Add PreCourse-2 PR

Exercise_1.py

@@ -1,22 +1,30 @@
-# Python code to implement iterative Binary  
-# Search. 
-
-# It returns location of x in given array arr  
-# if present, else returns -1 
-def binarySearch(arr, l, r, x): 
-
-  #write your code here
-
-
-
-# Test array 
-arr = [ 2, 3, 4, 10, 40 ] 
+# Time complexity: O(log n)
+# Space complexity: O(1)
+
+# It returns location of x in given array arr
+# if present, else returns -1
+def binarySearch(arr, l, r, x):
+    while l <= r:
+        mid = (l + r) // 2
+
+        if arr[mid] == x:
+            return mid
+        elif arr[mid] < x:
+            l = mid + 1
+        else:
+            r = mid - 1
+
+    return -1
+
+
+# Test array
+arr = [2, 3, 4, 10, 40]
 x = 10
-  
-# Function call 
-result = binarySearch(arr, 0, len(arr)-1, x) 
-  
-if result != -1: 
-    print "Element is present at index % d" % result 
-else: 
-    print "Element is not present in array"
+
+# Function call
+result = binarySearch(arr, 0, len(arr) - 1, x)
+
+if result != -1:
+    print("Element is present at index % d" % result)
+else:
+    print("Element is not present in array")

Exercise_2.py

@@ -1,23 +1,40 @@
-# Python program for implementation of Quicksort Sort 
-
-# give you explanation for the approach
-def partition(arr,low,high):
-
-
-    #write your code here
-
-
-# Function to do Quick sort 
-def quickSort(arr,low,high): 
-
-    #write your code here
-
-# Driver code to test above 
-arr = [10, 7, 8, 9, 1, 5] 
-n = len(arr) 
-quickSort(arr,0,n-1) 
-print ("Sorted array is:") 
-for i in range(n): 
-    print ("%d" %arr[i]), 
-
-
+
+# Time complexity: O(n log n)
+# Space complexity: O(log n)
+
+# The approach is to use the partition function to place the pivot in its correct position,
+# and then recursively sort the sub-arrays on either side of the pivot.
+def partition(arr, low, high):
+    # Select the rightmost element as pivot
+    pivot = arr[high]
+    # Index of smaller element (initially -1)
+    i = -1
+
+    for j in range(low, high):
+        # If current element is smaller than or equal to pivot
+        if arr[j] <= pivot:
+            i = i + 1
+            arr[i], arr[j] = arr[j], arr[i]
+
+    # Place pivot in its correct position
+    arr[i + 1], arr[high] = arr[high], arr[i + 1]
+    return i + 1
+
+# Function to do Quick sort
+def quickSort(arr, low, high):
+    if low < high:
+        # Partition the array
+        pi = partition(arr, low, high)
+
+        # Recursively sort elements before and after partition
+        quickSort(arr, low, pi - 1)
+        quickSort(arr, pi + 1, high)
+
+
+# Driver code to test above
+arr = [10, 7, 8, 9, 1, 5]
+n = len(arr)
+quickSort(arr, 0, n-1)
+print("Sorted array is:")
+for i in range(n):
+    print("%d" % arr[i]),

Exercise_3.py

@@ -1,26 +1,41 @@
-# Node class  
-class Node:  
-
-    # Function to initialise the node object  
-    def __init__(self, data):  
-
-class LinkedList: 
-
-    def __init__(self): 
-
-
-    def push(self, new_data): 
-
-
-    # Function to get the middle of  
-    # the linked list 
-    def printMiddle(self): 
-
-# Driver code 
-list1 = LinkedList() 
-list1.push(5) 
-list1.push(4) 
-list1.push(2) 
-list1.push(3) 
-list1.push(1) 
-list1.printMiddle() 
+# Time complexity: O(n)
+# Space complexity: O(1)
+
+class Node:
+    # Function to initialise the node object
+    def __init__(self, data):
+        self.data = data
+        self.next = None
+
+class LinkedList:
+
+    def __init__(self):
+        self.head = None
+
+    def push(self, new_data):
+        new_node = Node(new_data)
+        new_node.next = self.head
+        self.head = new_node
+
+    # Function to get the middle of
+    # the linked list
+    def printMiddle(self):
+        slow = self.head
+        fast = self.head
+
+        if self.head is not None:
+            while fast is not None and fast.next is not None:
+                fast = fast.next.next
+                slow = slow.next
+
+            print("The middle element is: ", slow.data)
+
+
+# Driver code
+list1 = LinkedList()
+list1.push(5)
+list1.push(4)
+list1.push(2)
+list1.push(3)
+list1.push(1)
+list1.printMiddle()

Exercise_4.py

@@ -1,12 +1,42 @@
+# Time complexity: O(n log n)
+# Space complexity: O(n)
+
 # Python program for implementation of MergeSort 
 def mergeSort(arr):
-
-  #write your code here
+    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 += 1
+            else:
+                arr[k] = right[j]
+                j += 1
+            k += 1
+
+        while i < len(left):
+            arr[k] = left[i]
+            i += 1
+            k += 1
+
+        while j < len(right):
+            arr[k] = right[j]
+            j += 1
+            k += 1
 
 # Code to print the list 
 def printList(arr): 
-
-    #write your code here
+    for i in range(len(arr)):
+        print(arr[i], end=" ")
+    print()
 
 # driver code to test the above code 
 if __name__ == '__main__': 

Exercise_5.py

@@ -1,10 +1,37 @@
+# Time complexity: O(n log n)
+# Space complexity: O(log n)
+
 # Python program for implementation of Quicksort
+def partition(arr, low, high):
+    # Select the rightmost element as pivot
+    pivot = arr[high]
+
+    # Index of the smaller element within the current subarray
+    i = low - 1
+
+    for j in range(low, high):
+        if arr[j] <= pivot:
+            i += 1
+            arr[i], arr[j] = arr[j], arr[i]
+
+    # Place the pivot in its correct position
+    arr[i + 1], arr[high] = arr[high], arr[i + 1]
+    return i + 1
+
+
+def quick_sort_iterative(arr, low, high):
+    if low >= high:
+        return
 
-# This function is same in both iterative and recursive
-def partition(arr, l, h):
-  #write your code here
+    stack = [(low, high)]
 
+    while stack:
+        low, high = stack.pop()
+        pivot_index = partition(arr, low, high)
 
-def quickSortIterative(arr, l, h):
-  #write your code here
+        # Push subarrays containing at least two elements
+        if low < pivot_index - 1:
+            stack.append((low, pivot_index - 1))
 
+        if pivot_index + 1 < high:
+            stack.append((pivot_index + 1, high))