Completed PreCourse 2

Exercise_1.java

@@ -1,9 +1,31 @@
 class BinarySearch { 
-    // Returns index of x if it is present in arr[l.. r], else return -1 
+    // Returns index of x if it is present in arr[l.. r], else return -1
+    //time - O(log n)
+    // space - O(1)
     int binarySearch(int arr[], int l, int r, int x) 
     { 
         //Write your code here
-    } 
+        if (r == 0) // if size of array is zero then return -1
+            return -1;
+        while(l <= r)
+        {
+            int mid = l + (r - l)/2;
+            if(arr[mid] == x)
+            {
+                return mid;
+            }
+            else if(arr[mid] < x)
+            {
+                l = mid + 1;
+            }
+            else
+            {
+                r = mid - 1;
+            }
+
+        }
+        return -1;
+    }
 
     // Driver method to test above 
     public static void main(String args[]) 

Exercise_2.java

@@ -6,22 +6,41 @@ class QuickSort
        smaller (smaller than pivot) to left of 
        pivot and all greater elements to right 
        of pivot */
+    // time - O(nlog(n))
+    // space - O(n)
     void swap(int arr[],int i,int j){
+        int temp = arr[i];
+        arr[i] = arr[j];
+        arr[j] = temp;
         //Your code here   
     }
 
     int partition(int arr[], int low, int high) 
     { 
-   	//Write code here for Partition and Swap 
+   	//Write code here for Partition and Swap
+        int pivot = arr[high];
+        int i = low -1;
+        for(int j = low; j < high; j++)
+        {
+            if(arr[j] <= pivot) {
+                i++;
+                swap(arr, i, j);
+            }
+        }
+        swap(arr, i + 1, high);
+        return i + 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 pivot = partition(arr, low, high);
+            sort(arr, low, pivot - 1);
+            sort(arr, pivot + 1, high);
+        }
     } 
 
     /* A utility function to print array of size n */

Exercise_3.java

@@ -1,5 +1,6 @@
 class LinkedList 
-{ 
+{
+    //time - O(n)
     Node head; // head of linked list 
 
     /* Linked list node */
@@ -20,6 +21,14 @@ void printMiddle()
     { 
         //Write your code here
 	//Implement using Fast and slow pointers
+        Node fast = head;
+        Node slow = head;
+        while(fast != null && fast.next != null)
+        {
+            slow = slow.next;
+            fast = fast.next.next;
+        }
+        System.out.println(slow.data);
     } 
 
     public void push(int new_data) 

Exercise_4.java

@@ -2,18 +2,57 @@ class MergeSort
 { 
     // Merges two subarrays of arr[]. 
     // First subarray is arr[l..m] 
-    // Second subarray is arr[m+1..r] 
+    // Second subarray is arr[m+1..r]
+    // Time - O(n log n)
+    // space - O(n)
     void merge(int arr[], int l, int m, int r) 
     {  
-       //Your code here  
-    } 
+       //Your code here
+        int n1 = m - l + 1; // size of first array
+        int n2 = r - m;
+        int [] subArray1 = new int[n1];
+        int [] subarray2 = new int[n2];
+        for(int i=0;i<n1;i++)
+            subArray1[i] = arr[l+i];
+        for (int j=0;j<n2;j++)
+            subarray2[j] = arr[m+1+j];
+        int i = 0, j = 0, k = l;
+        while (i < n1 && j < n2) {
+            if (subArray1[i] <= subarray2[j]) {
+                arr[k] = subArray1[i];
+                i++;
+            } else {
+                arr[k] = subarray2[j];
+                j++;
+            }
+            k++;
+        }
+        while (i < n1) {
+            arr[k] = subArray1[i];
+            i++;
+            k++;
+        }
+        while (j < n2) {
+            arr[k] = subarray2[j];
+            j++;
+            k++;
+        }
+
+    }
+
 
     // Main function that sorts arr[l..r] using 
     // merge() 
     void sort(int arr[], int l, int r) 
     { 
 	//Write your code here
-        //Call mergeSort from here 
+        //Call mergeSort from here
+        if(l < r){
+            int m = l+(r-l)/2; // middle point
+            sort(arr, l, m); // sort the first half
+            sort(arr, m+1, r); // sort the second half
+            merge(arr,l,m,r); // merge the sorted half
+        }
     } 
 
     /* A utility function to print array of size n */

Exercise_5.java

@@ -1,20 +1,51 @@
-class IterativeQuickSort { 
+import java.util.Stack;
+//time - O(n log n)
+// space - O(log n )
+class IterativeQuickSort {
     void swap(int arr[], int i, int j) 
     { 
-	//Try swapping without extra variable 
+	//Try swapping without extra variable
+        if (i == j) return;
+        arr[i] = arr[i]^arr[j];
+        arr[j] = arr[i]^arr[j];
+        arr[i] = arr[i]^arr[j];
     } 
 
     /* This function is same in both iterative and 
        recursive*/
     int partition(int arr[], int l, int h) 
     { 
-        //Compare elements and swap.
-    } 
+        int pivot = arr[h];
+        int i = (l - 1);
+        for (int j = l; j < h; j++){
+            if (arr[j] <= pivot){
+                i++;
+                swap(arr, i, j);
+            }
+        }
+        swap(arr, i + 1, h);
+
+        return i+1;
+    }
 
     // Sorts arr[l..h] using iterative QuickSort 
     void QuickSort(int arr[], int l, int h) 
     { 
         //Try using Stack Data Structure to remove recursion.
+        Stack<int[]> stack = new Stack<>();
+        stack.push(new int[]{l,h});
+
+        while (!stack.isEmpty()){
+            int[] temp = stack.pop();
+            l = temp[0];
+            h = temp[1];
+            if(l < h){
+                int pi = partition(arr, l, h);
+                stack.push(new int[]{l,pi-1});
+                stack.push(new int[]{pi+1, h});
+            }
+        }
+
     } 
 
     // A utility function to print contents of arr