Geeting Feedback for all problems of PreCourse-2

Exercise_1.py

@@ -1,3 +1,14 @@
+# Time Complexity : O(log(base 2)(N))
+# Space Complexity : O(1)
+# Did this code successfully run on Leetcode : Could not find the problem on leetcode
+# Any problem you faced while coding this : No
+
+
+# Your code here along with comments explaining your approach
+# We can use Binary Search when the array is sorted. It reduces the search time of O(N) i.e. linear to O(log(base 2)(N)) i.e. logarithmic
+# I am assuming the input array on which we are applying the Binary Search would always be sorted
+# Reducing the search space by half on every iteration
+
 # Python code to implement iterative Binary  
 # Search. 
 
@@ -6,6 +17,20 @@
 def binarySearch(arr, l, r, x): 
 
   #write your code here
+  if((len(arr) == 0) or (not (0 <= l <= len(arr)-1)) or (not (0 <= r <= len(arr)-1)) or (x < arr[0]) or (x > arr[-1])):
+     return -1
+
+  while(l <= r):
+     mid = ((2 * r) - (r - l)) // 2
+     if(x == arr[mid]):
+        return mid
+     elif(x < arr[mid]):
+        r = mid - 1
+     else:
+        l = mid + 1
+
+  return -1
+
 
 
 
@@ -14,9 +39,45 @@ def binarySearch(arr, l, r, x):
 x = 10
 
 # Function call 
-result = binarySearch(arr, 0, len(arr)-1, x) 
-
+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")
+
+result = binarySearch(arr, 0, len(arr)-1, 0)
+if result != -1: 
+    print("Element is present at index %d" % result) 
+else: 
+    print("Element is not present in array")
+
+result = binarySearch(arr, 0, len(arr)-1, 50)
+if result != -1: 
+    print("Element is present at index %d" % result) 
+else: 
+    print("Element is not present in array")
+
+result = binarySearch(arr, 0, len(arr)-1, 6)
+if result != -1: 
+    print("Element is present at index %d" % result) 
+else: 
+    print("Element is not present in array")
+
+result = binarySearch(arr, 0, len(arr)-1, 2)
+if result != -1: 
+    print("Element is present at index %d" % result) 
+else: 
+    print("Element is not present in array")
+
+result = binarySearch(arr, 0, -1, 2)
+if result != -1: 
+    print("Element is present at index %d" % result) 
+else: 
+    print("Element is not present in array")
+
+result = binarySearch(arr, len(arr), 3, 2)
 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")
+

Exercise_2.py

@@ -1,23 +1,90 @@
+# Time Complexity : Best and Average case: O(N*LogN) when partition happens approx from the middle that is position of pivot 
+# element is mostly near the middle of the array.
+# Worst Case: O(N**2) = O(N^2): When array is already sorted in Ascending or Descending Order. In this case partitions are very
+# imbalanced. The number of partitions would be O(N). Also our partition function is already O(N). So overall Time complexity would be O(N**2)
+# Space Complexity : O(1) extra space. O(N) auxiliary recursive stack space
+# Did this code successfully run on Leetcode : Could not find on Leetcode
+# Any problem you faced while coding this : I went through Algorithm explanation and psuedo code. Then I was able to implement it.
+# There are many ways to implement the partition function. Can you please guide which one is better?
+
+
+# Your code here along with comments explaining your approach
+# Here I have written the code for Sorting in Ascending Order.
+# It is based on choosing pivot and then partitioning the array
+# Here I am taking pivot as the last element that is arr[high] for the range of [low, high]
+# Then we place the pivot on its correct place by bringing all smaller and equal to pivot elements on the Left Portion and larger than pivot 
+# as the right portion
+# Then we recursively apply the pivot and partition logic on the Left portion and the Right Portion
+# If we want to sort the array in descending order, I believe with minor tweak in the partition function "if(arr[j] >= pivot)" , 
+# would help us to do it. It would bring the larger and equal to pivot elements to the left
+
 # 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]
+    # used to bring the smaller or equal to pivot elements to the left portion
+    idx = low - 1
+
+    for j in range(low, high):
+        if(arr[j] <= pivot):
+            idx += 1
+            arr[j], arr[idx] = arr[idx], arr[j]
+
+    # bring the pivot to its correct place
+    idx += 1
+    arr[high], arr[idx] = arr[idx], arr[high]
+    return idx
+
 
 
 # Function to do Quick sort 
-def quickSort(arr,low,high): 
-
+def quickSort(arr,low,high):
     #write your code here
-
+    if(low < high):
+        pIndex = partition(arr,low,high)
+        quickSort(arr, low, pIndex - 1)
+        quickSort(arr, pIndex + 1, high)
+
 # Driver code to test above 
-arr = [10, 7, 8, 9, 1, 5] 
+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], end="")
+
+print()
+arr = [6, 5, 4, 3, 2, 1]
+n = len(arr) 
+quickSort(arr,0,n-1) 
+print("Sorted array is:") 
+for i in range(n): 
+    print("%d " %arr[i], end="")
+
+print()
+arr = [7, 8, 9, 10, 11, 12, 13]
+n = len(arr) 
+quickSort(arr,0,n-1) 
+print("Sorted array is:") 
+for i in range(n): 
+    print("%d " %arr[i], end="")
+
+print()
+arr = [7, 7, 7, 7, 7, 7]
+n = len(arr) 
+quickSort(arr,0,n-1) 
+print("Sorted array is:") 
+for i in range(n): 
+    print("%d " %arr[i], end="")
+
+print()
+arr = []
 n = len(arr) 
 quickSort(arr,0,n-1) 
-print ("Sorted array is:") 
+print("Sorted array is:") 
 for i in range(n): 
-    print ("%d" %arr[i]), 
+    print("%d " %arr[i], end="")
 
 

Exercise_3.py

@@ -1,26 +1,73 @@
+# Time Complexity : O(len(LinkedList) / 2) = O(N / 2) - Taken for printMiddle() function
+# Space Complexity : O(len(LinkedList)) = O(N) = Non-Contiguous space of O(N). Each node stores data and reference to the next node.
+# Did this code successfully run on Leetcode : Yes
+# Any problem you faced while coding this : No
+
+
+# Your code here along with comments explaining your approach
+# If length of LinkedList is Odd, then we have only one middle
+# If length of LinkedList is Even, then we have two middle elements. Here I am returning the First Middle.
+# Example if LinkedList is [1,2,3,4] then my first middle would be 2
+# Here I am using fast and slow pointer approach. Our fast pointer travels at a speed of 2 times the speed of the slow pointer.
+# So when my fast pointer has covered a distance of 2*x, our slow pointer reaches a distance of x. Using this analogy, when
+# our fast pointer reaches the last node, our slow pointer has reached the middle of the LinkedList
+
+
 # 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): 
+    def __init__(self):
+        self.head = None
+        self.tail = None
 
 
-    def push(self, new_data): 
+    def push(self, new_data):
+        newNode = Node(new_data)
+        if(not self.head):
+            self.head = newNode
+            self.tail = newNode
+        else:
+            self.tail.next = newNode
+            self.tail = newNode
+
 
 
     # Function to get the middle of  
     # the linked list 
-    def printMiddle(self): 
+    def printMiddle(self):
+        if(not self.head):
+            print("LinkedList is Empty")
+            return
+
+        slow = self.head
+        fast = self.head
+
+        while(fast.next and fast.next.next):
+            fast = fast.next.next
+            slow = slow.next
+
+        print(slow.data)
+
+
+
 
 # Driver code 
-list1 = LinkedList() 
-list1.push(5) 
-list1.push(4) 
+list1 = LinkedList()
+list1.printMiddle()
+list1.push(5)
+list1.printMiddle() 
+list1.push(4)
+list1.printMiddle() 
 list1.push(2) 
 list1.push(3) 
 list1.push(1) 
-list1.printMiddle() 
+list1.printMiddle()
+list1.push(20)
+list1.printMiddle()

Exercise_4.py

@@ -1,12 +1,65 @@
+# Time Complexity : O(N * (Log(Base 2) N)) -- O(Log(Base 2) N) is for the steps taken to dividing the array into 2 parts on each step.
+# O(N) is for the merging step
+# Space Complexity : O(N) -- creating a temp array when merging the left and right parts
+# Did this code successfully run on Leetcode : Could not find it on Leetcode
+# Any problem you faced while coding this : I went through Algorithm explanation and psuedo code and then was able to implement it
+
+
+# Your code here along with comments explaining your approach
+# Here I have written the code for Sorting in Ascending Order. I believe with minor tweak in the merge routine we can Sort the array in
+# Descending Order as well. Keep dividing the array into half length each until we reach 1 element. Then when we merge, we compare
+# the elements of two divided arrays and place the elements in a sorted way in the new array and then merge it with the actual array
+
 # Python program for implementation of MergeSort 
 def mergeSort(arr):
 
   #write your code here
+  def mergeSortRecur(arr, low, high):
+    # base case to stop the recursion
+    if(low >= high):
+      return
+
+    mid = (high + low) // 2
+    # divide into left part
+    mergeSortRecur(arr, low, mid)
+    # divide into right part
+    mergeSortRecur(arr, mid + 1, high)
+
+    # merge routine
+    p1 = low
+    p2 = mid + 1
+    temp = []
+    while((p1 <= mid) and (p2 <= high)):
+      if(arr[p1] <= arr[p2]):
+        temp.append(arr[p1])
+        p1 += 1
+      else:
+        temp.append(arr[p2])
+        p2 += 1
+
+    while(p1 <= mid):
+      temp.append(arr[p1])
+      p1 += 1
+
+    while(p2 <= high):
+      temp.append(arr[p2])
+      p2 += 1
+
+    # update the actual array
+    k = low
+    for i in range(len(temp)):
+      arr[k] = temp[i]
+      k += 1
+
+  if((len(arr) == 0) or (len(arr) == 1)):
+    return
+  mergeSortRecur(arr, 0, len(arr) - 1)
 
 # Code to print the list 
-def printList(arr): 
+def printList(arr):
 
-    #write your code here
+  #write your code here
+  print(arr)
 
 # driver code to test the above code 
 if __name__ == '__main__': 
@@ -15,4 +68,18 @@ def printList(arr):
     printList(arr) 
     mergeSort(arr) 
     print("Sorted array is: ", end="\n") 
+    printList(arr)
+    print("-----------------")
+    arr = [12]  
+    print ("Given array is", end="\n")  
+    printList(arr) 
+    mergeSort(arr) 
+    print("Sorted array is: ", end="\n") 
+    printList(arr)
+    print("-----------------")
+    arr = []  
+    print ("Given array is", end="\n")  
     printList(arr) 
+    mergeSort(arr) 
+    print("Sorted array is: ", end="\n") 
+    printList(arr)