {
x, y := i+dirs[k], j+dirs[k+1]
if x >= 0 && x < m && y >= 0 && y < n && grid[x][y] == 0 {
res &= dfs(x, y)
}
}
return res
}
for i, row := range grid {
for j, v := range row {
if v == 0 {
ans += dfs(i, j)
}
}
}
return
}type unionFind struct {
p, size []int
}
func newUnionFind(n int) *unionFind {
p := make([]int, n)
size := make([]int, n)
for i := range p {
p[i] = i
size[i] = 1
}
return &unionFind{p, size}
}
func (uf *unionFind) find(x int) int {
if uf.p[x] != x {
uf.p[x] = uf.find(uf.p[x])
}
return uf.p[x]
}
func (uf *unionFind) union(a, b int) {
pa, pb := uf.find(a), uf.find(b)
if pa != pb {
if uf.size[pa] > uf.size[pb] {
uf.p[pb] = pa
uf.size[pa] += uf.size[pb]
} else {
uf.p[pa] = pb
uf.size[pb] += uf.size[pa]
}
}
}
func closedIsland(grid [][]int) (ans int) {
m, n := len(grid), len(grid[0])
uf := newUnionFind(m*n + 1)
for i, row := range grid {
for j, v := range row {
if i == 0 || i == m-1 || j == 0 || j == n-1 {
uf.union(i*n+j, m*n)
}
if v == 0 {
if i+1 < m && grid[i+1][j] == 0 {
uf.union(i*n+j, (i+1)*n+j)
}
if j+1 < n && grid[i][j+1] == 0 {
uf.union(i*n+j, i*n+j+1)
}
}
}
}
for i, row := range grid {
for j, v := range row {
if v == 0 && uf.find(i*n+j) == i*n+j {
ans++
}
}
}
return
}function closedIsland(grid: number[][]): number {
const m = grid.length;
const n = grid[0].length;
const dirs = [-1, 0, 1, 0, -1];
const dfs = (i: number, j: number): number => {
let res = i > 0 && j > 0 && i < m - 1 && j < n - 1 ? 1 : 0;
grid[i][j] = 1;
for (let k = 0; k < 4; ++k) {
const [x, y] = [i + dirs[k], j + dirs[k + 1]];
if (x >= 0 && y >= 0 && x < m && y < n && grid[x][y] === 0) {
res &= dfs(x, y);
}
}
return res;
};
let ans = 0;
for (let i = 0; i < m; ++i) {
for (let j = 0; j < n; j++) {
if (grid[i][j] === 0) {
ans += dfs(i, j);
}
}
}
return ans;
}function closedIsland(grid: number[][]): number {
const m = grid.length;
const n = grid[0].length;
const uf = new UnionFind(m * n + 1);
for (let i = 0; i < m; ++i) {
for (let j = 0; j < n; ++j) {
if (i === 0 || i === m - 1 || j === 0 || j === n - 1) {
uf.union(i * n + j, m * n);
}
if (grid[i][j] === 0) {
if (i + 1 < m && grid[i + 1][j] === 0) {
uf.union(i * n + j, (i + 1) * n + j);
}
if (j + 1 < n && grid[i][j + 1] === 0) {
uf.union(i * n + j, i * n + j + 1);
}
}
}
}
let ans = 0;
for (let i = 0; i < m; ++i) {
for (let j = 0; j < n; j++) {
if (grid[i][j] === 0 && uf.find(i * n + j) === i * n + j) {
++ans;
}
}
}
return ans;
}
class UnionFind {
private p: number[];
private size: number[];
constructor(n: number) {
this.p = Array(n)
.fill(0)
.map((_, i) => i);
this.size = Array(n).fill(1);
}
find(x: number): number {
if (this.p[x] !== x) {
this.p[x] = this.find(this.p[x]);
}
return this.p[x];
}
union(a: number, b: number): void {
const [pa, pb] = [this.find(a), this.find(b)];
if (pa === pb) {
return;
}
if (this.size[pa] > this.size[pb]) {
this.p[pb] = pa;
this.size[pa] += this.size[pb];
} else {
this.p[pa] = pb;
this.size[pb] += this.size[pa];
}
}
}public class Solution {
private int m;
private int n;
private int[][] grid;
public int ClosedIsland(int[][] grid) {
m = grid.Length;
n = grid[0].Length;
this.grid = grid;
int ans = 0;
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (grid[i][j] == 0) {
ans += dfs(i, j);
}
}
}
return ans;
}
private int dfs(int i, int j) {
int res = i > 0 && i < m - 1 && j > 0 && j < n - 1 ? 1 : 0;
grid[i][j] = 1;
int[] dirs = {-1, 0, 1, 0, -1};
for (int k = 0; k < 4; ++k) {
int x = i + dirs[k], y = j + dirs[k + 1];
if (x >= 0 && x < m && y >= 0 && y < n && grid[x][y] == 0) {
res &= dfs(x, y);
}
}
return res;
}
}class UnionFind {
private int[] p;
private int[] size;
public UnionFind(int n) {
p = new int[n];
size = new int[n];
for (int i = 0; i < n; ++i) {
p[i] = i;
size[i] = 1;
}
}
public int find(int x) {
if (p[x] != x) {
p[x] = find(p[x]);
}
return p[x];
}
public void union(int a, int b) {
int pa = find(a), pb = find(b);
if (pa != pb) {
if (size[pa] > size[pb]) {
p[pb] = pa;
size[pa] += size[pb];
} else {
p[pa] = pb;
size[pb] += size[pa];
}
}
}
}
public class Solution {
public int ClosedIsland(int[][] grid) {
int m = grid.Length, n = grid[0].Length;
UnionFind uf = new UnionFind(m * n + 1);
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (i == 0 || i == m - 1 || j == 0 || j == n - 1) {
uf.union(i * n + j, m * n);
}
if (grid[i][j] == 0) {
if (i + 1 < m && grid[i + 1][j] == 0) {
uf.union(i * n + j, (i + 1) * n + j);
}
if (j + 1 < n && grid[i][j + 1] == 0) {
uf.union(i * n + j, i * n + j + 1);
}
}
}
}
int ans = 0;
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (grid[i][j] == 0 && uf.find(i * n + j) == i * n + j) {
++ans;
}
}
}
return ans;
}
}