Completed PreCourse-2

Exercise_1.cpp

@@ -1,11 +1,26 @@
+//Time Complexity : O(logn)
+// Space Complexity : O(logn)
 #include <stdio.h> 
 
 // A recursive binary search function. It returns 
 // location of x in given array arr[l..r] is present, 
 // otherwise -1 
 int binarySearch(int arr[], int l, int r, int x) 
 {   
-    //Your Code here 
+    if(l > r){
+        return -1;
+    }
+    int mid = l + (r-1) / 2;
+
+    if (arr[mid] == x){
+        return mid;
+    }
+
+    if(arr[mid] > x){
+        return binarySearch(arr,l,mid-1,x);
+    }
+
+    return binarySearch(arr,mid+1,r,x);
 } 
 
 int main(void) 

Exercise_2.cpp

@@ -4,7 +4,9 @@ using namespace std;
 // A utility function to swap two elements  
 void swap(int* a, int* b)  
 {  
-    //Your Code here 
+    int temp = *a;
+    *a = *b;
+    *b = temp;
 }  
 
 /* This function takes last element as pivot, places  
@@ -14,7 +16,18 @@ to left of pivot and all greater elements to right
 of pivot */
 int partition (int arr[], int low, int high)  
 {  
-    //Your Code here 
+    int pivot = arr[high];
+    int i = low - 1;
+
+    for(int j = low;j <= high -1 ; j++){
+        if (arr[j] < pivot){
+
+            i++;
+            swap(&arr[i], &arr[j]);  
+    }
+    swap(&arr[i + 1], &arr[high]);
+    return i + 1;
+    }
 }  
 
 /* The main function that implements QuickSort  
@@ -23,7 +36,12 @@ low --> Starting index,
 high --> Ending index */
 void quickSort(int arr[], int low, int high)  
 {  
-    //Your Code here 
+    if (low < high)
+    {
+        int pi = partition(arr, low, high);
+        quickSort(arr, low, pi - 1);
+        quickSort(arr, pi + 1, high);
+    }
 }  
 
 /* Function to print an array */

Exercise_3.cpp

@@ -11,8 +11,19 @@ struct Node
 /* Function to get the middle of the linked list*/
 void printMiddle(struct Node *head)  
 {  
-  //YourCode here
-  //Use fast and slow pointer technique
+ if (head == NULL)
+        return;
+
+    struct Node* slow = head;
+    struct Node* fast = head;
+
+    while (fast != NULL && fast->next != NULL)
+    {
+        slow = slow->next;         
+        fast = fast->next->next;  
+    }
+
+    printf("Middle element is [%d]\n", slow->data);
 }  
 
 // Function to add a new node  

Exercise_4.cpp

@@ -6,14 +6,46 @@
 // Second subarray is arr[m+1..r] 
 void merge(int arr[], int l, int m, int r) 
 { 
-    //Your code here
+    int n1 = m - l + 1;
+    int n2 = r - m;
+
+    int L[n1], R[n2];
+
+    for (int i = 0; i < n1; i++)
+        L[i] = arr[l + i];
+    for (int j = 0; j < n2; j++)
+        R[j] = arr[m + 1 + j];
+
+    int i = 0, j = 0, k = l;
+
+    while (i < n1 && j < n2)
+    {
+        if (L[i] <= R[j])
+            arr[k++] = L[i++];
+        else
+            arr[k++] = R[j++];
+    }
+
+    while (i < n1)
+        arr[k++] = L[i++];
+
+    while (j < n2)
+        arr[k++] = R[j++];
 } 
 
 /* l is for left index and r is right index of the 
    sub-array of arr to be sorted */
 void mergeSort(int arr[], int l, int r) 
 { 
-    //Your code here
+    if (l < r)
+    {
+        int m = l + (r - l) / 2;
+
+        mergeSort(arr, l, m);
+        mergeSort(arr, m + 1, r);
+
+        merge(arr, l, m, r);
+    }
 } 
 
 /* UTILITY FUNCTIONS */

Exercise_5.cpp

@@ -1,3 +1,6 @@
+//Time Complexity : O(n logn)
+// Space Complexity : O(logn)
+
 #include <bits/stdc++.h> 
 using namespace std; 
 
@@ -12,15 +15,56 @@ void swap(int* a, int* b)
 /* This function is same in both iterative and recursive*/
 int partition(int arr[], int l, int h) 
 { 
-    //Do the comparison and swapping here 
+    int pivot = arr[h];
+    int i = l - 1;
+
+    for (int j = l; j <= h - 1; j++)
+    {
+        if (arr[j] <= pivot)
+        {
+            i++;
+            swap(&arr[i], &arr[j]);
+        }
+    }
+
+    swap(&arr[i + 1], &arr[h]);
+    return i + 1;
 } 
 
 /* A[] --> Array to be sorted,  
 l --> Starting index,  
 h --> Ending index */
 void quickSortIterative(int arr[], int l, int h) 
 { 
-    //Try to think that how you can use stack here to remove recursion.
+    // Create an explicit stack
+    stack<int> st;
+
+    // Push initial values
+    st.push(l);
+    st.push(h);
+
+    // Pop until stack is empty
+    while (!st.empty())
+    {
+        h = st.top(); st.pop();
+        l = st.top(); st.pop();
+
+        int p = partition(arr, l, h);
+
+        // If elements on left side of pivot
+        if (p - 1 > l)
+        {
+            st.push(l);
+            st.push(p - 1);
+        }
+
+        // If elements on right side of pivot
+        if (p + 1 < h)
+        {
+            st.push(p + 1);
+            st.push(h);
+        }
+    }
 } 
 
 // A utility function to print contents of arr