Question

1 algorithm for any topic​

Answer 1

Explanation:

Analysis of Algorithms:

Asymptotic Analysis

Worst, Average and Best Cases

Asymptotic Notations

Little o and little omega notations

Lower and Upper Bound Theory

Analysis of Loops

Solving Recurrences

Amortized Analysis

What does ‘Space Complexity’ mean?

Pseudo-polynomial Algorithms

NP-Completeness Introduction

Polynomial Time Approximation Scheme

A Time Complexity Question

Time Complexity of building a heap

Time Complexity where loop variable is incremented by 1, 2, 3, 4 ..

Time Complexity of Loop with Powers

Performance of loops (A caching question

Answer 2

Let’s look at a very simple algorithm called find_max().

Problem: Given a list of positive numbers, return the largest number on the list.

Inputs: A list L of positive numbers. This list must contain at least one number. (Asking for the largest number in a list of no numbers is not a meaningful question.)

Outputs: A number n, which will be the largest number of the list.

Algorithm:

Set max to 0.

For each number x in the list L, compare it to max. If x is larger, set max to x.

max is now set to the largest number in the list.

An implementation in Python:

def find_max (L):

max = 0

for x in L:

if x > max:

max = x

return max

Does this meet the criteria for being an algorithm?

Is it unambiguous? Yes. Each step of the algorithm consists of primitive operations, and translating each step into Python code is very easy.

Does it have defined inputs and outputs? Yes.

Is it guaranteed to terminate? Yes. The list L is of finite length, so after looking at every element of the list the algorithm will stop.

Does it produce the correct result? Yes. In a formal setting you would provide a careful proof of correctness. In the next section I’ll sketch a proof for an alternative solution to this problem.

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