problem: 0074 search a 2d matrix

0074 Search a 2D Matrix/0074 Search a 2D Matrix.md

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+# 0074. Search a 2D Matrix
+
+* Difficulty: medium
+* Link: https://leetcode.com/problems/search-a-2d-matrix/
+* Topics: https://www.notion.so/Binary-Search-a35f22a087844ae2b1736e1c8baaf125
+* highlight: 可以分兩半的位置→左下角 (/右上角)
+
+# Clarification
+
+1. Check the inputs and outputs
+    - INPUT:
+        - List[List[int]] matrix
+        - int target
+    - OUTPUT: bool
+
+# Solution
+
+### Thought Process
+
+- 從左下角 (或右上角) 開始搜尋
+    - 當 target > 當前值 ⇒ 在當前值的右半部
+    - 當 target < 當前值 ⇒ 在當前值的上半部
+
+    ![Untitled](./Untitled.png)
+
+- Implement
+
+    ```python
+    class Solution:
+        def searchMatrix(self, matrix: List[List[int]], target: int) -> bool:
+            # search from left down corner
+            i = 0
+            j = len(matrix[0]) - 1
+            while i < len(matrix) and j >= 0:
+                if target == matrix[i][j]:
+                    return True
+                if target > matrix[i][j]:
+                    i += 1
+                else:
+                    j -= 1
+            return False
+    ```
+
+
+### Complexity
+
+- Time complexity: O(log n)
+- Space complexity: O(1)