diff --git a/code@xukaixuan/basic_theory/binary_search.js b/code@xukaixuan/basic_theory/binary_search.js
new file mode 100644
index 0000000..90f3b94
--- /dev/null
+++ b/code@xukaixuan/basic_theory/binary_search.js
@@ -0,0 +1,88 @@
+/**
+ * 二分查找
+ */
+
+ // 查找等于第一个给定的值
+const binaryFindFirst = (sortedArr,target) =>{
+    if (sortedArr.length === 0) return -1
+    let low = 0
+    let high = sortedArr.length-1
+    while(low <=high) {
+        const mid = Math.floor((low+high)/2)
+
+        if (target < sortedArr[mid]){
+            high = mid -1
+        }else if (target> sortedArr[mid]){
+            low = mid +1
+        }else{
+            if (mid ===0||sortedArr[mid-1]<target)return mid
+            high = mid -1
+        }
+    }
+    return -1
+}
+
+// 查找最后一个相等的数
+
+const binaryFindLast = (sortedArr,target) =>{
+    if (sortedArr.length ===0) return -1
+    let low =0
+    let high = sortedArr.length-1
+    while(low <=high){
+        const mid = Math.floor((low+high)/2)
+        if (target<sortedArr[mid]){
+            high = mid -1
+        } else if(target>sortedArr[mid]){
+            low = mid +1
+        }else {
+            if (mid ===sortedArr.length -1||sortedArr[mid+1]>target) return mid
+            low = mid + 1
+        }
+    }
+    return -1
+}
+
+// 查找第一个大于等于给定元素的值
+const binaryFindFiRstBig =  (sortedArr,target) =>{
+    if (sortedArr.length === 0) return -1
+    let low = 0
+    let high = sortedArr.length-1
+    while(low< high){
+        const mid = Math.floor((low+high)/2)
+        if (sortedArr[mid] >= target){
+            if (mid ===0||sortedArr[mid-1]<target) return mid
+            high = mid -1
+        }else {
+            low = mid +1
+        }
+    }
+return -1
+}
+
+// 查找最后一个小于等于给定值得元素
+const binaryFindLastSmall =  (sortedArr,target) =>{
+    if (sortedArr.length === 0) return -1
+    let low = 0
+    let high = sortedArr.length-1
+    while(low <=  high){
+        const mid = Math.floor((low+high)/2)
+        if (sortedArr[mid]<target){
+            high = mid -1
+        }else {
+            if (mid ===sortedArr.length-1 ||sortedArr[mid+1]>target) return mid
+            low = mid +1
+        }
+    }
+return -1
+}
+
+const arr = [1, 2, 3, 4, 4, 4, 4, 4, 6, 7, 8, 8, 9]
+const first = biaryFindFirst(arr, 4)
+console.log(`FindFirst: ${first}`)
+
+const last = biaryFindLast(arr, 4)
+console.log(`FindLast: ${last}`)
+const FisrtBig = biaryFindFistBig(arr, 5)
+console.log(`FindFisrtBig: ${FisrtBig}`)
+const LastSmall = biaryFindLastSmall(arr, 4)
+console.log(`FindLastSmall: ${LastSmall}`)
\ No newline at end of file
diff --git a/code@xukaixuan/demo 33 binary_search/33.search-in-rotated-sorted-array.py b/code@xukaixuan/demo 33 binary_search/33.search-in-rotated-sorted-array.py
new file mode 100644
index 0000000..f1c6f42
--- /dev/null
+++ b/code@xukaixuan/demo 33 binary_search/33.search-in-rotated-sorted-array.py	
@@ -0,0 +1,34 @@
+#
+# @lc app=leetcode id=33 lang=python3
+#
+# [33] Search in Rotated Sorted Array
+#
+class Solution:
+    def search(self, nums: List[int], target: int) -> int:
+        def search(self, nums, target):
+        if not nums:
+            return -1
+
+        low, high = 0, len(nums) - 1
+
+        while low <= high:
+            mid = (low + high) / 2
+            if target == nums[mid]:
+                return mid
+
+            if nums[low] <= nums[mid]:
+                if nums[low] <= target <= nums[mid]:
+                    high = mid - 1
+                else:
+                    low = mid + 1
+            else:
+                if nums[mid] <= target <= nums[high]:
+                    low = mid + 1
+                else:
+                    high = mid - 1
+
+        return -1
+
+
+        
+
diff --git a/code@xukaixuan/demo 33 binary_search/readme.md b/code@xukaixuan/demo 33 binary_search/readme.md
new file mode 100644
index 0000000..0e3e3f5
--- /dev/null
+++ b/code@xukaixuan/demo 33 binary_search/readme.md	
@@ -0,0 +1,27 @@
+## Search in Rotated Sorted Array
+
+Tags
+
+array | binary-search
+
+## description 
+Suppose an array sorted in ascending order is rotated at some pivot unknown to you beforehand.
+
+(i.e.,``` [0,1,2,4,5,6,7]``` might become ```[4,5,6,7,0,1,2]```).
+
+You are given a target value to search. If found in the array return its index, otherwise return -1.
+
+You may assume no duplicate exists in the array.
+
+Your algorithm's runtime complexity must be in the order of ```O(log n)```.
+
+```
+Example 1:
+
+Input: nums = [4,5,6,7,0,1,2], target = 0
+Output: 4
+Example 2:
+
+Input: nums = [4,5,6,7,0,1,2], target = 3
+Output: -1
+```
\ No newline at end of file
diff --git a/code@xukaixuan/demo 34 binary_search/34.find-first-and-last-position-of-element-in-sorted-array.py b/code@xukaixuan/demo 34 binary_search/34.find-first-and-last-position-of-element-in-sorted-array.py
new file mode 100644
index 0000000..9043625
--- /dev/null
+++ b/code@xukaixuan/demo 34 binary_search/34.find-first-and-last-position-of-element-in-sorted-array.py	
@@ -0,0 +1,65 @@
+#
+# @lc app=leetcode id=34 lang=python
+#
+# [34] Find First and Last Position of Element in Sorted Array
+#
+class Solution(object):
+    def searchRange(self, nums, target):
+        """
+        :type nums: List[int]
+        :type target: int
+        :rtype: List[int]
+        """
+        lo,hi = 0,len(nums)-1
+        first,last = -1,-1
+        while(lo <=hi):
+            mid = lo +( hi -lo)//2
+            if target< nums[mid]:
+                hi = mid -1
+            elif target >  nums[mid]:
+                lo = mid + 1
+            else :
+                if (mid == 0 or nums[mid-1] < target):
+                    first = mid
+                hi = mid-1
+        lo,hi = 0,len(nums)-1
+        while(lo <= hi):
+            mid = lo +( hi -lo)//2
+            if target< nums[mid]:
+                hi = mid -1
+            elif target >  nums[mid]:
+                lo = mid + 1
+            else :
+                if (mid == len(nums)-1 or nums[mid+1] > target):
+                    last = mid
+                lo = mid+1
+        return [first,last]
+
+
+## most voted 
+
+def searchRange(self, nums, target):
+    def binarySearchLeft(A, x):
+        left, right = 0, len(A) - 1
+        while left <= right:
+            mid = (left + right) / 2
+            if x > A[mid]: left = mid + 1
+            else: right = mid - 1
+        return left
+
+    def binarySearchRight(A, x):
+        left, right = 0, len(A) - 1
+        while left <= right:
+            mid = (left + right) / 2
+            if x >= A[mid]: left = mid + 1
+            else: right = mid - 1
+        return right
+        
+    left, right = binarySearchLeft(nums, target), binarySearchRight(nums, target)
+    return (left, right) if left <= right else [-1, -1]
+
+        
+          
+
+        
+
diff --git a/code@xukaixuan/demo 34 binary_search/readme.md b/code@xukaixuan/demo 34 binary_search/readme.md
new file mode 100644
index 0000000..a575ace
--- /dev/null
+++ b/code@xukaixuan/demo 34 binary_search/readme.md	
@@ -0,0 +1,26 @@
+# Search Insert Position
+
+
+## description
+Given a sorted array and a target value, return the index if the target is found. If not, return the index where it would be if it were inserted in order.
+
+You may assume no duplicates in the array.
+```
+Example 1:
+
+Input: [1,3,5,6], 5
+Output: 2
+Example 2:
+
+Input: [1,3,5,6], 2
+Output: 1
+Example 3:
+
+Input: [1,3,5,6], 7
+Output: 4
+Example 4:
+
+Input: [1,3,5,6], 0
+Output: 0
+```
+