Complete PreCourse-2

Exercise_1.java

@@ -1,8 +1,29 @@
-class BinarySearch { 
+// Time Complexity: O(log N)
+// Space Complexity: O(log N) -> due to using recursion
+
+class BinarySearch {
     // Returns index of x if it is present in arr[l.. r], else return -1 
     int binarySearch(int arr[], int l, int r, int x) 
-    { 
-        //Write your code here
+    {
+        // only work if the arr is sorted
+        if (r >= l) {
+            //get the mid
+            int mid = l + (r -l)/2;
+
+            // if the value is in the middle return it
+            if (arr[mid] == x) {
+                return mid;
+            }
+
+            // if the value of the mid element is greater than the value x then only look at the left half
+            if (arr[mid] > x) {
+                return binarySearch(arr, l, mid - 1, x);
+            }
+
+            // the only remaining scenario where the value of x is greater than the mid element
+            return binarySearch(arr, mid+1, r, x);
+        }
+        return -1;
     } 
 
     // Driver method to test above 

Exercise_2.java

@@ -1,48 +1,65 @@
-class QuickSort 
-{ 
-    /* This function takes last element as pivot, 
-       places the pivot element at its correct 
-       position in sorted array, and places all 
-       smaller (smaller than pivot) to left of 
-       pivot and all greater elements to right 
+// Time Complexity: O(N log N) -> Pivot splitting the array into halves
+// Space Complexity: O(log N)
+
+class QuickSort
+{
+    /* This function takes last element as pivot,
+       places the pivot element at its correct
+       position in sorted array, and places all
+       smaller (smaller than pivot) to left of
+       pivot and all greater elements to right
        of pivot */
     void swap(int arr[],int i,int j){
-        //Your code here   
+        int temp = arr[i];
+        arr[i] = arr[j];
+        arr[j] = temp;
     }
-
-    int partition(int arr[], int low, int high) 
-    { 
-   	//Write code here for Partition and Swap 
-    } 
-    /* The main function that implements QuickSort() 
-      arr[] --> Array to be sorted, 
-      low  --> Starting index, 
+
+    int partition(int arr[], int low, int high)
+    {
+   	    int pivot = arr[high];
+        int index = low - 1;
+        for (int j = low; j <= high-1; j++){
+            if (arr[j] < pivot) {
+                index++;
+                swap(arr, index, j);
+            }
+        }
+        swap(arr, index + 1, high);
+        return index+1;
+    }
+    /* The main function that implements QuickSort()
+      arr[] --> Array to be sorted,
+      low  --> Starting index,
       high  --> Ending index */
-    void sort(int arr[], int low, int high) 
-    {  
-            // Recursively sort elements before 
-            // partition and after partition 
-    } 
-
+    void sort(int arr[], int low, int high)
+    {
+        if (low < high) {
+            int pivotIndex = partition(arr, low, high);
+            sort(arr, low, pivotIndex - 1);
+            sort(arr, pivotIndex + 1, high);
+        }
+    }
+
     /* A utility function to print array of size n */
-    static void printArray(int arr[]) 
-    { 
-        int n = arr.length; 
-        for (int i=0; i<n; ++i) 
-            System.out.print(arr[i]+" "); 
-        System.out.println(); 
-    } 
-  
-    // Driver program 
-    public static void main(String args[]) 
-    { 
-        int arr[] = {10, 7, 8, 9, 1, 5}; 
-        int n = arr.length; 
-  
-        QuickSort ob = new QuickSort(); 
-        ob.sort(arr, 0, n-1); 
-  
-        System.out.println("sorted array"); 
-        printArray(arr); 
-    } 
-} 
+    static void printArray(int arr[])
+    {
+        int n = arr.length;
+        for (int i=0; i<n; ++i)
+            System.out.print(arr[i]+" ");
+        System.out.println();
+    }
+
+    // Driver program
+    public static void main(String args[])
+    {
+        int arr[] = {10, 7, 8, 9, 1, 5};
+        int n = arr.length;
+
+        QuickSort ob = new QuickSort();
+        ob.sort(arr, 0, n-1);
+
+        System.out.println("sorted array");
+        printArray(arr);
+    }
+}

Exercise_3.java

@@ -1,53 +1,61 @@
-class LinkedList 
-{ 
-    Node head; // head of linked list 
-
+//Time Complexity: O(N)
+//Space Complexity: O(1);
+
+class LinkedList
+{
+    Node head; // head of linked list
+
     /* Linked list node */
-    class Node 
-    { 
-        int data; 
-        Node next; 
-        Node(int d) 
-        { 
-            data = d; 
-            next = null; 
-        } 
-    } 
-  
+    class Node
+    {
+        int data;
+        Node next;
+        Node(int d)
+        {
+            data = d;
+            next = null;
+        }
+    }
+
     /* Function to print middle of linked list */
    //Complete this function
-    void printMiddle() 
-    { 
-        //Write your code here
-	//Implement using Fast and slow pointers
-    } 
-
-    public void push(int new_data) 
-    { 
-        Node new_node = new Node(new_data); 
-        new_node.next = head; 
-        head = new_node; 
-    } 
+    void printMiddle()
+    {
+        Node slowPointer = head;
+        Node fastPointer = head;
+        while (fastPointer != null && fastPointer.next != null) {
+            slowPointer = slowPointer.next;
+            fastPointer = fastPointer.next.next;
+        }
+        System.out.println("The middle element is: " + slowPointer.data);
+    }
+
+    public void push(int new_data)
+    {
+        Node new_node = new Node(new_data);
+        new_node.next = head;
+        head = new_node;
+    }
+
+    public void printList()
+    {
+        Node tnode = head;
+        while (tnode != null)
+        {
+            System.out.print(tnode.data+"->");
+            tnode = tnode.next;
+        }
+        System.out.println("NULL");
+    }
 
-    public void printList() 
-    { 
-        Node tnode = head; 
-        while (tnode != null) 
-        { 
-            System.out.print(tnode.data+"->"); 
-            tnode = tnode.next; 
-        } 
-        System.out.println("NULL"); 
-    } 
-
-    public static void main(String [] args) 
-    { 
-        LinkedList llist = new LinkedList(); 
-        for (int i=15; i>0; --i) 
-        { 
-            llist.push(i); 
-            llist.printList(); 
-            llist.printMiddle(); 
-        } 
-    } 
-} 
+    public static void main(String [] args)
+    {
+        LinkedList llist = new LinkedList();
+        for (int i=15; i>0; --i)
+        {
+            llist.push(i);
+            llist.printList();
+            llist.printMiddle();
+        }
+    }
+}