1. Factorial Calculation

Implement a function factorial(n) that calculates the factorial of a given number n. Choose the correct implementation.

function factorial(n) {  
    if (n <= 1) {  
        return 1;  
    }  
    return <code>  
}

Pick ONE option

• return n * factorial(n - 1)
• return factorial(n) * n

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2. Prime Number Check

Write a function isPrime that returns true if a number n is prime and false otherwise. Select the correct implementation.

function isPrime(n) {  
    if (n <= 1) {  
        return false;  
    }  
    for (i = 2; i < n; i++) {  
        if (<code>) {  
            return false;  
        }  
    }  
    return true;  
}

Pick ONE option

• if (n % i === 0)

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4. Balancing Server Loads with Dynamic Data Structure

A web server distributes load across multiple servers to balance traffic. To ensure real-time load balancing, the server with the least load should be dynamically selected as requests arrive. Which implementation method best achieves real-time selection of the least-loaded server?

Pick ONE option

initialize array loads  
sort loads in ascending order  
return first element as least-loaded server  

initialize min-heap loads  
for each request:  
    server = extract_min loads  
    process request on server  
    re-insert server with updated load  

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5. Real-Time Navigation System Using Dijkstra’s Algorithm

A company developing a real-time navigation system needs an efficient algorithm to find the shortest path from a user’s location to a destination across a large network of roads and intersections. The system must update dynamically as new road conditions and traffic data are received.
Which of the following pseudocode implementations best suits the requirement for finding the shortest path in a weighted graph?

Pick ONE option

initialize empty queue path  
enqueue start node to path  
while path is not empty:  
    node = dequeue path  
    if node is destination:  
        return shortest path  
    add all connected nodes to path  

initialize empty set visited  
initialize stack path  
push start node to path  
while path is not empty:  
    node = pop path  
    if node is destination:  
        return path  
    for each neighbor of node:  
        if neighbor not in visited:  
            push neighbor to path  

initialize priority queue pq  
initialize distances to infinity for all nodes  
set distance of start node to 0  
add start node to pq  
while pq is not empty:  
    node = extract_min pq  
    for each neighbor of node:  
        if distance to neighbor > distance to node + edge weight:  
            update distance to neighbor  
            add neighbor to pq  

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