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This approach uses a Breadth-First Search (BFS) algorithm to explore each group of farmland on the matrix.
Starting from a farmland cell (1), the BFS can be used to explore all connected cells that belong to the same group, thereby finding the bottom-right corner of that group. Use a queue to facilitate the exploration of individual farmlands.
Mark cells as visited as you explore them to ensure each cell is processed only once.
Time Complexity: O(m * n), as each cell is visited at most once.
Space Complexity: O(m * n) in the worst case due to additional space used for storing visited cells and the queue.
1#include <stdio.h>
2#include <stdlib.h>
3#include <stdbool.h>
4#include <string.h>
5
6void bfs(int** land, bool** visited, int m, int n, int start_row, int start_col, int* end_row, int* end_col) {
7 int directions[2][2] = {{0, 1}, {1, 0}};
8 int queue[m * n][2];
9 int front = 0, back = 0;
10 queue[back][0] = start_row;
11 queue[back][1] = start_col;
12 back++;
13 visited[start_row][start_col] = true;
14 *end_row = start_row;
15 *end_col = start_col;
16
17 while (front < back) {
18 int row = queue[front][0];
19 int col = queue[front][1];
20 front++;
21 *end_row = row;
22 *end_col = col;
23
24 for (int i = 0; i < 2; i++) {
25 int new_row = row + directions[i][0];
26 int new_col = col + directions[i][1];
27 if (new_row < m && new_col < n && !visited[new_row][new_col] && land[new_row][new_col] == 1) {
28 visited[new_row][new_col] = true;
29 queue[back][0] = new_row;
30 queue[back][1] = new_col;
31 back++;
32 }
33 }
34 }
35}
36
37int** findFarmland(int** land, int m, int n, int* returnSize, int** returnColumnSizes) {
38 bool** visited = (bool**)malloc(m * sizeof(bool*));
39 for (int i = 0; i < m; i++) {
40 visited[i] = (bool*)calloc(n, sizeof(bool));
41 }
42
43 int** results = (int**)malloc(m * n * sizeof(int*));
44 *returnColumnSizes = (int*)malloc(m * n * sizeof(int));
45 int count = 0;
46
47 for (int i = 0; i < m; i++) {
48 for (int j = 0; j < n; j++) {
49 if (land[i][j] == 1 && !visited[i][j]) {
50 int end_row, end_col;
51 bfs(land, visited, m, n, i, j, &end_row, &end_col);
52
53 results[count] = (int*)malloc(4 * sizeof(int));
54 results[count][0] = i;
55 results[count][1] = j;
56 results[count][2] = end_row;
57 results[count][3] = end_col;
58 (*returnColumnSizes)[count] = 4;
59 count++;
60 }
61 }
62 }
63
64 *returnSize = count;
65 for (int i = 0; i < m; i++) {
66 free(visited[i]);
67 }
68 free(visited);
69 return results;
70}
The solution uses BFS to identify connected farmland cells that form a rectangle. By starting from each unvisited '1' cell, the algorithm explores in the right and downward directions to find the boundaries. Each boundary-found block is recorded.
This approach implements a Union-Find (also called Disjoint Set Union) data structure to efficiently group farmland cells together. After processing all connections, each cell will belong to a group denoted by its root, and by traversing all cells, we can identify the top-left and bottom-right corners of each group.
Time Complexity: O(m * n * α(n)), with α being the inverse Ackermann function, which grows very slowly, making this almost O(m * n).
Space Complexity: O(m * n) due to storage for parents and ranks of each cell.
#include <unordered_map>
using namespace std;
class Solution {
public:
vector<int> parent, rank;
int find(int x) {
if (parent[x] != x) {
parent[x] = find(parent[x]);
}
return parent[x];
}
void unionSets(int x, int y) {
int rootX = find(x);
int rootY = find(y);
if (rootX != rootY) {
if (rank[rootX] > rank[rootY]) {
parent[rootY] = rootX;
} else if (rank[rootX] < rank[rootY]) {
parent[rootX] = rootY;
} else {
parent[rootY] = rootX;
rank[rootX]++;
}
}
}
vector<vector<int>> findFarmland(vector<vector<int>>& land) {
int m = land.size();
int n = land[0].size();
parent.resize(m * n);
rank.resize(m * n, 0);
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (land[i][j] == 1) {
int index = i * n + j;
parent[index] = index;
if (i > 0 && land[i-1][j] == 1) {
unionSets(index, (i-1) * n + j);
}
if (j > 0 && land[i][j-1] == 1) {
unionSets(index, i * n + (j-1));
}
}
}
}
unordered_map<int, vector<int>> bounds;
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (land[i][j] == 1) {
int root = find(i * n + j);
if (!bounds.count(root)) {
bounds[root] = {i, j, i, j};
} else {
bounds[root][0] = min(bounds[root][0], i);
bounds[root][1] = min(bounds[root][1], j);
bounds[root][2] = max(bounds[root][2], i);
bounds[root][3] = max(bounds[root][3], j);
}
}
}
}
vector<vector<int>> results;
for (auto& bound : bounds) {
results.push_back(bound.second);
}
return results;
}
};
This implementation in C++ uses the Union-Find structure to unite connected farmland cells. The results are determined by traversing the parent nodes to derive rectangular coordinates.