From b8dde4c1d678ae4be4412b8624eddf9c2d945242 Mon Sep 17 00:00:00 2001
From: Divyam22 <divyam2219@gmail.com>
Date: Sat, 23 Aug 2025 21:09:56 -0400
Subject: [PATCH] Done with Binary-Search-2

---
 Problem1.py | 69 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 Problem2.py | 26 ++++++++++++++++++++
 2 files changed, 95 insertions(+)
 create mode 100644 Problem1.py
 create mode 100644 Problem2.py

diff --git a/Problem1.py b/Problem1.py
new file mode 100644
index 00000000..5809b87b
--- /dev/null
+++ b/Problem1.py
@@ -0,0 +1,69 @@
+"""
+TC: O(log(N)) {since we perform binary search to first find the element, and then do two binary searches in each half to search for
+                the lowest and the highest. Since constants dont matter in time complexities, we get O(log(N)) t.c.}
+SC: O(1)        {we dont use any extra spaces}
+
+The problem succesfully ran on LeetCode
+"""
+
+class Solution:
+    def searchRange(self, nums: List[int], target: int) -> List[int]:
+        if len(nums) == 0:
+            return [-1,-1]
+        if len(nums) == 1:
+            return [0,0] if nums[0] == target else [-1,-1]
+        
+        def expand(idx):
+            # for searching the lowest occurence
+            low = 0
+            high = idx
+
+            lowest = high
+
+            while low <= high:
+                mid = low + (high - low)//2
+                if nums[mid] == target:
+                    high = mid - 1
+                    lowest = mid
+                elif nums[mid] < target:
+                    low = mid + 1
+                else:
+                    break
+            
+            # searching for the highest
+            low = idx
+            high = len(nums)-1
+            highest = low
+
+            while low <= high:
+                mid = low + (high - low)//2
+                if target == nums[mid]:
+                    low = mid + 1
+                    highest = mid
+                elif target < nums[mid]:
+                    high = mid - 1
+                else:
+                    break
+            return [lowest, highest]
+
+
+
+
+
+        low, high = 0, len(nums) - 1
+
+        while low <= high:
+            mid = low + (high - low)//2
+
+            if target == nums[mid]:
+                start, end = expand(mid)
+                return [start, end]
+            
+            if nums[mid] < target:
+                low = mid + 1
+            else:
+                high = mid - 1
+        
+        return [-1, -1]
+       
+       
\ No newline at end of file
diff --git a/Problem2.py b/Problem2.py
new file mode 100644
index 00000000..e71b6309
--- /dev/null
+++ b/Problem2.py
@@ -0,0 +1,26 @@
+"""
+TC: O(log(N)) {The minimum always lie in the unsorted half of the array, hence we discard the sorted half of the array 
+                and continue our search on the other half, we get O(log(N)) t.c.}
+SC: O(1)        {we dont use any extra spaces}
+
+The problem succesfully ran on LeetCode
+"""
+
+class Solution:
+    def findMin(self, nums: List[int]) -> int:
+        if len(nums) == 1:
+            return nums[0]
+        low, high = 0, len(nums)-1
+
+        while low<=high:
+            mid = low + (high-low)//2
+
+            if nums[low] <= nums[high]:
+                return nums[low]
+            
+            if nums[low] <= nums[mid]:
+                low = mid + 1
+            else:
+                high = mid 
+            
+