Pre-Course 2

Exercise_1.py

@@ -1,13 +1,34 @@
+# Time Complexity : O(logn)
+# Space Complexity :O(1)
+# Did this code successfully run on Leetcode : Yes
+# Any problem you faced while coding this : Used the white board to design the algo and psuedo code which helped to solve it on first try
+
+
+# Your code here along with comments explaining your approach
 # 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
-
-
+  while l <= r:
+      '''Setting the mid point'''
+      m = (l+r)//2
+      '''
+        If the mid point is the target return the mid point
+        If the mid point is on the left of the target move the left to the right of midpoint
+        If the mid point is on the right of the target move the right to the left of the midpoint
+      '''
+      if arr[m] == x:
+          return m
+      elif arr[m] < x:
+          l = m+1
+      else:
+          r = m-1
+
+  '''Return -1 since the element hasn't been found'''
+  return -1
 
 # Test array 
 arr = [ 2, 3, 4, 10, 40 ] 
@@ -17,6 +38,6 @@ 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")

Exercise_2.py

@@ -1,17 +1,58 @@
+# Time Complexity : 
+#     Average case: O(nlogn)
+#     Worst case: O(n^2)
+# Space Complexity :
+#     Average case: O(logn)
+#     Worst case: O(n)
+# Did this code successfully run on Leetcode : Yes
+# Any problem you faced while coding this : 
+#                     I watched youtube video to understand the algorithm, made a psuedo code.
+#                     Found the leetcode post helpful http://leetcode.com/discuss/post/1083445/how-quick-sort-works-and-the-problems-th-1h5f/
+#                     Wrote down the notes for it so I do not forget it again, and memorized the word pivot with quick sort.
+
 # Python program for implementation of Quicksort Sort 
 
 # give you explanation for the approach
 def partition(arr,low,high):
-
+    '''
+    We choose the first element as a pivot.
+    We start a wall as second element where all the elements left 
+    of it are always smaller than pivot.
+    We iterate thought the array and find elements smaller than pivot, swap it with the current position of wall
+    and move the wall to the right.
+    Finally we will have the first element as pivot and all the elements smaller than the pivot will be on the 
+    left of the wall. So now we swap the pivot with the element closest to the wall which is exactly the correct
+    placement of the pivot. 
+    Now all the elements to the left of it are smaller and all the elements to the right are bigger than the pivot.
+    '''
 
     #write your code here
+    pivot = arr[low]
+    leftwall = low + 1
+
+    for j in range(low+1, high+1):
+        if arr[j] <= pivot:
+            arr[leftwall], arr[j] = arr[j], arr[leftwall]
+            leftwall += 1
+
+    arr[leftwall - 1], arr[low] = arr[low], arr[leftwall - 1]
+    return leftwall - 1
 
 
 # Function to do Quick sort 
 def quickSort(arr,low,high): 
-
+    '''
+    First we find the correct position of a pivot, then we sort the left half of the pivot
+    and the right half of the pivot which will eventually sort the entire array as the recurssion reaches to all
+    the elements of the array.
+    '''
     #write your code here
-
+    if low < high:
+        p = partition(arr, low, high)
+        quickSort(arr, low, p-1)
+        quickSort(arr, p+1, high)
+    return arr
+
 # Driver code to test above 
 arr = [10, 7, 8, 9, 1, 5] 
 n = len(arr) 

Exercise_3.py

@@ -1,20 +1,63 @@
+# Time Complexity : O(n)
+# Space Complexity : O(1)
+# Did this code successfully run on Leetcode : Yes
+# Any problem you faced while coding this : No problem, just used the two pointers
+
 # Node class  
 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): 
+        if self.head is not None:
+            curr = self.head
+
+            while curr.next is not None:
+                curr = curr.next
+
+            curr.next = Node(new_data)
+
+        else:
+            self.head = Node(new_data)
 
 
     # Function to get the middle of  
     # the linked list 
-    def printMiddle(self): 
+    def printMiddle(self):
+        '''
+        p1 moves one node at a time
+        p2 moves two nodes at a time
+        When the p2 reaches to the end of the linked list, p1 is at the middle node.
+        If there are 2 middle nodes, then the p1 will be at the second middle node. (Requirement by leetcode)
+        odd is the pointer next to the p2.
+        even is the next to odd which will be the next position of p2.
+        '''
+        p1 = self.head
+        p2 = self.head.next
+
+        if p1 is None or p2 is None:
+            return p1.data
+
+        while True:
+            p1 = p1.next
+            odd = p2.next
+
+            if odd is None:
+                return p1.data
+
+            even = p2.next.next
+            if even is None:
+                return p1.data
+
+            p2 = even
 
 # Driver code 
 list1 = LinkedList() 
@@ -23,4 +66,4 @@ def printMiddle(self):
 list1.push(2) 
 list1.push(3) 
 list1.push(1) 
-list1.printMiddle() 
+print(list1.printMiddle()) 

Exercise_4.py

@@ -1,18 +1,74 @@
-# Python program for implementation of MergeSort 
-def mergeSort(arr):
+# Time Complexity : O(nlogn)
+# Space Complexity : O(n)
+# Did this code successfully run on Leetcode : Yes
+# Any problem you faced while coding this : I came up with the merge function with extra space using result array
+#                           But I wanted to merge inplace since that would be efficient, came to know about
+#                           Gap method but didn't spend too much time there and marked as a algorithm to learn
+#                           once I am done with week 4 since it was difficult to understand.
+
+
+# Python program for implementation of MergeSort
+def mergeSort(arr, l, h):
 
   #write your code here
+  '''
+  If the array is of length 1, do nothing.
+  Find a midpoint and call mergeSort on both left and right parts of midpoint.
+  merge both the left and right parts once they are sorted individually.
+  '''
+  if l == h:
+     return
+  m = l + (h-l) // 2
+
+  mergeSort(arr, l, m)
+  if m+1 < h:
+    mergeSort(arr, m+1, h)
+  merge(arr, l, m, h)
+
+def merge(arr, l, m, h):
+  '''
+  i goes through the left part of the array
+  j goes through the right part of the array
+
+  We choose the smallest number from both the parts and add it to the results array
+  once any one part is fully added in the result array, we add the rest of the elements to result
+
+  Finally we put the sorted array result into the appropriate place in the arr array.
+  '''
+  i = l
+  j = m+1
+  result = []
+
+  while i <= m and j <= h:
+    if arr[i] <= arr[j]:
+      result.append(arr[i])
+      i+=1
+    else:
+      result.append(arr[j])
+      j+=1
+
+  if i <= m:
+     for x in arr[i:m+1]:
+       result.append(x)
+
+  if j <= h:
+     for x in arr[j:h+1]:
+       result.append(x) 
+
+  for i in range(len(result)):
+     arr[l+i] = result[i]
 
 # Code to print the list 
 def printList(arr): 
 
     #write your code here
-
+    print(arr)
+
 # 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) 
+    mergeSort(arr, 0, len(arr)-1) 
     print("Sorted array is: ", end="\n") 
     printList(arr) 

Exercise_5.py

@@ -1,10 +1,38 @@
+# Time Complexity : 
+#     Average case: O(nlogn)
+#     Worst case: O(n^2)
+# Space Complexity :
+#     Average case: O(logn)
+#     Worst case: O(n)
+# Did this code successfully run on Leetcode : Yes
+# Any problem you faced while coding this : 
+#                     I was struggling to do it iteratively as could not understand how to keep track of the 
+#                     sorted pivots and how to sort the pivots every time with a different range of elements
+#                     in the array. Then I saw that I can use the partition funtion from previous implementation
+#                     so I just used the white board to come up with the idea of storing the partitions which are unsorted.
 # Python program for implementation of Quicksort
 
 # This function is same in both iterative and recursive
 def partition(arr, l, h):
   #write your code here
+  pivot = arr[l]
+  leftwall = l + 1
 
+  for j in range(l+1, h+1):
+      if arr[j] <= pivot:
+          arr[leftwall], arr[j] = arr[j], arr[leftwall]
+          leftwall += 1
+
+  arr[leftwall - 1], arr[l] = arr[l], arr[leftwall - 1]
+  return leftwall - 1
 
 def quickSortIterative(arr, l, h):
   #write your code here
-
+  partitions = [(l, h)]
+  while len(partitions) > 0:
+      low, high = partitions.pop()
+      p = partition(arr, low, high)
+      if low < p-1:
+          partitions.append((low, p-1))
+      if high > p+1:
+          partitions.append((p+1, high))