01-matrix

OJ notes/pages/Leetcode 01-Matrix.md

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+# Leetcode 01-Matrix
+
+#### 2022-07-17 03:15
+
+> ##### Algorithms:
+> #algorithm #BFS 
+> ##### Data structures:
+> #DS #vector_2d 
+> ##### Difficulty:
+> #coding_problem #difficulty-medium 
+> ##### Additional tags:
+> #leetcode #CS_list_need_understanding 
+> ##### Revisions:
+> N/A
+
+##### Related topics:
+```expander
+tag:#BFS
+```
+ 
+ 
+
+##### Links:
+- [Link to problem](https://leetcode.com/problems/01-matrix/)
+___
+### Problem
+
+Given an `m x n` binary matrix `mat`, return _the distance of the nearest_ `0` _for each cell_.
+
+The distance between two adjacent cells is `1`.
+
+#### Examples
+
+**Example 1:**
+
+![](https://assets.leetcode.com/uploads/2021/04/24/01-1-grid.jpg)
+
+```
+**Input:** mat = [[0,0,0],[0,1,0],[0,0,0]]
+**Output:** [[0,0,0],[0,1,0],[0,0,0]]
+```
+
+**Example 2:**
+
+![](https://assets.leetcode.com/uploads/2021/04/24/01-2-grid.jpg)
+
+```
+**Input:** mat = [[0,0,0],[0,1,0],[1,1,1]]
+**Output:** [[0,0,0],[0,1,0],[1,2,1]]
+```
+
+#### Constraints
+
+-   `m == mat.length`
+-   `n == mat[i].length`
+-   `1 <= m, n <= 104`
+-   `1 <= m * n <= 104`
+-   `mat[i][j]` is either `0` or `1`.
+-   There is at least one `0` in `mat`.
+
+### Thoughts
+
+> [!summary]
+> This is a #BFS problem, because it needs to find
+>  a smallest distance
+
+#### Why not DFS
+
+I tried with DFS, but
+1. it is not suitable for finding smallest distance 
+2. and is easy to go into a infinite loop.
+3. Also, it is hard to determine whether to revisit (update) 
+   the distance.
+
+#### BFS
+
+Start searching from 0s, because the search direction matters.
+
+pseudo code:
+
+- Initialization stage:
+	- add every 0 to queue
+	- make every 1 a infinite large number, (10001 this case)
+
+- while queue is not empty
+	- check for neighbors
+		- if OOB, skip
+		- if the value of neighbor's distance is higher than 
+		  the node, update it, and add it to queue(also update 
+		  his neighbors)
+
+### Solution
+
+```cpp
+class Solution {
+  const int MAX = 10002;
+
+public:
+  vector<vector<int>> updateMatrix(vector<vector<int>> &mat) {
+    // Shouldn't use DFS, since DFS is likely to run into a loop
+    queue<pair<int, int>> todo;
+    int m = mat.size(), n = mat[0].size();
+    for (int i = 0; i < m; i++) {
+      for (int j = 0; j < n; j++) {
+        if (mat[i][j] == 0) {
+          todo.push({i, j});
+        } else {
+          mat[i][j] = MAX;
+        }
+      }
+    }
+
+    int offset[] = {-1, 1};
+    int x, y;
+    int newX, newY;
+    int dist;
+    while (!todo.empty()) {
+      x = todo.front().first;
+      y = todo.front().second;
+      todo.pop();
+      dist = mat[x][y];
+
+      for (int i : offset) {
+        newX = x + i;
+        if (newX < m && newX >= 0) {
+          if (mat[newX][y] > dist + 1) {
+            mat[newX][y] = dist + 1;
+            todo.push({newX, y});
+          }
+        }
+        newY = y + i;
+        if (newY < n && newY >= 0) {
+          if (mat[x][newY] > dist + 1) {
+            mat[x][newY] = dist + 1;
+            todo.push({x, newY});
+          }
+        }
+      }
+    }
+    return mat;
+  }
+};
+```