Unit 1: Linear structure implementation

• Insert at position pos: shift elements right from the end, then place the item and increase n.
• Delete at position pos: shift elements left from pos + 1 and decrease n.
• Matrix multiplication: possible only if columns of A = rows of B.

cfor (i = 0; i < m; i++)
    for (j = 0; j < p; j++) {
        c[i][j] = 0;
        for (k = 0; k < n; k++)
            c[i][j] += a[i][k] * b[k][j];
    }

cstruct node { int data; struct node *next; };
struct node *start = NULL;

void insert_begin(int x) {
    struct node *t = malloc(sizeof(struct node));
    t->data = x;
    t->next = start;
    start = t;
}
void delete_begin() {
    if (start == NULL) { printf("Underflow"); return; }
    struct node *t = start;
    start = start->next;
    free(t);
}

• Doubly linked list nodes add a prev pointer; when inserting, update both neighbours' links.
• Circular list creation: the last node's next points to start; traversal stops when the pointer comes back to start.

c#define MAX 50
int stack[MAX], top = -1;
void push(int x) { if (top == MAX - 1) printf("Overflow"); else stack[++top] = x; }
int pop() { if (top == -1) { printf("Underflow"); return -1; } return stack[top--]; }

Postfix evaluation: for each symbol, if it is a digit push it; if it is an operator, pop b then a, compute a op b and push the result.

• Recursive factorial: long fact(int n) { return n <= 1 ? 1 : n * fact(n - 1); }
• Circular queue with modulo arithmetic:

cint q[MAX], front = -1, rear = -1;
void enqueue(int x) {
    if ((rear + 1) % MAX == front) { printf("Queue full"); return; }
    if (front == -1) front = 0;
    rear = (rear + 1) % MAX;
    q[rear] = x;
}