Cadet College (Combined) — Lecturer ICT — Exam: 11.05.2025প্রশ্ন ও সমাধান

RDBMS (Relational Database Management System) is a database system that stores data in structured tables (relations) made of rows and columns, uses SQL to manipulate data, and enforces relationships and integrity constraints between tables via keys (e.g., MySQL, Oracle, PostgreSQL, SQL Server).

Types of keys:

Key	Definition	Example (Student table: roll, name, email, dept_id)
Super key	Any set of one or more attributes that can uniquely identify a row (may include extra, unnecessary attributes)	{roll}, {roll, name}, {email, name}
Candidate key	A minimal super key — no attribute can be removed without losing uniqueness	{roll}, {email}
Primary key	The candidate key chosen by the designer as the main identifier; cannot be NULL, must be unique	roll (chosen as PK)
Foreign key	An attribute in one table referencing the primary key of another table, enforcing referential integrity	dept_id in Student references dept_id (PK) in Department

erDiagram
    STUDENT }o--|| DEPARTMENT : belongs_to
    STUDENT {
        int roll PK
        string name
        string email
        int dept_id FK
    }
    DEPARTMENT {
        int dept_id PK
        string dept_name
    }

• Every candidate key is a super key, but not every super key is a candidate key (super keys can contain redundant attributes).
• Every primary key is a candidate key, but only one candidate key per table is chosen as the primary key — the remaining candidate keys are called alternate keys.

Exam takeaway: Super key (any unique combo) is a superset of Candidate key (minimal unique combo) which is a superset of Primary key (the chosen candidate key); Foreign key links tables by referencing another table's primary key.

Stack is a LIFO (Last-In-First-Out) linear data structure — the last element inserted is the first one removed. It exposes exactly two core mutating operations: push and pop, tracked via a top pointer/index.

• Push(x): insert element x on top of the stack.
  1. Check for overflow (stack full, in a fixed-size array implementation).
  2. Increment top.
  3. Store x at stack[top].
• Pop(): remove and return the top element.
  1. Check for underflow (stack empty — top == -1).
  2. Read the value at stack[top].
  3. Decrement top.

flowchart TD
    subgraph Push
    P1{Stack full?} -- Yes --> P2([Overflow])
    P1 -- No --> P3[top = top+1] --> P4[stack top = x]
    end
    subgraph Pop
    Q1{Stack empty?} -- Yes --> Q2([Underflow])
    Q1 -- No --> Q3[x = stack top] --> Q4[top = top-1]
    end

#define MAX 100
int stack[MAX], top = -1;

void push(int x) {
    if (top == MAX - 1) { printf("Overflow\n"); return; }
    stack[++top] = x;
}
int pop() {
    if (top == -1) { printf("Underflow\n"); return -1; }
    return stack[top--];
}

Both operations run in O(1) time since only the top pointer changes — no shifting of other elements is needed (unlike inserting/deleting at an arbitrary array position).

Real-world uses: function call stack (recursion), undo/redo, expression evaluation (infix→postfix), browser back-button history.

Exam takeaway: push = increment top then insert (check overflow first); pop = read then decrement top (check underflow first); both O(1).