Completed PreCourse 2

Exercise_1.java

@@ -1,8 +1,22 @@
+// Time Complexity : O(log n)
+// Space Complexity : 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) 
     { 
-        //Write your code here
+        while (l < r) {
+            int mid = l + (r-l)/2;
+            if (arr[mid] == x) {
+                return mid;
+            } else if (x > arr[mid]) {
+                l = mid;
+            } else {
+                r = mid;
+            }
+        }
+
+        return -1;
     } 
 
     // Driver method to test above 

Exercise_2.java

@@ -1,3 +1,6 @@
+// Time Complexity: O(n log n)
+// Space Complexity: O(1). It will be O(n) if we are considering the space used by the recursive stack.
+
 class QuickSort 
 { 
     /* This function takes last element as pivot, 
@@ -7,21 +10,41 @@ class QuickSort
        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 
+        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, high, i+1);
+
+        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 
+        if (low < high) {
+            int pivotIdx = partition(arr, low, high);
+
+            sort(arr, low, pivotIdx - 1);
+            sort(arr, pivotIdx + 1, high);
+        }
     } 
 
     /* A utility function to print array of size n */

Exercise_3.java

@@ -1,3 +1,6 @@
+// Time Complexity: O(n) as we have to traverse all elements in the linked list.
+// Space Complexity: O(1)
+
 class LinkedList 
 { 
     Node head; // head of linked list 
@@ -18,8 +21,15 @@ class Node
    //Complete this function
     void printMiddle() 
     { 
-        //Write your code here
-	//Implement using Fast and slow pointers
+        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

@@ -1,19 +1,52 @@
+// Time Complexity: O(n log n) as we keep dividing the array into two halves.
+// Space Complexity: O(n) as we use a temp array for sorting the elements.
+
 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) 
+    void merge(int arr[], int start, int mid, int right) 
     {  
-       //Your code here  
+       int i = start, j = mid;
+
+       int[] temp = new int[right - start];
+       int tempIdx = 0;
+
+       while (i < mid && j < right) {
+            if (arr[i] < arr[j]) {
+                temp[tempIdx++] = arr[i++];
+            } else {
+                temp[tempIdx++] = arr[j++];
+            }
+       }
+
+       while (i < mid) {
+            temp[tempIdx++] = arr[i++];
+       }
+
+       while (j < right) {
+            temp[tempIdx++] = arr[j++];
+       }
+
+       for(int k=start; k<right; k++) {
+        arr[k] = temp[k-start];
+       }
     } 
 
     // Main function that sorts arr[l..r] using 
     // merge() 
-    void sort(int arr[], int l, int r) 
+    void sort(int arr[], int start, int end) 
     { 
-	//Write your code here
-        //Call mergeSort from here 
+        if (end - start < 2) {
+            return;
+        }
+
+        int mid = (start + end) / 2;
+        sort(arr, start, mid);
+        sort(arr, mid, end);
+
+        merge(arr, start, mid, end);
     } 
 
     /* A utility function to print array of size n */
@@ -34,7 +67,7 @@ public static void main(String args[])
         printArray(arr); 
 
         MergeSort ob = new MergeSort(); 
-        ob.sort(arr, 0, arr.length-1); 
+        ob.sort(arr, 0, arr.length); 
 
         System.out.println("\nSorted array"); 
         printArray(arr); 

Exercise_5.java

@@ -1,20 +1,60 @@
+// Time Complexity: O(n log n)
+// Space Complexity: O(n) as we are using auxiliary space in the form of stack
+
+import java.util.*;
+
 class IterativeQuickSort { 
+
     void swap(int arr[], int i, int j) 
     { 
-	//Try swapping without extra variable 
+        int temp = arr[i];
+        arr[i] = arr[j];
+        arr[j] = temp;
     } 
 
     /* This function is same in both iterative and 
        recursive*/
-    int partition(int arr[], int l, int h) 
+    int partition(int arr[], int low, int high) 
     { 
-        //Compare elements 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, high, i+1);
+
+        return i+1;
     } 
 
     // Sorts arr[l..h] using iterative QuickSort 
-    void QuickSort(int arr[], int l, int h) 
+    void QuickSort(int arr[], int low, int high) 
     { 
-        //Try using Stack Data Structure to remove recursion.
+        Stack<Integer> stack = new Stack<>();
+        stack.push(low);
+        stack.push(high);
+
+        while (!stack.isEmpty()) {
+            high = stack.pop();
+            low = stack.pop();
+
+            int pivotIdx = partition(arr, low, high);
+
+            if (pivotIdx - 1 > low) {
+                stack.push(low);
+                stack.push(pivotIdx - 1);
+            }
+
+            if (pivotIdx + 1 < high) {
+                stack.push(pivotIdx + 1);
+                stack.push(high);
+            }
+        }
     } 
 
     // A utility function to print contents of arr