The efficiency of an algorithm is
5n2. If each step takes
1 nanosecond (10−9 seconds), how long will
the algorithm take to process an input of size 1000?

Question

The efficiency of an algorithm is
    5n2. If each step takes
    1 nanosecond (10−9 seconds), how long will
    the algorithm take to process an input of size 1000?

Accepted Answer

Ans. For n = 1000:

  
    
      5 × (1000)2 × 10−9
      = 5 × 10−3 seconds
      = 5 milliseconds
    
  

  
    💡 Explanation:

    
      First, substitute n = 1000 into the efficiency
      expression:
    

    
      
        5n2
        = 5 × (1000)2
        = 5 × 1,000,000
        = 5,000,000 steps
      
    

    
      Since each step takes
      1 nanosecond = 10−9 seconds, the total
      execution time is:
    

    
      
        5,000,000 × 10−9 seconds
        = 5 × 10−3 seconds
      
    

    
      Since 10−3 seconds = 1 millisecond,
      the algorithm takes 5 milliseconds.

The efficiency of an algorithm is 5n². If each step takes 1 nanosecond (10⁻⁹ seconds), how long will the algorithm take to process an input of size 1000?

Answer with Explanation

The efficiency of an algorithm is 5n2. If each step takes 1 nanosecond (10−9 seconds), how long will the algorithm take to process an input of size 1000?

Answer with Explanation

The efficiency of an algorithm is 5n². If each step takes 1 nanosecond (10⁻⁹ seconds), how long will the algorithm take to process an input of size 1000?