Added some commits in Sort section (#14)

* Update1: Bubble Sort(Removing Extra Iterations)

Removed the extra iterations in simple bubble_sort() function, so as the real meaning of bubble sort come out.

* Update 1. Bubble_Sort.ipynb

* Update Quick sort comments

Added extra comments in functions, for better understanding.

* Update 5. Quick_Sort.ipynb

* Update P01_Fibonnaci.py

Added the recursion+memoization method for Fibonacci sequence.

Author: kehsihba19

Diff for: Dynamic Programming/P01_Fibonnaci.py

@@ -19,6 +19,15 @@ def fibonacciRec(number):
     else:
         return (fibonacciRec(number - 1) + fibonacciRec(number - 2))
 
+# improved recursive fibonacci function
+def fib_memoization(n, lookup): 
+    if n == 0 or n == 1 : 
+        lookup[n] = n 
+    if lookup[n] is None: 
+        lookup[n] = fib(n-1 , lookup)  + fib(n-2 , lookup)  
+    return lookup[n]
+
+
 if __name__ == '__main__':
     userInput = int(input('Enter the number: '))
 
@@ -37,3 +46,9 @@ def fibonacciRec(number):
     result = fibonacciRec(userInput)
     stopTime = time.time()
     print('Time:', (stopTime - startTime), 'Result:', result)
+    
+    startTime = time.time()
+    lookup=[None]*(101) 
+    result = fib_memoization(userInput,lookup)
+    stopTime = time.time()
+    print('Time:', (stopTime - startTime), 'Result:', result)

Diff for: Sorting/1. Bubble_Sort.ipynb

@@ -16,8 +16,9 @@
    "outputs": [],
    "source": [
     "def bubble_sort(array):\n",
-    "    for i in range(len(array) - 1):\n",
-    "        for j in range(len(array) - 1):\n",
+    "    n=len(array)\n",
+    "    for i in range(0,n):\n",
+    "        for j in range(0,n-i-1):\n",
     "            if array[j] > array[j + 1]:\n",
     "                array[j], array[j + 1] = array[j + 1], array[j] # swap"
    ]

Diff for: Sorting/5. Quick_Sort.ipynb

@@ -14,11 +14,15 @@
    "outputs": [],
    "source": [
     "def partition(array, low, high):\n",
-    "    i = low - 1\n",
-    "    pivot = array[high]\n",
+    "    i = low - 1            # index of smaller element\n",
+    "    pivot = array[high]    # pivot \n",
     "    \n",
     "    for j in range(low, high):\n",
+    "        # If current element is smaller than the pivot\n",
+    "        \n",
     "        if array[j] < pivot:\n",
+    "        # increment index of smaller element\n",
+    "        \n",
     "            i += 1\n",
     "            array[i], array[j] = array[j], array[i]\n",
     "            \n",
@@ -27,8 +31,12 @@
     "\n",
     "def quick_sort(array, low, high):\n",
     "    if low < high:\n",
+    "        # pi is partitioning index, arr[p] is now\n", 
+    "        # at right place \n",
     "        temp = partition(array, low, high)\n",
     "        \n",
+    "        # Separately sort elements before\n", 
+    "        # partition and after partition \n",
     "        quick_sort(array, low, temp - 1)\n",
     "        quick_sort(array, temp + 1, high)"
    ]