Abstract Data Type: Stack

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Shanon Gilmore
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1 Abstract Data Type: Stack Stack operations may involve initializing the stack, using it and then de-initializing it. Apart from these basic stuffs, a stack is used for the following two primary operations push() Pushing (storing) an element on the stack. pop() Removing (accessing) an element from the stack. To use a stack efficiently, we need to check the status of stack as well. For the same purpose, the following functionality is added to stacks isfull() check if stack is full. isempty() check if stack is empty. Algorithm of isfull() function begin procedure isfull if top equals to MAXSIZE return false Algorithm of isempty() function begin procedure isempty if top less than 0 return false

2 Algorithm for Push() function begin procedure push: stack, data if stack is full return null top top + 1 stack[top] data Algorithm for Push() function begin procedure pop: stack if stack is empty return null data stack[top] top top - 1 return data Abstract Data Type: Queue A Queue contains elements of same type arranged in sequential order. Operations takes place at both ends, insertion is done at end and deletion is done at front. Following operations can be performed: enqueue() Insert an element at the end of the queue. dequeue() Remove and return the first element of queue, if the queue is not empty. isempty() Return true if the queue is empty, otherwise return false. isfull() Return true if the queue is full, otherwise return false.

3 Algorithm for isfull() operation: begin procedure isfull if rear equals to MAXSIZE return false Algorithm for isempty() operation: begin procedure isempty if front is less than MIN OR front is greater than rear return false Algorithm for enqueue operation: procedure enqueue(data) if queue is full return overflow rear rear + 1 queue[rear] data

4 Algorithm for dequeue operation: procedure dequeue if queue is empty return underflow end if data = queue[front] front front + 1 Algorithm for Tower of Hanoi problem Procedure Hanoi(disk, source, dest, aux) IF disk == 1, THEN move disk from source to dest ELSE Hanoi(disk - 1, source, aux, dest) // Step 1 move disk from source to dest // Step 2 Hanoi(disk - 1, aux, dest, source) // Step 3 END IF END Procedure All algorithms must satisfy the following criteria: 1. Zero or more input values 2. One or more output values 3. Clear and unambiguous instructions 4. Atomic steps that take constant time 5. No infinite sequence of steps (help, the halting problem) 6. Feasible with specified computational device

5 Representing 2-D Array using Row-major order representation and calculating address for data access Address Calculation Formula: Matrix[i][j] = B + (i * n + j ) * w Where, B = Base Address i,j = data in i th row, j th column n = no. of columns w = sizeof (Data_type) C program to perform Selection Sort on a set of unsorted elements void swap(int *xp, int *yp) int temp = *xp; *xp = *yp; *yp = temp; void selectionsort(int arr[], int n) int i, j, min; for (i = 0; i < n-1; i++) min = i; for (j = i+1; j < n; j++) if (arr[j] < arr[min]) min = j; swap(&arr[min], &arr[i]); void printarray(int arr[], int size)

6 int i; for (i=0; i < size; i++) printf("%d ", arr[i]); printf("\n"); int main() int arr[] = 64, 25, 12, 22, 11; int n = sizeof(arr)/sizeof(arr[0]); selectionsort(arr, n); printf("sorted array: \n"); printarray(arr, n); return 0; C program to perform Bubble Sort on a set of unsorted elements void swap(int *xp, int *yp) int temp = *xp; *xp = *yp; *yp = temp; // A function to implement bubble sort void bubblesort(int arr[], int n) int i, j; for (i = 0; i < n-1; i++) // Last i elements are already in place for (j = 0; j < n-i-1; j++)

7 if (arr[j] > arr[j+1]) swap(&arr[j], &arr[j+1]); /* Function to print an array */ void printarray(int arr[], int size) int i; for (i=0; i < size; i++) printf("%d ", arr[i]); printf("n"); // Driver program to test above functions int main() int arr[] = 64, 34, 25, 12, 22, 11, 90; int n = sizeof(arr)/sizeof(arr[0]); bubblesort(arr, n); printf("sorted array: \n"); printarray(arr, n); return 0;

8 C program to search an element in an array using Binary Search algorithm (Recursive) #include <stdio.h> int binarysearch(int arr[], int l, int h, int num) if (h >= l) int mid = l + (h - l)/2; if (arr[mid] == num) return mid; if (arr[mid] > num) return -1; int main( ) return binarysearch(arr, l, mid-1, num); return binarysearch(arr, mid+1, h, num); int arr[] = 2, 3, 4, 10, 40; int size = sizeof(arr)/ sizeof(arr[0]); int num = 10; int result = binarysearch(arr, 0, size-1, num); if (result == -1) printf("element is not present in array") printf("element is present at index %d", result); return 0;

9 C program to search an element in an array using Binary Search algorithm (Iterative) int binarysearch(int arr[], int l, int h, int num) while (l <= h) int mid = l + (h-l)/2; if (arr[mid] == num) return mid; if (arr[mid] < num) l = mid + 1; h = mid - 1; return -1; int main(void) int arr[] = 2, 3, 4, 10, 40; int size = sizeof(arr)/ sizeof(arr[0]); int num = 10; int result = binarysearch(arr, 0, size-1, num); if (result == -1) printf("element is not present in array") printf("element is present at index %d", result); return 0;

Queue: Queue Representation: Basic Operations:

Queue: Queue Representation: Basic Operations: Queue: Queue is an abstract data structure, somewhat similar to Stacks. Unlike stacks, a queue is open at both its ends. One end is always used to insert data (enqueue) and the other is used to remove