PreCourse-2 Completed

Exercise_1.java

@@ -1,21 +1,61 @@
+// Time Complexity : O(log n) → Because with each step, we cut down the search space by half.
+// Space Complexity : O(1) → No extra space used apart from a few variables.
+// Did this code successfully run on Leetcode: Yes
+// Any problem you faced while coding this: No
+
 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
+
+    /**
+     * Binary Search Algorithm
+     * 
+     * @param arr - The sorted input array
+     * @param l - Left boundary of the search space
+     * @param r - Right boundary of the search space
+     * @param x - Element to search for
+     * @return - Index of the element if found, otherwise -1
+     */
+    int binarySearch(int arr[], int l, int r, int x) { 
+        // Continue searching while left index <= right index
+        while (l <= r) {
+            // ✅ To prevent integer overflow, use this formula
+            int mid = l + (r - l) / 2;
+
+            // ✅ Case 1: If middle element is equal to target → return mid
+            if (arr[mid] == x) {
+                return mid;
+            } 
+            // ✅ Case 2: If middle element is smaller than target → search right side
+            else if (arr[mid] < x) {
+                l = mid + 1;
+            } 
+            // ✅ Case 3: If middle element is greater than target → search left side
+            else {
+                r = mid - 1;
+            }
+        }
+
+        // ✅ If element is not present in the array
+        return -1;
     } 
-
-    // Driver method to test above 
-    public static void main(String args[]) 
-    { 
+
+    // ✅ Driver method to test the code
+    public static void main(String args[]) { 
         BinarySearch ob = new BinarySearch(); 
+
+        // ✅ Sample Input and Explanation:
+        // Sorted array (binary search only works on sorted arrays)
         int arr[] = { 2, 3, 4, 10, 40 }; 
         int n = arr.length; 
-        int x = 10; 
+        int x = 10; // Element to search for
+
+        // ✅ Call binary search
         int result = ob.binarySearch(arr, 0, n - 1, x); 
-        if (result == -1) 
-            System.out.println("Element not present"); 
-        else
-            System.out.println("Element found at index " + result); 
+
+        // ✅ Output the result
+        if (result == -1) {
+            System.out.println("Element not present in the array.");
+        } else {
+            System.out.println("Element found at index " + result);
+        }
     } 
-} 
+}

Exercise_2.java

@@ -1,3 +1,11 @@
+// Time Complexity :O(NlogN) → Because we are dividing the array into two halves at each step.
+// Space Complexity :O(NlogN)
+// Did this code successfully run on Leetcode :
+// Any problem you faced while coding this :No
+
+
+// Your code here along with comments explaining your approach
+
 class QuickSort 
 { 
     /* This function takes last element as pivot, 
@@ -8,11 +16,24 @@ class QuickSort
        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 
+   	//Write code here for Partition and Swap
+       int pivot = arr[high];
+       int swapIndex = low;
+       for(int i=low; i<high; i++){
+            if (arr[i]<=pivot){
+                swap(arr, i, swapIndex);
+                swapIndex++;
+            }
+       } 
+       swap(arr,swapIndex,high);
+       return swapIndex;
     } 
     /* The main function that implements QuickSort() 
       arr[] --> Array to be sorted, 
@@ -22,6 +43,11 @@ void sort(int arr[], int low, int high)
     {  
             // Recursively sort elements before 
             // partition and after partition 
+            if(low<high){
+                int partitionIndex = partition(arr, low, high);
+                sort(arr, low, partitionIndex-1);
+                sort(arr, partitionIndex+1, high);
+            }
     } 
 
     /* A utility function to print array of size n */

Exercise_3.java

@@ -1,3 +1,8 @@
+// Time Complexity : O(n) → Because we need to traverse the list once to find the middle.
+// Space Complexity : O(1) → No extra space used apart from a few pointers.
+// Did this code successfully run on Leetcode: Yes
+// Any problem you faced while coding this: Nope
+
 class LinkedList 
 { 
     Node head; // head of linked list 
@@ -20,6 +25,16 @@ 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;
+        }
+        if (slow!=null){
+            System.out.println("Middle element is :"+slow.data);
+        }
+
     } 
 
     public void push(int new_data) 

Exercise_4.java

@@ -1,3 +1,10 @@
+// Time Complexity : O(n * log n) → because we split the array into halves and merge them back.
+// Space Complexity: O(n) → because of the temporary arrays used for merging.
+// Did this code successfully run on Leetcode : 
+// Any problem you faced while coding this : No
+
+
+
 class MergeSort 
 { 
     // Merges two subarrays of arr[]. 
@@ -6,6 +13,39 @@ class MergeSort
     void merge(int arr[], int l, int m, int r) 
     {  
        //Your code here  
+       int length1 = m-l+1;
+       int length2 = r-m;
+       int[] left = new int[length1];
+       int [] right = new int[length2];
+       for(int i = 0; i < length1; i++){
+            left[i]= arr[l+i];
+       }
+       for(int j = 0; j < length2; j++){
+            right[j] = arr[m+1+j];
+       }
+       int i=0;
+       int j =0;
+       int k =l;
+       while(i<length1 && j<length2){
+            if(left[i]<=right[j]){
+                arr[k] = left[i];
+                i++;
+            }else{
+                arr[k] = right[j];
+                j++;
+            }
+            k++;
+       }
+       while(i<length1){
+        arr[k] = left[i];
+        i++;
+        k++;
+       }
+       while(j<length2){
+        arr[k] = right[j];
+        j++;
+        k++;
+       }
     } 
 
     // Main function that sorts arr[l..r] using 
@@ -14,6 +54,12 @@ void sort(int arr[], int l, int r)
     { 
 	//Write your code here
         //Call mergeSort from here 
+        if(l<r){
+            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 */

Exercise_5.java

@@ -1,36 +1,75 @@
+// Time Complexity : O(n * log n) in average case, O(n^2) in worst case
+// Space Complexity : O(log n) due to the stack used for iterative calls
+// Did this code successfully run on Leetcode : Yes
+// Any problem you faced while coding this : No
+
+
 class IterativeQuickSort { 
-    void swap(int arr[], int i, int j) 
-    { 
-	//Try swapping without extra variable 
+    void swap(int arr[], int i, int j) {
+        // Swapping without extra variable 
+        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.
+    /* This function is same in both iterative and recursive */
+    int partition(int arr[], int l, int h) { 
+        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.
+    void QuickSort(int arr[], int l, int h) { 
+        // Create an auxiliary stack
+        int[] stack = new int[h - l + 1];
+        int top = -1;
+
+        // Push initial values to stack
+        stack[++top] = l;
+        stack[++top] = h;
+
+        while (top >= 0) {
+            // Pop h and l
+            h = stack[top--];
+            l = stack[top--];
+
+            // Partition the array and get the pivot
+            int p = partition(arr, l, h);
+
+            // If there are elements on the left side of pivot, push them to stack
+            if (p - 1 > l) {
+                stack[++top] = l;
+                stack[++top] = p - 1;
+            }
+
+            // If there are elements on the right side of pivot, push them to stack
+            if (p + 1 < h) {
+                stack[++top] = p + 1;
+                stack[++top] = h;
+            }
+        }
     } 
 
-    // A utility function to print contents of arr 
-    void printArr(int arr[], int n) 
-    { 
-        int i; 
-        for (i = 0; i < n; ++i) 
+    // A utility function to print contents of array
+    void printArr(int arr[], int n) { 
+        for (int i = 0; i < n; ++i) 
             System.out.print(arr[i] + " "); 
+        System.out.println();
     } 
 
     // Driver code to test above 
-    public static void main(String args[]) 
-    { 
+    public static void main(String args[]) { 
         IterativeQuickSort ob = new IterativeQuickSort(); 
         int arr[] = { 4, 3, 5, 2, 1, 3, 2, 3 }; 
         ob.QuickSort(arr, 0, arr.length - 1); 
         ob.printArr(arr, arr.length); 
     } 
-} 
+}