Questions

Put a checkmark in the box corresponding to true statements.
- Abstract data types have exactly one implementation.
- Data structures are generally useful to store and retrieve data.
- A data type generally comes with allowed operations.
- In data structures classes, ergonomics is the main metrics to compare programs.
- In data structures classes, hardware is generally ignored.
Rank the following from 1 (“best”, fast to execute, slow to grow) to 5 (“worst”, fast to grow, slow to execute):
- cubic
- linear
- linearithmic
- logarithmic
- exponential
Solution

From fastest to execute to slowest to execute:
1. logarithmic
2. linear
3. linearithmic
4. cubic
5. exponential

Complete the following sentences:

A quadratic order of magnitude is denoted ͟ ͟ ͟ ͟ ͟ ͟ ͟ ͟ ͟ ͟ ͟ ͟.
A ͟ ͟ ͟ ͟ ͟ ͟ ͟ ͟ ͟ ͟ ͟ ͟ order of magnitude is denoted $O (c)$ .
A factorial order of magnitude is denoted ͟ ͟ ͟ ͟ ͟ ͟ ͟ ͟ ͟ ͟ ͟ ͟.

Solution

A quadratic order of magnitude is denoted ͟O͟(͟n͟²͟)͟.
A ͟c͟o͟n͟s͟t͟a͟n͟t͟ order of magnitude is denoted $O (c)$ .
A factorial order of magnitude is denoted ͟O͟(͟n͟!͟)͟.

Problems

Write a code snippet (no need to include using statements or Main header) that displays the sum of all the values in a score int array that you can suppose declared and initialized. What is the worst case time complexity of the algorithm you wrote, relative to the size $n$ of the array score?
Solution
```
 int sum = 0;
 for(int i = 0; i < score.Length; i++){sum += score[i];}
 Console.WriteLine($"The sum is {sum}.");
```
This algorithm is linear: it goes through the array once. </detail>{=html}