UNIT 2: STACK & RECURSION Programs demonstrated in class. Tojo Mathew Asst. Professor CSE Dept., NIE Mysuru.

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1 UNIT 2: STACK & RECURSION Programs demonstrated in class. Tojo Mathew Asst. Professor CSE Dept., NIE Mysuru.

2 Table of Contents 1. C Program to Check for balanced parenthesis by using Stacks Program for items implementation of stack using local stack instance & without dynamic memory allocation Program for evaluation of postfix expression Infix to Postfix conversion with support for parenthesis Stack Implementation with dynamic memory allocation for container array Recursion : Factorial Recursion : Binary Search Recursion : nth Fibonacci number...21

3 1. C Program to Check for balanced parenthesis by using Stacks #include <stdio.h> #include <string.h> #define TRUE 1 #define FALSE 0 int getch() return 0; #define STACKSIZE 10 / The Stack defintion used by the program struct Stack int top; int items[stacksize]; ; / Stack is full when top is equal to the last index int full(struct Stack* stack) return stack->top == STACKSIZE - 1; / Stack is empty when top is equal to -1 int empty(struct Stack* stack) return stack->top == -1; / Function to add an item to stack. It increases top by 1 void push(struct Stack* stack, int item) if (full(stack)) return; stack->items[++stack->top] = item; / Function to remove an item from stack. It decreases top by 1 int pop(struct Stack* stack) if (empty(stack))

4 printf("stack empty\n"); return -1000; return stack->items[stack->top--]; int stacktop(struct Stack* stack) if (empty(stack)) printf("stack empty\n"); return -1000; return stack->items[stack->top]; int main() int i; char expr[30], a; printf("enter the expression:\n"); scanf("%s",expr); struct Stack s; int valid = TRUE; for (i = 0; i < strlen(expr); i++) if ((expr[i] == '(') (expr[i] == '') (expr[i] == '[')) push(&s,expr[i]); if ((expr[i] == ')') (expr[i] == '') (expr[i] == ']')) if (empty(&s)) valid =FALSE;

5 a = pop(&s); char b = (a =='('?')':a ==''?'':']'); if(b!= expr[i]) valid = FALSE; if (empty(&s)) printf("stack not empty\n"); valid = FALSE; if (valid) printf("%s is valid!!",expr); printf("%s is not valid.!!",expr); getch();

6 2. Program for items implementation of stack using local stack instance & without dynamic memory allocation. #include <stdio.h> #include <stdlib.h> #include <limits.h> #define STACKSIZE 10 / A structure to represent a stack struct Stack int top; int items[stacksize]; ; / Stack is full when top is equal to the last index int full(struct Stack* stack) return stack->top == STACKSIZE - 1; / Stack is empty when top is equal to -1 int empty(struct Stack* stack) return stack->top == -1; / Function to add an item to stack. It increases top by 1 void push(struct Stack* stack, int item) if (full(stack)) return; stack->items[++stack->top] = item; printf("%d pushed to stack\n", item); / Function to remove an item from stack. It decreases top by 1 int pop(struct Stack* stack) if (empty(stack)) printf("stack empty\n"); return -1000;

7 return stack->items[stack->top--]; int stacktop(struct Stack* stack) if (empty(stack)) printf("stack empty\n"); return -1000; return stack->items[stack->top]; / Not part of standard stack specification. Use for our verification purpose. void display (struct Stack* s) int i; if (s->top == -1) printf ("Stack is empty\n"); return; printf ("\ncurrent contents of the stack is \n"); for (i = s->top; i >= 0; i--) printf ("%d\n", s->items[i]); printf ("\n"); / Driver program to test above functions int main() struct Stack st; st.top = -1; push(&st, 10);

8 push(&st, 20); push(&st, 40); push(&st, 10); push(&st, 20); push(&st, 40); printf("%d is at stack top\n", stacktop(&st)); display(&st); printf("%d popped from stack\n", pop(&st)); printf("%d popped from stack\n", pop(&st)); printf("%d popped from stack\n", pop(&st)); printf("%d popped from stack\n", pop(&st)); display(&st); return 0;

9 3. Program for evaluation of postfix expression // Sample input : 63*5+ (A postfix expression for 6*3+5 ) / Output : 23 #include<stdio.h> #include<ctype.h> / A minimal stack implementation specifically for this program. / Not recommended generally. int stack[20]; int top = -1; void push(int x) stack[++top] = x; int pop() return stack[top--]; // Stack ends int eval(int n1, int n2,char op) int result; switch(op) case '+': result = n1 + n2; break; case '-': result = n2 - n1; break; case '*': result = n1 * n2; break;

10 case '/': result = n2 / n1; break; return result; int main() char exp[20]; char *e; int n1,n2,n3,num; printf("enter the expression:: "); scanf("%s",exp); e = exp; while(*e!= '\0') if(isdigit(*e)) / E.g:Converting character '6' to number 6 using ASCII values num = *e - 48; // 48 => ASCII value of '0' push(num); n1 = pop(); n2 = pop(); n3 = eval(n1,n2,*e); push(n3); e++; printf("\nthe result of expression %s = %d\n\n",exp,pop()); return 0;

11 4.Infix to Postfix conversion with support for parenthesis. #include<stdio.h> #include<ctype.h> / A minimal stack implementation specifically for this program. / Not recommended generally. char stack[20]; int top = -1; void push(char x) stack[++top] = x; char pop() if(top == -1) return -1; return stack[top--]; int priority(char x) if(x == '(') return 0; if(x == '+' x == '-') return 1; if(x == '*' x == '/') return 2; return 0; int main() char exp[20]; char *e, x; printf("enter the expression :: "); scanf("%s",exp); e = exp;

12 while(*e!= '\0') if(isalnum(*e)) printf("%c",*e); if(*e == '(') push(*e); if(*e == ')') while((x = pop())!= '(') printf("%c", x); while(priority(stack[top]) >= priority(*e)) printf("%c",pop()); push(*e); e++; while(top!= -1) printf("%c",pop()); return 0;

13 5.Stack Implementation with dynamic memory allocation for container array. // Stack Implementation with dynamic memory allocation for container array. #include <stdio.h> #include <stdlib.h> // A structure to represent a stack struct Stack int *items; int top; int maxsize; ; // Initializing the stack void initstatck(struct Stack *ptr,int mx) ptr->top = -1; ptr->maxsize = mx; ptr->items = (int*)malloc(mx*sizeof(int)); // De-initialization of stack. void deinit(struct Stack *ptr) free(ptr->items); // Freeing the container memory ptr->top = -1; ptr->maxsize = -1; // Stack is full when top is equal to the last index int full(struct Stack* stack) return stack->top == stack->maxsize - 1; // Stack is empty when top is equal to -1 int empty(struct Stack* stack) return stack->top == -1; // Function to add an item to stack. It increases top by 1 void push(struct Stack* stack, int item) if (full(stack)) return; ++stack->top; *(stack->items+stack->top) = item; // stack->items[stack->top] = item; //Same as above statement printf("%d pushed to stack\n", item);

14 // Function to remove an item from stack. It decreases top by 1 int pop(struct Stack* stack) int ele; if (empty(stack)) printf("stack empty\n"); return -1000; ele = *(stack->items+stack->top); // ele = stack->items[stack->top]; // Same as above statement stack->top--; return ele; int stacktop(struct Stack* stack) if (empty(stack)) printf("stack empty\n"); return -1000; return stack->items[stack->top]; // Not part of standard stack specification. Use for our verification purpose. void display (struct Stack* s) int i; if (s->top == -1) printf ("Stack is empty\n"); return; printf ("\ncurrent contents of the stack is(top to bottom) \n"); for (i = s->top; i >= 0; i--) printf ("%d\n", s->items[i]); printf ("\n"); // Driver program to test above functions int main() struct Stack st; initstatck(&st,10);

15 push(&st, 10); push(&st, 20); push(&st, 40); push(&st, 10); push(&st, 20); push(&st, 40); printf("%d is at stack top\n", stacktop(&st)); display(&st); printf("%d popped from stack\n", pop(&st)); printf("%d popped from stack\n", pop(&st)); printf("%d popped from stack\n", pop(&st)); printf("%d popped from stack\n", pop(&st)); display(&st); deinit(&st); return 0;

16 6. Recursion : Factorial #include <stdio.h> int fact_1(int); int fact_2(int); int fact_3(int); int fact_4(int); int main() int num; int f; printf("enter a number to find it's Factorial: "); scanf("%d", &num); f = fact_1(num); printf("\nthe Factorial of %d is %d.\n", num, f); f = fact_2(num); printf("\nthe Factorial of %d is %d.\n", num, f); f = fact_3(num); printf("\nthe Factorial of %d is %d.\n", num, f); f = fact_3(num); printf("\nthe Factorial of %d is %d.\n", num, f); return 0; // Iterative Implementation int fact_1(int n) int i, prod = 1; for(i=n;i>=1;i--) prod = prod*i; return prod; // Recursive Implementation 1 int fact_2(int n) int x,y; if (n == 0)

17 //printf("0! = 1\n"); return 1; x = n-1; //printf("%d! = %d*%d!\t",n,n,x); y = fact_2(x); return n*y; // A Simplified form of the above. int fact_3(int n) if (n == 0) return 1; return n * fact_3(n - 1); // A More simplified form of the above. int fact_4(int n) return n == 0? 1: n * fact_4(n - 1);

18 7. Recursion : Binary Search #include <stdio.h> int binsearch_1(int [], int, int, int); // Iterative Solution int binsearch_2(int a[], int lo, int hi, int x); // Recursive Solution 1 int binsearch_3(int a[], int lo, int hi, int x); // Recursive Solution 2 int main() int x, size, i,pos = -1; int a[25]; printf("enter size of array a: "); scanf("%d", &size); printf("enter the numbers in sorted order:\n"); for(i = 0; i < size; i++) scanf("%d", &a[i]); printf("\n\n"); printf("enter x to search\n"); scanf("%d", &x); pos = binsearch_1(a, 0, size-1, x); if(pos == -1) printf("element not found\n"); printf("element found at index %d\n",pos); pos = binsearch_2(a, 0, size-1, x); if(pos == -1) printf("element not found\n"); printf("element found at index %d\n",pos); pos = binsearch_3(a, 0, size-1, x); if(pos == -1) printf("element not found\n"); printf("element found at index %d\n",pos); return 0;

19 // Iterative implementation int binsearch_1(int a[], int lo, int hi, int x) int mid,pos =-1; while (lo <= hi) mid = (lo + hi) / 2; if (a[mid] == x) pos = mid; break; if (a[mid] > x) hi = mid -1; if (a[mid] < x) lo = mid +1; return pos; // Recursive implementation : Elaborative way int binsearch_2(int a[], int lo, int hi, int x) int mid,pos; if (lo > hi) pos = -1; return pos; mid = (lo + hi) / 2; if (a[mid] == x) pos = mid; if (a[mid] > x) pos = binsearch_2(a, lo, mid - 1, x); if (a[mid] < x)

20 pos = binsearch_2(a, mid + 1, hi, x); return pos; // Recursive implementation : Simplified way int binsearch_3(int a[], int lo, int hi, int x) int mid; if (lo > hi) return -1; mid = (lo + hi) / 2; return (a[mid] == x? mid:a[mid] > x? binsearch_3(a, lo, mid - 1, x) : binsearch_3(a, mid + 1, hi, x));

21 8. Recursion : nth Fibonacci number #include <stdio.h> int fib_1(int); // Iterative Solution int fib_2(int); // Recursive Solution 1 int fib_3(int); // Recursive Solution 2 int fib_4(int); // Recursive Solution 2 int main() int num; int result; printf("enter the nth number in fibonacci series: "); scanf("%d", &num); result = fib_1(num); printf("the %dth number in fibonacci series is %d\n", num, result); result = fib_2(num); printf("the %dth number in fibonacci series is %d\n", num, result); result = fib_3(num); printf("the %dth number in fibonacci series is %d\n", num, result); result = fib_4(num); printf("the %dth number in fibonacci series is %d\n", num, result); return 0; // Iterative Solution int fib_1(int n) int low = 0, high = 1, num, i; if( n <= 1) return n; for (i = 2; i <= n; i++) num = low + high; low = high; high = num; return num;

22 // Recursive Solution. int fib_2(int n) int x,y; if (n <= 1) return n; x = fib_2(n-1); // Recursive Call 1 y = fib_2(n-2); // Recursive Call 2 return x+y; // Simplified recursive solution int fib_3(int n) if (n <= 1) return n; return fib_3(n - 1) + fib_3(n - 2); // More Simplified recursive solution int fib_4(int n) return (n <= 1)?n:fib_4(n - 1) + fib_4(n - 2);

Write a C program to add two Complex numbers using functions illustrating-

Write a C program to add two Complex numbers using functions illustrating- Scheme of valuvation Date : 29/8/2017 Marks: 40 Subject & Code : Data Structures and Applications (15CS33) Class : III A&B Name of Faculty : Ms. Saritha Time : 8:30 am to 10 am NOTE: ANSWER All FIVE QUESTIONS