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English Version

题目描述

给出一个二维数组 A,每个单元格为 0(代表海)或 1(代表陆地)。

移动是指在陆地上从一个地方走到另一个地方(朝四个方向之一)或离开网格的边界。

返回网格中无法在任意次数的移动中离开网格边界的陆地单元格的数量。

 

示例 1:

输入:[[0,0,0,0],[1,0,1,0],[0,1,1,0],[0,0,0,0]]
输出:3
解释: 
有三个 1 被 0 包围。一个 1 没有被包围,因为它在边界上。

示例 2:

输入:[[0,1,1,0],[0,0,1,0],[0,0,1,0],[0,0,0,0]]
输出:0
解释:
所有 1 都在边界上或可以到达边界。

 

提示:

  1. 1 <= A.length <= 500
  2. 1 <= A[i].length <= 500
  3. 0 <= A[i][j] <= 1
  4. 所有行的大小都相同

解法

并查集。

模板 1——朴素并查集:

# 初始化,p存储每个点的父节点
p = list(range(n))

# 返回x的祖宗节点
def find(x):
    if p[x] != x:
        # 路径压缩
        p[x] = find(p[x])
    return p[x]

# 合并a和b所在的两个集合
p[find(a)] = find(b)

模板 2——维护 size 的并查集:

# 初始化,p存储每个点的父节点,size只有当节点是祖宗节点时才有意义,表示祖宗节点所在集合中,点的数量
p = list(range(n))
size = [1] * n

# 返回x的祖宗节点
def find(x):
    if p[x] != x:
        # 路径压缩
        p[x] = find(p[x])
    return p[x]

# 合并a和b所在的两个集合
if find(a) != find(b):
    size[find(b)] += size[find(a)]
    p[find(a)] = find(b)

模板 3——维护到祖宗节点距离的并查集:

# 初始化,p存储每个点的父节点,d[x]存储x到p[x]的距离
p = list(range(n))
d = [0] * n

# 返回x的祖宗节点
def find(x):
    if p[x] != x:
        t = find(p[x])
        d[x] += d[p[x]]
        p[x] = t
    return p[x]

# 合并a和b所在的两个集合
p[find(a)] = find(b)
d[find(a)] = distance

Python3

class Solution:
    def numEnclaves(self, grid: List[List[int]]) -> int:
        m, n = len(grid), len(grid[0])
        p = list(range(m * n + 1))

        def find(x):
            if p[x] != x:
                p[x] = find(p[x])
            return p[x]

        for i in range(m):
            for j in range(n):
                if grid[i][j] == 1:
                    if i == 0 or i == m - 1 or j == 0 or j == n - 1:
                        p[find(i * n + j)] = find(m * n)
                    else:
                        for x, y in [[0, 1], [0, -1], [1, 0], [-1, 0]]:
                            if grid[i + x][j + y] == 1:
                                p[find(i * n + j)] = find((i + x) * n + j + y)

        res = 0
        for i in range(m):
            for j in range(n):
                if grid[i][j] == 1 and find(i * n + j) != find(m * n):
                    res += 1
        return res

Java

class Solution {
    private int[] p;
    private int[][] dirs = new int[][]{{0, -1}, {0, 1}, {1, 0}, {-1, 0}};

    public int numEnclaves(int[][] grid) {
        int m = grid.length, n = grid[0].length;
        p = new int[m * n + 1];
        for (int i = 0; i < p.length; ++i) {
            p[i] = i;
        }
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                if (grid[i][j] == 1) {
                    if (i == 0 || i == m - 1 || j == 0 || j == n - 1) {
                        p[find(i * n + j)] = find(m * n);
                    } else {
                        for (int[] e : dirs) {
                            if (grid[i + e[0]][j + e[1]] == 1) {
                                p[find(i * n + j)] = find((i + e[0]) * n + j + e[1]);
                            }
                        }
                    }
                }
            }
        }
        int res = 0;
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                if (grid[i][j] == 1 && find(i * n + j) != find(m * n)) {
                    ++res;
                }
            }
        }
        return res;
    }

    private int find(int x) {
        if (p[x] != x) {
            p[x] = find(p[x]);
        }
        return p[x];
    }
}

C++

class Solution {
public:
    vector<int> p;
    int dirs[4][2] = {{0, -1}, {0, 1}, {1, 0}, {-1, 0}};

    int numEnclaves(vector<vector<int>>& grid) {
        int m = grid.size(), n = grid[0].size();
        p.resize(m * n + 1);
        for (int i = 0; i < p.size(); ++i) p[i] = i;
        for (int i = 0; i < m; ++i)
        {
            for (int j = 0; j < n; ++j)
            {
                if (grid[i][j] == 1)
                {
                    if (i == 0 || i == m - 1 || j == 0 || j == n - 1) p[find(i * n + j)] = find(m * n);
                    else
                    {
                        for (auto e : dirs)
                        {
                            if (grid[i + e[0]][j + e[1]] == 1) p[find(i * n + j)] = find((i + e[0]) * n + j + e[1]);
                        }
                    }
                }
            }
        }
        int res = 0;
        for (int i = 0; i < m; ++i)
        {
            for (int j = 0; j < n; ++j)
            {
                if (grid[i][j] == 1 && find(i * n + j) != find(m * n)) ++res;
            }
        }
        return res;
    }

    int find(int x) {
        if (p[x] != x) p[x] = find(p[x]);
        return p[x];
    }
};

Go

var p []int

func numEnclaves(grid [][]int) int {
	m, n := len(grid), len(grid[0])
	p = make([]int, m*n+1)
	for i := 0; i < len(p); i++ {
		p[i] = i
	}
	dirs := [4][2]int{{0, -1}, {0, 1}, {1, 0}, {-1, 0}}
	for i := 0; i < m; i++ {
		for j := 0; j < n; j++ {
			if grid[i][j] == 1 {
				if i == 0 || i == m-1 || j == 0 || j == n-1 {
					p[find(i*n+j)] = find(m * n)
				} else {
					for _, e := range dirs {
						if grid[i+e[0]][j+e[1]] == 1 {
							p[find(i*n+j)] = find((i+e[0])*n + j + e[1])
						}
					}
				}
			}
		}
	}
	res := 0
	for i := 0; i < m; i++ {
		for j := 0; j < n; j++ {
			if grid[i][j] == 1 && find(i*n+j) != find(m*n) {
				res++
			}
		}
	}
	return res
}

func find(x int) int {
	if p[x] != x {
		p[x] = find(p[x])
	}
	return p[x]
}

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