problem: 0442 find all duplicates in an array

0442 Find All Duplicates in an Array/0442 Find All Duplicates in an Array.md

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+# 0442. Find All Duplicates in an Array
+
+- Difficulty: medium
+- Link: https://leetcode.com/problems/find-all-duplicates-in-an-array
+- Topics: Array-String
+
+# Clarification
+
+1. Check the inputs and outputs
+    - INPUT: List[int]
+    - OUTPUT: List[int]
+2. Check the main goal
+    - return the duplicate numbers
+    - time complexity $O(n)$
+    - space complexity $O(1)$
+
+# Naive Solution
+
+### Thought Process
+
+1. iterate the array
+    1. consider the element as the index
+    2. find the corresponding element 
+        1. is already negative → duplicate
+        2. times it with negative
+- Implement
+
+    ```python
+    class Solution:
+        def findDuplicates(self, nums: List[int]) -> List[int]:
+            """
+            1. iterate the array
+                a. consider the element as the index
+                b. find the corresponding element 
+                    i. is already negative → duplicate
+                    ii. times it with negative
+            """
+            result = []
+            for num in nums:
+                absNum = abs(num)
+                if nums[absNum - 1] < 0:
+                    result.append(absNum)
+                nums[absNum - 1] *= (-1)
+            return result
+    ```
+
+
+### Complexity
+
+- Time complexity: $O(n)$
+
+    ![Untitled](./Untitled.png)
+
+- Space complexity:$O(1)$