417

Author: lzl124631x

leetcode/417. Pacific Atlantic Water Flow/README.md

@@ -0,0 +1,82 @@
+# [417. Pacific Atlantic Water Flow (Medium)](https://leetcode.com/problems/pacific-atlantic-water-flow/)
+
+<p>Given an <code>m x n</code> matrix of non-negative integers representing the height of each unit cell in a continent, the "Pacific ocean" touches the left and top edges of the matrix and the "Atlantic ocean" touches the right and bottom edges.</p>
+
+<p>Water can only flow in four directions (up, down, left, or right) from a cell to another one with height equal or lower.</p>
+
+<p>Find the list of grid coordinates where water can flow to both the Pacific and Atlantic ocean.</p>
+
+<p><b>Note:</b></p>
+
+<ol>
+	<li>The order of returned grid coordinates does not matter.</li>
+	<li>Both <i>m</i> and <i>n</i> are less than 150.</li>
+</ol>
+
+<p>&nbsp;</p>
+
+<p><b>Example:</b></p>
+
+<pre>Given the following 5x5 matrix:
+
+  Pacific ~   ~   ~   ~   ~ 
+       ~  1   2   2   3  (5) *
+       ~  3   2   3  (4) (4) *
+       ~  2   4  (5)  3   1  *
+       ~ (6) (7)  1   4   5  *
+       ~ (5)  1   1   2   4  *
+          *   *   *   *   * Atlantic
+
+Return:
+
+[[0, 4], [1, 3], [1, 4], [2, 2], [3, 0], [3, 1], [4, 0]] (positions with parentheses in above matrix).
+</pre>
+
+<p>&nbsp;</p>
+
+
+**Related Topics**:  
+[Depth-first Search](https://leetcode.com/tag/depth-first-search/), [Breadth-first Search](https://leetcode.com/tag/breadth-first-search/)
+
+## Solution 1.
+
+We can also use a two bits for each cell to represent if it's reachable from top-left and/or bottom-right. Here for simplicity I just used two `vector<vector<int>>`.
+
+```cpp
+// OJ: https://leetcode.com/problems/pacific-atlantic-water-flow/
+// Author: github.com/lzl124631x
+// Time: O(MN)
+// Space: O(MN)
+class Solution {
+    int dirs[4][2] = {{0,1},{0,-1},{1,0},{-1,0}}, M, N;
+    void dfs(vector<vector<int>> &A, int x, int y, vector<vector<int>> &m) {
+        if (m[x][y]) return;
+        m[x][y] = 1;
+        for (auto &[dx, dy] : dirs) {
+            int a = x + dx, b = y + dy;
+            if (a < 0 || a >= M || b < 0 || b >= N || A[a][b] < A[x][y]) continue;
+            dfs(A, a, b, m);
+        }
+    }
+public:
+    vector<vector<int>> pacificAtlantic(vector<vector<int>>& A) {
+        if (A.empty() || A[0].empty()) return {};
+        M = A.size(), N = A[0].size();
+        vector<vector<int>> a(M, vector<int>(N)), b(M, vector<int>(N)), ans; 
+        for (int i = 0; i < M; ++i) {
+            dfs(A, i, 0, a);
+            dfs(A, i, N - 1, b);
+        }
+        for (int j = 0; j < N; ++j) {
+            dfs(A, 0, j, a);
+            dfs(A, M - 1, j, b);
+        }
+        for (int i = 0; i < M; ++i) {
+            for (int j = 0; j < N; ++j) {
+                if (a[i][j] && b[i][j]) ans.push_back({i, j});
+            }
+        }
+        return ans;
+    }
+};
+```