From bf493d486c458ee961e12808d837c0dbfab6aee5 Mon Sep 17 00:00:00 2001
From: RITIKA CHAUBE <ritikarchaube@gmail.com>
Date: Mon, 8 Jun 2026 16:13:24 -0400
Subject: [PATCH] Done with Precourse 2

---
 Exercise_1.py | 19 ++++++++++++++---
 Exercise_2.py | 27 +++++++++++++++++++------
 Exercise_3.py | 27 ++++++++++++++++++++-----
 Exercise_4.py | 49 +++++++++++++++++++++++++++++---------------
 Exercise_5.py | 56 +++++++++++++++++++++++++++++++++++++++++++++++----
 5 files changed, 144 insertions(+), 34 deletions(-)

diff --git a/Exercise_1.py b/Exercise_1.py
index 3e6adcf4..06de3c22 100644
--- a/Exercise_1.py
+++ b/Exercise_1.py
@@ -3,11 +3,24 @@
   
 # It returns location of x in given array arr  
 # if present, else returns -1 
+
+# Time and Space Complexity
+# Time Complexity is O(log N) where N is the nuber of elements that are present in the given arr
+# Space Complexity is O(1) as the variables are constant irrespective of the array size
 def binarySearch(arr, l, r, x): 
   
   #write your code here
+  while l<=r:
+     mid=(l+r)//2
+     if arr[mid]==x:
+        return mid
+     elif x<arr[mid]:
+        r=mid-1
+     else:
+        l=mid+1
   
-    
+  return -1 
+      
   
 # Test array 
 arr = [ 2, 3, 4, 10, 40 ] 
@@ -17,6 +30,6 @@ def binarySearch(arr, l, r, x):
 result = binarySearch(arr, 0, len(arr)-1, x) 
   
 if result != -1: 
-    print "Element is present at index % d" % result 
+    print ("Element is present at index % d" % result)
 else: 
-    print "Element is not present in array"
+    print ("Element is not present in array")
diff --git a/Exercise_2.py b/Exercise_2.py
index 35abf0dd..06a402c1 100644
--- a/Exercise_2.py
+++ b/Exercise_2.py
@@ -1,16 +1,31 @@
+# Time and Space Complexity
+# Space Complexity: O(lon N) where N is the number of elements present
+# Time Complexity: Average case is O(Nlog N) 
+# partition function has time complexity of O(N) and space complexity of O(1)
+# quickSort function has space complexity of O(N log N) and space complexity of O(log N)
+
 # Python program for implementation of Quicksort Sort 
   
-# give you explanation for the approach
+
 def partition(arr,low,high):
-  
-  
     #write your code here
+    pivot=arr[high]
+    i=low-1
+
+    for j in range(low,high):
+        if arr[j]<=pivot:
+            i+=1
+            arr[i],arr[j]=arr[j],arr[i]
+    arr[i+1],arr[high]=arr[high],arr[i+1]
+    return i+1
   
 
-# Function to do Quick sort 
 def quickSort(arr,low,high): 
-    
-    #write your code here
+    if low<high:
+        value=partition(arr,low,high)
+        quickSort(arr,low,value-1)
+        quickSort(arr,value+1,high)
+
   
 # Driver code to test above 
 arr = [10, 7, 8, 9, 1, 5] 
diff --git a/Exercise_3.py b/Exercise_3.py
index a26a69b8..b702170c 100644
--- a/Exercise_3.py
+++ b/Exercise_3.py
@@ -1,20 +1,37 @@
+# Time and Space Complexity
+# Space Complexity: O (N) where N denoted the number of elementes/nodes in the given LinkedList
+# Time Complexity: 
+# push function has the time complexity of O(1) amd space complexity of O(1)
+# printMiddle function has the time complexity of O(N) and space complexity of O(1)
+
 # Node class  
 class Node:  
   
     # Function to initialise the node object  
-    def __init__(self, data):  
+    def __init__(self, data):
+        self.data=data
+        self.next=None
         
 class LinkedList: 
   
     def __init__(self): 
-        
+        self.head=None
   
-    def push(self, new_data): 
-        
+    def push(self, new_data):
+        newNode=Node(new_data)
+        newNode.next=self.head
+        self.head=newNode
   
     # Function to get the middle of  
     # the linked list 
-    def printMiddle(self): 
+    def printMiddle(self):
+        slow=fast=self.head
+        while fast !=None and fast.next!=None:
+            fast=fast.next.next
+            slow=slow.next
+        print("Middle element is:",slow.data)
+        return slow.data
+
 
 # Driver code 
 list1 = LinkedList() 
diff --git a/Exercise_4.py b/Exercise_4.py
index 9bc25d3d..bfc665f2 100644
--- a/Exercise_4.py
+++ b/Exercise_4.py
@@ -1,18 +1,35 @@
-# Python program for implementation of MergeSort 
+#Kindly include Time and Space complexity at top of each file
+
+#Time and Space Complexity
+# Space Complexity : O(N)
+# Time Complexity : O(N log N) where N is the number of elements in the array
+
+ 
 def mergeSort(arr):
-  
-  #write your code here
-  
-# Code to print the list 
-def printList(arr): 
+  if len(arr)>1:
+     mid=len(arr)//2
+     left=arr[:mid]
+     right=arr[mid:]
+
+     mergeSort(left)
+     mergeSort(right)
+
+     i=j=k=0
+     while i<len(left) and j<len(right):
+        if left[i]<right[j]:
+           arr[k]=left[i]
+           i=i+1
+        else:
+           arr[k]=right[j]
+           j=j+1
+        k=k+1
     
-    #write your code here
-  
-# driver code to test the above code 
-if __name__ == '__main__': 
-    arr = [12, 11, 13, 5, 6, 7]  
-    print ("Given array is", end="\n")  
-    printList(arr) 
-    mergeSort(arr) 
-    print("Sorted array is: ", end="\n") 
-    printList(arr) 
+     while i<len(left):
+        arr[k]=left[i]
+        i=i+1
+        k=k+1
+     
+     while j<len(right):
+        arr[k]=right[j]
+        j=j+1
+        k=k+1
diff --git a/Exercise_5.py b/Exercise_5.py
index 1da24ffb..0a8c609e 100644
--- a/Exercise_5.py
+++ b/Exercise_5.py
@@ -1,10 +1,58 @@
-# Python program for implementation of Quicksort
+#Kindly include Time and Space complexity at top of each file
+
+#Time and Space Complexity
+# Space Complexity : O(N) due to the stack space that needs to be allocated
+# Time Complexity : O(N log N) where N is the number of elements in the array
+
 
-# This function is same in both iterative and recursive
 def partition(arr, l, h):
-  #write your code here
+  pivot=arr[h]
+  i=l-1
+  for j in range(l,h):
+    if arr[j]<=pivot:
+      i+=1
+      arr[i],arr[j]=arr[j],arr[i]
+
+  arr[i+1],arr[h]=arr[h],arr[i+1]
+  return i+1
+
 
 
 def quickSortIterative(arr, l, h):
-  #write your code here
+  size=h-l+1
+  stack=[0]*size
+  top=-1
+
+  top=top+1
+  stack[top]=l
+  top=top+1
+  stack[top]=h 
+
+  while top>=0:
+    h=stack[top]
+    top=top-1
+    l=stack[top]
+    top=top-1
+
+    p=partition(arr,l,h)
+
+    if l<p-1:
+      top = top + 1
+      stack[top] = l
+      top = top + 1
+      stack[top] = p - 1
+
+    if p+1<h:
+      top=top+1
+      stack[top]=p+1
+      top=top+1
+      stack[top]=h
+
+
+
+arr=[4,3,5,2,1,3,2,3]
+n=len(arr)
+quickSortIterative(arr,0,n-1)
+print(arr)
+