problem: 0704 binary search

Author: cychiu8

0704 Binary Search/0704 Binary Search.md

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+# 0704. Binary Search
+
+* Difficulty: easy
+* Link: https://leetcode.com/problems/binary-search/
+* Topics: Binary-Search
+
+# Clarification
+
+1. Check the inputs and outputs
+    - INPUT: List[int]
+    - OUTPUT: index of list
+2. Check the main goal
+    - the list is sorted
+    - time complexity in O(log n)
+
+# Naive Solution
+
+### Thought Process
+
+- 建立兩個指標
+    - left pointer: 陣列開頭的位置、值的下限)
+    - right pointer: 陣列結束的位置、值的上限
+1. 找中間指標對應的值
+    - = target ⇒ return
+    - < target ⇒ 調高下限 left pointer ++
+    - > target ⇒ 調低上限 right pointer - -
+- Implement
+    
+    ```python
+    class Solution:
+        def search(self, nums: List[int], target: int) -> int:
+            left = 0
+            right = len(nums) - 1
+            while left <= right:
+                mid = int((left + right) / 2)
+                if nums[mid] == target:
+                    return mid
+                if nums[mid] < target:
+                    left += 1
+                elif nums[mid] > target:
+                    right -= 1
+            return -1
+    ```
+    
+
+### Complexity
+
+- Time complexity: O(log n)
+- Space complexity: O(1)
+
+# Reference
+
+- ****[初學者學演算法｜從時間複雜度認識常見演算法](https://medium.com/appworks-school/%E5%88%9D%E5%AD%B8%E8%80%85%E5%AD%B8%E6%BC%94%E7%AE%97%E6%B3%95-%E5%BE%9E%E6%99%82%E9%96%93%E8%A4%87%E9%9B%9C%E5%BA%A6%E8%AA%8D%E8%AD%98%E5%B8%B8%E8%A6%8B%E6%BC%94%E7%AE%97%E6%B3%95-%E4%B8%80-b46fece65ba5)****