Completed Exercise 1,2,3,4,5

Exercise_1.java

@@ -1,17 +1,39 @@
+import java.util.Arrays;
+
+//Time: O(log n) for search.
+//Space: O(1)
 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) 
-    { 
+    int binarySearch(int arr[], int l, int r, int x) { 
         //Write your code here
+        //Rules of binary search are 1. array should be sorted, 2. we repeatedly check the middle element
+
+        if(arr == null || arr.length == 0) 
+            return -1;
+
+        Arrays.sort(arr);
+
+        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[]) 
     { 
         BinarySearch ob = new BinarySearch(); 
-        int arr[] = { 2, 3, 4, 10, 40 }; 
+        int arr[] = { 5, 3, 19, 30, 1 }; 
         int n = arr.length; 
-        int x = 10; 
+        int x = 3; 
         int result = ob.binarySearch(arr, 0, n - 1, x); 
         if (result == -1) 
             System.out.println("Element not present"); 

Exercise_2.java

@@ -1,3 +1,5 @@
+//TimeComplexity = O(nlogn), worst case O(n^2)
+//SpaceComplexity = O(logn)
 class QuickSort 
 { 
     /* This function takes last element as pivot, 
@@ -7,12 +9,30 @@ class QuickSort
        pivot and all greater elements to right 
        of pivot */
     void swap(int arr[],int i,int j){
-        //Your code here   
+
+        if (i == j) return;           
+        int tmp = arr[i];
+        arr[i] = arr[j];
+        arr[j] = tmp;
+
     }
 
     int partition(int arr[], int low, int high) 
     { 
    	//Write code here for Partition and Swap 
+    int pivot = arr[high];
+    int i = low - 1;
+
+    for(int j = low; j<= high -1; 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, 
@@ -22,6 +42,13 @@ void sort(int arr[], int low, int high)
     {  
             // Recursively sort elements before 
             // partition and after partition 
+
+            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

@@ -20,6 +20,19 @@ void printMiddle()
     { 
         //Write your code here
 	//Implement using Fast and slow pointers
+    if (head == null) {
+        return;
+    }
+
+    Node slow = head;
+    Node fast = 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

@@ -1,42 +1,86 @@
-class MergeSort 
-{ 
-    // Merges two subarrays of arr[]. 
-    // First subarray is arr[l..m] 
-    // Second subarray is arr[m+1..r] 
-    void merge(int arr[], int l, int m, int r) 
-    {  
-       //Your code here  
-    } 
-
-    // Main function that sorts arr[l..r] using 
-    // merge() 
-    void sort(int arr[], int l, int r) 
+    import java.util.Arrays;
+
+    //Time Complexity = O(nlogn)
+    //Space Complexity = O(n)
+
+    class MergeSort 
     { 
-	//Write your code here
-        //Call mergeSort from here 
-    } 
-
-    /* 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 method 
-    public static void main(String args[]) 
-    { 
-        int arr[] = {12, 11, 13, 5, 6, 7}; 
-
-        System.out.println("Given Array"); 
-        printArray(arr); 
-
-        MergeSort ob = new MergeSort(); 
-        ob.sort(arr, 0, arr.length-1); 
-
-        System.out.println("\nSorted array"); 
-        printArray(arr); 
-    } 
-} 
+        // Merges two subarrays of arr[]. 
+        // First subarray is arr[l..m] 
+        // Second subarray is arr[m+1..r] 
+        void merge(int arr[], int l, int m, int r) 
+        {  
+        //Your code here  
+        int[] left = Arrays.copyOfRange(arr, l, m+1);
+        int[] right = Arrays.copyOfRange(arr, m+ 1, r+1);
+        int i = 0;
+        int j = 0;
+        int k  = l;
+
+        while(i < left.length && j < right.length) {
+            if (left[i] <= right[j]) {
+                arr[k] = left[i];
+
+                i++;
+            } else {
+                arr[k] = right[j];
+                j++;
+            }
+            k++;
+        }
+
+        while (i < left.length) {
+            arr[k] = left[i];
+            i++;
+            k++;
+        }
+        while (j < right.length) {
+            arr[k] = right[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 
+            if (l >= r) {
+                return;
+            }
+
+            int mid = l + (r - l) / 2;
+
+            sort(arr, l, mid);
+            sort(arr, mid+1, r);
+            merge(arr, l, mid, r);
+
+        } 
+
+        /* 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 method 
+        public static void main(String args[]) 
+        { 
+            int arr[] = {12, 11, 13, 5, 6, 7}; 
+
+            System.out.println("Given Array"); 
+            printArray(arr); 
+
+            MergeSort ob = new MergeSort(); 
+            ob.sort(arr, 0, arr.length-1); 
+
+            System.out.println("\nSorted array"); 
+            printArray(arr); 
+        } 
+    } 

Exercise_5.java

@@ -1,20 +1,68 @@
+//Time Complexity = O(nlogn) Worst case O(n^2)
+//Space Complexity = O(logn) Worst case O(n)
 class IterativeQuickSort { 
     void swap(int arr[], int i, int j) 
     { 
 	//Try swapping without extra variable 
+
+        if (i == j) return; 
+        arr[i] ^= arr[j];
+        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 -1; 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.
+        if (l >= h) return;
+
+        int[] stack = new int[h - l + 1];
+        int top = -1;
+
+
+        stack[++top] = l;
+        stack[++top] = h;
+
+
+        while (top >= 0) {
+            h = stack[top--];
+            l = stack[top--];
+
+            int p = partition(arr, l, h);
+
+            if (p - 1 > l) {
+                stack[++top] = l;
+                stack[++top] = p - 1;
+            }
+
+            if (p + 1 < h) {
+                stack[++top] = p + 1;
+                stack[++top] = h;
+            }
+        }
+
     } 
 
     // A utility function to print contents of arr