# Algorithm Comparison and Instances

## Prerequisites
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* Asymptotics Notation
* Basic Mathematical Concept
* Growth of Functions

### Question 1
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How to compare an insertion sort taking $\ c1*n^2$ time and a merge sort taking $\ c2＊nlogn$ time? Which $\ c1$ is much more smaller than $\ c2$.(You can use different methods to prove it)

### Question 2
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Suppose that computer A executes 10 billion instructions per second and computer B executes 10 million instructions per second. How long will it take to sort 10 million numbers on computer A using an algorithm costing $\ 2*n^2$. And how long will it take to sort 10 million numbers on computer B using an algorithm costing $\ 50*nlog(n)$ ?

### Question 3
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Use the method of Question1 and Question2 (or you can use any methods), please answer the following question.

:::spoiler open the questions
1. $\ O(10000nlog) > O(0.00001 n^2)$ **(True or False)**
2. Compare the following functions and **sort them in ascending growth order**. (a)$\ log(n!)$ (b)$\ 1001^ {log(n)}$ (C )$\ (n-10)!$ (d)$\ n*2^n$

:::

## Hint
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### Answer 1
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### Answer 2
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### Answer 3
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>[name=罐子]

###### tags: `Algorithm`