Gain insights into algorithms and their implementation for problem-solving in Python. Learn about recursion, dynamic programming, greedy algorithms, and graph algorithms to enhance coding proficiency and problem-solving skills.

As a developer, mastering the concepts of algorithms and being proficient in implementing them is essential to improving problem-solving skills. This course aims to equip you with an in-depth understanding of algorithms and how they can be utilized for problem-solving in Python.

Starting with the basics, you'll gain a foundational understanding of what algorithms are, with topics ranging from simple multiplication algorithms to analyzing algorithms. Then, you’ll delve into more advanced topics like recursion, backtracking, dynamic programming, and greedy algorithms. You'll also learn about basic graph algorithms, depth-first search, shortest paths, minimum spanning trees, and all-pairs shortest paths. 

By the end of this course, you'll have acquired a wide range of skills that will significantly enhance your ability to solve problems efficiently in Python. Through this course, not only will you improve your coding skills, but you will also gain confidence in tackling complex problems.

Mastering Algorithms for Problem Solving in Python

Calculating the expected size of each file

In “sorting the files on a tape” example, what order would result in the minimum expected cost?

In “sorting the files on a tape” example, what order would result in the minimum expected cost?

Before we implement the greedy algorithm to the “scheduling classes” problem, what is the algorithm's time complexity?

Before we implement the greedy algorithm to the “scheduling classes” problem, what is the algorithm’s time complexity?

After we've implemented the greedy algorithm to the “scheduling classes” problem (as shown below), what is the time complexity?

$\underline{GreedySchedule(S[1..n],F[1..n]):} 
\\ \hspace{0.4cm}
\text{sort\ F and permute S to match}
\\ \hspace{0.4cm}
count ← 1
\\ \hspace{0.4cm}
X [count] ← 1
\\ \hspace{0.4cm}
for\space i ← 2 \space to\space n
\\ \hspace{1cm}
if\space S[i] > F[X[count]]
\\ \hspace{1.7cm}
count ← count + 1
\\ \hspace{1.7cm}
X [count] ← i
\\ \hspace{0.4cm}
return\space X [1 .. count]$



After we’ve implemented the greedy algorithm to the “scheduling classes” problem (as shown below), what is the time complexity?
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><munder accentunder="true"><mrow><mi>G</mi><mi>r</mi><mi>e</mi><mi>e</mi><mi>d</mi><mi>y</mi><mi>S</mi><mi>c</mi><mi>h</mi><mi>e</mi><mi>d</mi><mi>u</mi><mi>l</mi><mi>e</mi><mo stretchy="false">(</mo><mi>S</mi><mo stretchy="false">[</mo><mn>1..</mn><mi>n</mi><mo stretchy="false">]</mo><mo separator="true">,</mo><mi>F</mi><mo stretchy="false">[</mo><mn>1..</mn><mi>n</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo>:</mo></mrow><mo stretchy="true">‾</mo></munder><mspace linebreak="newline"></mspace><mspace width="1.1381em"/><mtext>sort F and permute S to match</mtext><mspace linebreak="newline"></mspace><mspace width="1.1381em"/><mi>c</mi><mi>o</mi><mi>u</mi><mi>n</mi><mi>t</mi><mo>←</mo><mn>1</mn><mspace linebreak="newline"></mspace><mspace width="1.1381em"/><mi>X</mi><mo stretchy="false">[</mo><mi>c</mi><mi>o</mi><mi>u</mi><mi>n</mi><mi>t</mi><mo stretchy="false">]</mo><mo>←</mo><mn>1</mn><mspace linebreak="newline"></mspace><mspace width="1.1381em"/><mi>f</mi><mi>o</mi><mi>r</mi><mtext> </mtext><mi>i</mi><mo>←</mo><mn>2</mn><mtext> </mtext><mi>t</mi><mi>o</mi><mtext> </mtext><mi>n</mi><mspace linebreak="newline"></mspace><mspace width="2.8453em"/><mi>i</mi><mi>f</mi><mtext> </mtext><mi>S</mi><mo stretchy="false">[</mo><mi>i</mi><mo stretchy="false">]</mo><mo>&gt;</mo><mi>F</mi><mo stretchy="false">[</mo><mi>X</mi><mo stretchy="false">[</mo><mi>c</mi><mi>o</mi><mi>u</mi><mi>n</mi><mi>t</mi><mo stretchy="false">]</mo><mo stretchy="false">]</mo><mspace linebreak="newline"></mspace><mspace width="4.837em"/><mi>c</mi><mi>o</mi><mi>u</mi><mi>n</mi><mi>t</mi><mo>←</mo><mi>c</mi><mi>o</mi><mi>u</mi><mi>n</mi><mi>t</mi><mo>+</mo><mn>1</mn><mspace linebreak="newline"></mspace><mspace width="4.837em"/><mi>X</mi><mo stretchy="false">[</mo><mi>c</mi><mi>o</mi><mi>u</mi><mi>n</mi><mi>t</mi><mo stretchy="false">]</mo><mo>←</mo><mi>i</mi><mspace linebreak="newline"></mspace><mspace width="1.1381em"/><mi>r</mi><mi>e</mi><mi>t</mi><mi>u</mi><mi>r</mi><mi>n</mi><mtext> </mtext><mi>X</mi><mo stretchy="false">[</mo><mn>1..</mn><mi>c</mi><mi>o</mi><mi>u</mi><mi>n</mi><mi>t</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">\underline{GreedySchedule(S[1..n],F[1..n]):} 
\\ \hspace{0.4cm}
\text{sort\ F and permute S to match}
\\ \hspace{0.4cm}
count ← 1
\\ \hspace{0.4cm}
X [count] ← 1
\\ \hspace{0.4cm}
for\space i ← 2 \space to\space n
\\ \hspace{1cm}
if\space S[i] &gt; F[X[count]]
\\ \hspace{1.7cm}
count ← count + 1
\\ \hspace{1.7cm}
X [count] ← i
\\ \hspace{0.4cm}
return\space X [1 .. count]</annotation></semantics></math>GreedySchedule(S[1..n],F[1..n]):​sort F and permute S to matchcount←1X[count]←1for i←2 to nif S[i]&gt;F[X[count]]count←count+1X[count]←ireturn X[1..count]

Where does the root lie in the Huffman code tree if the number of characters in the input data is $n$?

Where does the root lie in the Huffman code tree if the number of characters in the input data is <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math>n?

What is the time complexity of the Boston Pool and Gale-Shapley algorithm?

What is the time complexity of the Boston Pool and Gale-Shapley algorithm?

Reinforce your knowledge of greedy algorithms and their applications in problem solving.

Getting Started

Introduction to Algorithm

Recursion

Backtracking

Dynamic Programming

Greedy Algorithms

Prove Your Skills: A Five-Chapter Assessment

Basic Graph Algorithms

Depth-First Search

Minimum Spanning Trees

Shortest Paths

All-Pairs Shortest Paths

Pushing Your Limits: A Comprehensive Assessment

Wrapping up

Quiz: Greedy Algorithms